TSTP Solution File: SEU244+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU244+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 : n018.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 12:08:56 EDT 2022
% Result : Theorem 232.38s 232.69s
% Output : CNFRefutation 247.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 258
% Syntax : Number of formulae : 6080 (1923 unt; 137 typ; 0 def)
% Number of atoms : 68822 (22948 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 153369 (27259 ~;28030 |; 928 &;96705 @)
% ( 125 <=>; 322 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 245 ( 245 >; 0 *; 0 +; 0 <<)
% Number of symbols : 140 ( 137 usr; 12 con; 0-5 aty)
% Number of variables : 17654 ( 0 ^17620 !; 34 ?;17654 :)
% 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_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_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_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY6427,type,
sK11_SY6427: $i > $i > $i ).
thf(tp_sK12_SY6429,type,
sK12_SY6429: $i > $i > $i ).
thf(tp_sK13_F,type,
sK13_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i > $i ).
thf(tp_sK15_SY6430,type,
sK15_SY6430: $i > $i > $i > $i ).
thf(tp_sK16_SY6434,type,
sK16_SY6434: $i > $i > $i > $i ).
thf(tp_sK17_B,type,
sK17_B: $i > $i ).
thf(tp_sK18_SY6435,type,
sK18_SY6435: $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY6436,type,
sK20_SY6436: $i > $i > $i ).
thf(tp_sK21_C,type,
sK21_C: $i > $i > $i ).
thf(tp_sK22_SY6437,type,
sK22_SY6437: $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY6439,type,
sK25_SY6439: $i > $i > $i ).
thf(tp_sK26_D,type,
sK26_D: $i > $i > $i > $i ).
thf(tp_sK27_C,type,
sK27_C: $i > $i > $i ).
thf(tp_sK28_SY6441,type,
sK28_SY6441: $i > $i > $i ).
thf(tp_sK29_C,type,
sK29_C: $i > $i > $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK30_SY6442,type,
sK30_SY6442: $i > $i > $i ).
thf(tp_sK31_D,type,
sK31_D: $i > $i > $i > $i ).
thf(tp_sK32_C,type,
sK32_C: $i > $i > $i ).
thf(tp_sK33_SY6444,type,
sK33_SY6444: $i > $i > $i ).
thf(tp_sK34_D,type,
sK34_D: $i > $i > $i > $i ).
thf(tp_sK35_C,type,
sK35_C: $i > $i > $i ).
thf(tp_sK36_C,type,
sK36_C: $i > $i > $i ).
thf(tp_sK37_SY6446,type,
sK37_SY6446: $i > $i > $i ).
thf(tp_sK38_C,type,
sK38_C: $i > $i > $i ).
thf(tp_sK39_B,type,
sK39_B: $i > $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY6448,type,
sK41_SY6448: $i > $i > $i ).
thf(tp_sK42_C,type,
sK42_C: $i > $i > $i ).
thf(tp_sK43_C,type,
sK43_C: $i > $i > $i ).
thf(tp_sK44_SY6449,type,
sK44_SY6449: $i > $i > $i ).
thf(tp_sK45_B,type,
sK45_B: $i > $i ).
thf(tp_sK46_E,type,
sK46_E: $i > $i > $i > $i > $i ).
thf(tp_sK47_D,type,
sK47_D: $i > $i > $i > $i ).
thf(tp_sK48_SY6453,type,
sK48_SY6453: $i > $i > $i > $i ).
thf(tp_sK49_E,type,
sK49_E: $i > $i > $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK50_D,type,
sK50_D: $i > $i > $i > $i ).
thf(tp_sK51_SY6455,type,
sK51_SY6455: $i > $i > $i > $i ).
thf(tp_sK52_D,type,
sK52_D: $i > $i > $i > $i ).
thf(tp_sK53_D,type,
sK53_D: $i > $i > $i > $i ).
thf(tp_sK54_SY6456,type,
sK54_SY6456: $i > $i > $i > $i ).
thf(tp_sK55_E,type,
sK55_E: $i > $i > $i > $i > $i ).
thf(tp_sK56_D,type,
sK56_D: $i > $i > $i > $i ).
thf(tp_sK57_SY6458,type,
sK57_SY6458: $i > $i > $i > $i ).
thf(tp_sK58_D,type,
sK58_D: $i > $i > $i > $i ).
thf(tp_sK59_SY6459,type,
sK59_SY6459: $i > $i > $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK60_C,type,
sK60_C: $i > $i > $i ).
thf(tp_sK61_SY6460,type,
sK61_SY6460: $i > $i > $i ).
thf(tp_sK62_D,type,
sK62_D: $i > $i > $i > $i ).
thf(tp_sK63_B,type,
sK63_B: $i > $i ).
thf(tp_sK64_SY6461,type,
sK64_SY6461: $i > $i ).
thf(tp_sK65_C,type,
sK65_C: $i > $i > $i ).
thf(tp_sK66_SY6462,type,
sK66_SY6462: $i > $i > $i ).
thf(tp_sK67_C,type,
sK67_C: $i > $i > $i ).
thf(tp_sK68_D,type,
sK68_D: $i > $i > $i > $i ).
thf(tp_sK69_D,type,
sK69_D: $i > $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK70_B,type,
sK70_B: $i > $i ).
thf(tp_sK71_SY6463,type,
sK71_SY6463: $i > $i ).
thf(tp_sK72_B,type,
sK72_B: $i > $i ).
thf(tp_sK73_SY6464,type,
sK73_SY6464: $i > $i ).
thf(tp_sK74_B,type,
sK74_B: $i > $i ).
thf(tp_sK75_SY6465,type,
sK75_SY6465: $i > $i ).
thf(tp_sK76_SY6467,type,
sK76_SY6467: $i > $i ).
thf(tp_sK77_B,type,
sK77_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_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(23,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(24,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(26,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(29,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(30,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(34,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(36,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(39,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(44,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(46,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(49,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(56,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(60,axiom,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(61,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(69,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(70,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(80,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(85,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(95,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(106,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
thf(107,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',d8_relat_2) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(112,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
thf(116,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(118,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_wellord1) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(122,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(124,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(132,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_well_founded_in @ A @ B )
<=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(138,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(148,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(151,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d16_relat_2) ).
thf(152,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(155,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(156,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_2) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(158,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(168,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(169,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(195,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(196,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(198,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(201,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(203,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(204,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(206,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(212,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(215,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(217,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(218,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(231,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(244,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(249,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(261,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(263,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(267,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(275,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(277,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',l4_wellord1) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
thf(293,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/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
thf(298,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
thf(299,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_wellord1) ).
thf(300,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[299]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[300]) ).
thf(302,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(303,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(304,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(305,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(306,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(307,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(308,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(309,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(310,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(313,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(314,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(316,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(319,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(321,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(322,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(325,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(326,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(327,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(328,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(329,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(331,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(333,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(334,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(335,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(336,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(337,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)],[110]) ).
thf(338,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)],[111]) ).
thf(339,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
& ( in @ C @ ( relation_dom @ A ) )
& ( ( apply @ A @ B )
= ( apply @ A @ C ) ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(340,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)],[114]) ).
thf(341,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)],[115]) ).
thf(342,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(343,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( well_orders @ A @ B )
<=> ( ( is_reflexive_in @ A @ B )
& ( is_transitive_in @ A @ B )
& ( is_antisymmetric_in @ A @ B )
& ( is_connected_in @ A @ B )
& ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(344,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)],[121]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(347,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)],[127]) ).
thf(348,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)],[128]) ).
thf(349,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)],[130]) ).
thf(350,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_well_founded_in @ A @ B )
<=> ! [C: $i] :
~ ( ( subset @ C @ B )
& ( C != empty_set )
& ! [D: $i] :
~ ( ( in @ D @ C )
& ( disjoint @ ( fiber @ A @ D ) @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(351,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)],[134]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ! [B: $i] :
~ ( ( subset @ B @ ( relation_field @ A ) )
& ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ( disjoint @ ( fiber @ A @ C ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(353,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)],[141]) ).
thf(354,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)],[147]) ).
thf(355,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)],[148]) ).
thf(356,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(357,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(358,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)],[153]) ).
thf(359,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)],[154]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(361,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(362,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)],[157]) ).
thf(363,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(364,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)],[159]) ).
thf(365,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)],[161]) ).
thf(366,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(371,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)],[182]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(373,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(374,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)],[187]) ).
thf(375,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(376,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(378,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(379,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(380,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(381,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(383,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(384,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(385,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(386,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(387,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(388,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(389,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(390,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(392,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)],[240]) ).
thf(393,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(394,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(396,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(398,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)],[252]) ).
thf(399,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(402,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)],[260]) ).
thf(403,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(405,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(407,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(408,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(409,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(410,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)],[268]) ).
thf(411,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(413,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(414,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(415,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(416,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(417,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(418,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)],[287]) ).
thf(419,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)],[289]) ).
thf(420,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)],[293]) ).
thf(421,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)],[298]) ).
thf(422,plain,
( ( ( relation @ sK1_A )
=> ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
<=> ( well_ordering @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[301]) ).
thf(423,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[422]) ).
thf(424,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
<=> ( well_ordering @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[422]) ).
thf(425,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
=> ( well_ordering @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[424]) ).
thf(426,plain,
( ( ( well_ordering @ sK1_A )
=> ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[424]) ).
thf(427,plain,
( ( ~ ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
=> ( well_ordering @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[425]) ).
thf(428,plain,
( ( ~ ( ( well_ordering @ sK1_A )
=> ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[426]) ).
thf(429,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
& ~ ( well_ordering @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(430,plain,
( ( ( well_ordering @ sK1_A )
& ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(431,plain,
( ( ( relation @ sK2_A )
& ( relation_empty_yielding @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[302]) ).
thf(432,plain,
( ( ( relation @ sK3_A )
& ( relation_empty_yielding @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[303]) ).
thf(433,plain,
( ( ( function @ sK4_A )
& ( relation @ sK4_A )
& ( one_to_one @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[304]) ).
thf(434,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(435,plain,
( ( ( function @ sK6_A )
& ( relation @ sK6_A )
& ( one_to_one @ sK6_A )
& ( empty @ sK6_A )
& ( epsilon_transitive @ sK6_A )
& ( epsilon_connected @ sK6_A )
& ( ordinal @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
thf(436,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[307]) ).
thf(437,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[308]) ).
thf(438,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(439,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(441,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(442,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(443,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[315]) ).
thf(445,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( function @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(447,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( function @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(448,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(449,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(450,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[323]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(452,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(453,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(454,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[329]) ).
thf(456,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(458,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(459,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( function @ ( function_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( relation @ ( function_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(460,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_reflexive_in @ A @ ( relation_field @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(461,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(462,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK10_C @ B @ A ) @ B )
& ( in @ ( sK11_SY6427 @ B @ A ) @ B )
& ( in @ ( sK12_SY6429 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY6427 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK11_SY6427 @ B @ A ) @ ( sK12_SY6429 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK12_SY6429 @ 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)],[337]) ).
thf(463,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY6433: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ SY6433 ) @ A )
| ~ ( in @ ( ordered_pair @ SY6433 @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK16_SY6434 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_SY6434 @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ 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 @ ( sK13_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(464,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK17_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK18_SY6435 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK17_B @ A ) )
= ( apply @ A @ ( sK18_SY6435 @ A ) ) )
& ( ( sK17_B @ A )
!= ( sK18_SY6435 @ A ) ) )
| ( one_to_one @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( apply @ A @ B )
!= ( apply @ A @ C ) )
| ( B = C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(465,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_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)],[340]) ).
thf(466,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK21_C @ B @ A )
!= ( sK22_SY6437 @ B @ A ) )
& ( in @ ( sK21_C @ B @ A ) @ B )
& ( in @ ( sK22_SY6437 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK21_C @ B @ A ) @ ( sK22_SY6437 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ B @ A ) @ ( sK21_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)],[341]) ).
thf(467,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[342]) ).
thf(468,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ~ ( is_transitive_in @ A @ B )
| ~ ( is_antisymmetric_in @ A @ B )
| ~ ( is_connected_in @ A @ B )
| ~ ( is_well_founded_in @ A @ B )
| ( well_orders @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(469,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6438: $i] :
~ ( in @ ( ordered_pair @ SY6438 @ ( sK24_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK24_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ B @ A ) @ ( sK24_C @ B @ A ) ) @ A )
| ( in @ ( sK24_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 @ ( sK23_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[344]) ).
thf(470,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6440: $i] :
( ( ( sK27_C @ B @ A )
!= ( apply @ A @ SY6440 ) )
| ~ ( in @ SY6440 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( ( sK27_C @ B @ A )
= ( apply @ A @ ( sK28_SY6441 @ B @ A ) ) )
& ( in @ ( sK28_SY6441 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK26_D @ C @ B @ A ) ) )
& ( in @ ( sK26_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(471,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(472,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK29_C @ B @ A ) @ B )
& ( in @ ( sK30_SY6442 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK29_C @ B @ A ) @ ( sK30_SY6442 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK30_SY6442 @ B @ A ) @ ( sK29_C @ B @ A ) ) @ A )
& ( ( sK29_C @ B @ A )
!= ( sK30_SY6442 @ 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)],[347]) ).
thf(473,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6443: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ SY6443 ) @ A )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ ( sK33_SY6444 @ B @ A ) ) @ A )
| ( in @ ( sK32_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 @ ( sK31_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[348]) ).
thf(474,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)],[349]) ).
thf(475,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY6445: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6445 ) @ ( sK35_C @ B @ A ) )
| ~ ( in @ SY6445 @ ( sK35_C @ B @ A ) ) )
& ( ( sK35_C @ B @ A )
!= empty_set )
& ( subset @ ( sK35_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK34_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK34_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[350]) ).
thf(476,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ 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)],[351]) ).
thf(477,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY6447: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6447 ) @ ( sK39_B @ A ) )
| ~ ( in @ SY6447 @ ( sK39_B @ A ) ) )
& ( ( sK39_B @ A )
!= empty_set )
& ( subset @ ( sK39_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK38_C @ B @ A ) ) @ B )
& ( in @ ( sK38_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(478,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ 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)],[353]) ).
thf(479,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK42_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK42_C @ B @ A ) @ ( sK42_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)],[354]) ).
thf(480,plain,
( ( ! [A: $i] :
( ( ! [SY6450: $i,SY6451: $i] :
( ( sK45_B @ A )
!= ( ordered_pair @ SY6450 @ SY6451 ) )
& ( in @ ( sK45_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY6449 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(481,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(482,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ( is_connected_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_connected_in @ A @ ( relation_field @ A ) )
| ( connected @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(483,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6452: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ SY6452 ) @ A )
| ~ ( in @ SY6452 @ B ) )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ ( sK48_SY6453 @ C @ B @ A ) ) @ A )
& ( in @ ( sK48_SY6453 @ C @ B @ A ) @ B ) )
| ( in @ ( sK47_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 @ ( sK46_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK46_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(484,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6454: $i] :
( ~ ( in @ ( ordered_pair @ SY6454 @ ( sK50_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY6454 @ B ) )
| ~ ( in @ ( sK50_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK51_SY6455 @ C @ B @ A ) @ ( sK50_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_SY6455 @ C @ B @ A ) @ B ) )
| ( in @ ( sK50_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 @ ( sK49_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK49_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(485,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ D ) @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(486,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_antisymmetric_in @ A @ ( relation_field @ A ) )
| ( antisymmetric @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(487,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ 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)],[362]) ).
thf(488,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6457: $i] :
( ~ ( in @ SY6457 @ ( relation_dom @ A ) )
| ~ ( in @ SY6457 @ B )
| ( ( sK56_D @ C @ B @ A )
!= ( apply @ A @ SY6457 ) ) )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK57_SY6458 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK57_SY6458 @ C @ B @ A ) @ B )
& ( ( sK56_D @ C @ B @ A )
= ( apply @ A @ ( sK57_SY6458 @ C @ B @ A ) ) ) )
| ( in @ ( sK56_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ E @ ( relation_dom @ A ) )
| ~ ( in @ E @ B )
| ( D
!= ( apply @ A @ E ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK55_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK55_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK55_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(489,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ 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)],[364]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK60_C @ B @ A )
!= ( sK61_SY6460 @ B @ A ) )
| ~ ( in @ ( sK60_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( ( sK60_C @ B @ A )
= ( sK61_SY6460 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK60_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ 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)],[365]) ).
thf(491,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(492,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(496,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)],[371]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(498,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(499,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)],[374]) ).
thf(500,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ A )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(501,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK62_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK62_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK62_D @ C @ B @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
| ( B
= ( relation_dom_restriction @ C @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ B ) )
| ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(503,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( ( relation_dom @ A )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(504,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(505,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(506,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_well_founded_in @ A @ ( relation_field @ A ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(508,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK63_B @ A ) @ ( sK64_SY6461 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(509,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(510,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(511,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(512,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[387]) ).
thf(513,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(515,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK67_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK67_C @ B @ A ) )
!= ( sK67_C @ B @ A ) ) )
| ( ( relation_dom @ B )
!= A )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( ( apply @ B @ C )
= C ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ( relation_dom @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[391]) ).
thf(517,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)],[392]) ).
thf(518,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[393]) ).
thf(519,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(521,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ~ ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) )
| ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(523,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)],[398]) ).
thf(524,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(525,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(526,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(527,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 @ ( sK68_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK68_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK68_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(528,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(530,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(531,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_dom @ B ) )
| ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(534,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(535,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 @ ( sK69_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK69_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK69_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[410]) ).
thf(536,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(537,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[413]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[414]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(541,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_rng @ C ) )
| ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(542,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ C ) )
| ~ ( in @ B @ A )
| ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(543,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK70_B @ A )
!= ( sK71_SY6463 @ A ) )
& ( in @ ( sK70_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK71_SY6463 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK70_B @ A ) @ ( sK71_SY6463 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ A ) @ ( sK70_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)],[418]) ).
thf(544,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK72_B @ A ) @ ( sK73_SY6464 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK73_SY6464 @ A ) @ ( sK72_B @ A ) ) @ A )
& ( ( sK72_B @ A )
!= ( sK73_SY6464 @ 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)],[419]) ).
thf(545,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK75_SY6465 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK75_SY6465 @ A ) @ ( sK76_SY6467 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK76_SY6467 @ 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)],[420]) ).
thf(546,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK77_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK77_B @ A ) @ ( sK77_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)],[421]) ).
thf(547,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK77_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK77_B @ A ) @ ( sK77_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)],[546]) ).
thf(548,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK75_SY6465 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK75_SY6465 @ A ) @ ( sK76_SY6467 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK76_SY6467 @ 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)],[545]) ).
thf(549,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK72_B @ A ) @ ( sK73_SY6464 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK73_SY6464 @ A ) @ ( sK72_B @ A ) ) @ A )
& ( ( sK72_B @ A )
!= ( sK73_SY6464 @ 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)],[544]) ).
thf(550,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK70_B @ A )
!= ( sK71_SY6463 @ A ) )
& ( in @ ( sK70_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK71_SY6463 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK70_B @ A ) @ ( sK71_SY6463 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ A ) @ ( sK70_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)],[543]) ).
thf(551,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ C ) )
| ~ ( in @ B @ A )
| ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(552,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_rng @ C ) )
| ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(557,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(558,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 @ ( sK69_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK69_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK69_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(559,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(562,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_dom @ B ) )
| ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(563,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(564,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(565,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(566,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 @ ( sK68_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK68_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK68_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(567,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(569,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(570,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)],[523]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ~ ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) )
| ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(572,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(575,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(576,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)],[517]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK67_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK67_C @ B @ A ) )
!= ( sK67_C @ B @ A ) ) )
| ( ( relation_dom @ B )
!= A )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( ( apply @ B @ C )
= C ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ( relation_dom @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(578,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(579,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(580,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(581,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(582,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(583,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(584,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(585,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK63_B @ A ) @ ( sK64_SY6461 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(586,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(587,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_well_founded_in @ A @ ( relation_field @ A ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(588,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(589,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(590,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( ( relation_dom @ A )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(591,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK62_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK62_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK62_D @ C @ B @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
| ( B
= ( relation_dom_restriction @ C @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ B ) )
| ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(592,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(593,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ A )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(594,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)],[499]) ).
thf(595,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(596,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(597,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)],[496]) ).
thf(598,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(599,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(600,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(601,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(602,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK60_C @ B @ A )
!= ( sK61_SY6460 @ B @ A ) )
| ~ ( in @ ( sK60_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( ( sK60_C @ B @ A )
= ( sK61_SY6460 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK60_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ 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)],[490]) ).
thf(604,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ 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)],[489]) ).
thf(605,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6457: $i] :
( ~ ( in @ SY6457 @ ( relation_dom @ A ) )
| ~ ( in @ SY6457 @ B )
| ( ( sK56_D @ C @ B @ A )
!= ( apply @ A @ SY6457 ) ) )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK57_SY6458 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK57_SY6458 @ C @ B @ A ) @ B )
& ( ( sK56_D @ C @ B @ A )
= ( apply @ A @ ( sK57_SY6458 @ C @ B @ A ) ) ) )
| ( in @ ( sK56_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ E @ ( relation_dom @ A ) )
| ~ ( in @ E @ B )
| ( D
!= ( apply @ A @ E ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK55_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK55_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK55_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(606,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ 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)],[487]) ).
thf(607,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_antisymmetric_in @ A @ ( relation_field @ A ) )
| ( antisymmetric @ A ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(608,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ D ) @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(609,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6454: $i] :
( ~ ( in @ ( ordered_pair @ SY6454 @ ( sK50_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY6454 @ B ) )
| ~ ( in @ ( sK50_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK51_SY6455 @ C @ B @ A ) @ ( sK50_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_SY6455 @ C @ B @ A ) @ B ) )
| ( in @ ( sK50_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 @ ( sK49_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK49_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(610,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6452: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ SY6452 ) @ A )
| ~ ( in @ SY6452 @ B ) )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ ( sK48_SY6453 @ C @ B @ A ) ) @ A )
& ( in @ ( sK48_SY6453 @ C @ B @ A ) @ B ) )
| ( in @ ( sK47_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 @ ( sK46_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK46_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(611,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ( is_connected_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_connected_in @ A @ ( relation_field @ A ) )
| ( connected @ A ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(612,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(613,plain,
( ( ! [A: $i] :
( ( ! [SY6450: $i,SY6451: $i] :
( ( sK45_B @ A )
!= ( ordered_pair @ SY6450 @ SY6451 ) )
& ( in @ ( sK45_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY6449 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(614,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK42_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK42_C @ B @ A ) @ ( sK42_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)],[479]) ).
thf(615,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ 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)],[478]) ).
thf(616,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY6447: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6447 ) @ ( sK39_B @ A ) )
| ~ ( in @ SY6447 @ ( sK39_B @ A ) ) )
& ( ( sK39_B @ A )
!= empty_set )
& ( subset @ ( sK39_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK38_C @ B @ A ) ) @ B )
& ( in @ ( sK38_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(617,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ 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)],[476]) ).
thf(618,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY6445: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6445 ) @ ( sK35_C @ B @ A ) )
| ~ ( in @ SY6445 @ ( sK35_C @ B @ A ) ) )
& ( ( sK35_C @ B @ A )
!= empty_set )
& ( subset @ ( sK35_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK34_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK34_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(619,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)],[474]) ).
thf(620,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6443: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ SY6443 ) @ A )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ ( sK33_SY6444 @ B @ A ) ) @ A )
| ( in @ ( sK32_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 @ ( sK31_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(621,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK29_C @ B @ A ) @ B )
& ( in @ ( sK30_SY6442 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK29_C @ B @ A ) @ ( sK30_SY6442 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK30_SY6442 @ B @ A ) @ ( sK29_C @ B @ A ) ) @ A )
& ( ( sK29_C @ B @ A )
!= ( sK30_SY6442 @ 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)],[472]) ).
thf(622,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(623,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6440: $i] :
( ( ( sK27_C @ B @ A )
!= ( apply @ A @ SY6440 ) )
| ~ ( in @ SY6440 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( ( sK27_C @ B @ A )
= ( apply @ A @ ( sK28_SY6441 @ B @ A ) ) )
& ( in @ ( sK28_SY6441 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK26_D @ C @ B @ A ) ) )
& ( in @ ( sK26_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(624,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6438: $i] :
~ ( in @ ( ordered_pair @ SY6438 @ ( sK24_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK24_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ B @ A ) @ ( sK24_C @ B @ A ) ) @ A )
| ( in @ ( sK24_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 @ ( sK23_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(625,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ~ ( is_transitive_in @ A @ B )
| ~ ( is_antisymmetric_in @ A @ B )
| ~ ( is_connected_in @ A @ B )
| ~ ( is_well_founded_in @ A @ B )
| ( well_orders @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(626,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(627,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK21_C @ B @ A )
!= ( sK22_SY6437 @ B @ A ) )
& ( in @ ( sK21_C @ B @ A ) @ B )
& ( in @ ( sK22_SY6437 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK21_C @ B @ A ) @ ( sK22_SY6437 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ B @ A ) @ ( sK21_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)],[466]) ).
thf(628,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_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)],[465]) ).
thf(629,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK17_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK18_SY6435 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK17_B @ A ) )
= ( apply @ A @ ( sK18_SY6435 @ A ) ) )
& ( ( sK17_B @ A )
!= ( sK18_SY6435 @ A ) ) )
| ( one_to_one @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( apply @ A @ B )
!= ( apply @ A @ C ) )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(630,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY6433: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ SY6433 ) @ A )
| ~ ( in @ ( ordered_pair @ SY6433 @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK16_SY6434 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_SY6434 @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ 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 @ ( sK13_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(631,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK10_C @ B @ A ) @ B )
& ( in @ ( sK11_SY6427 @ B @ A ) @ B )
& ( in @ ( sK12_SY6429 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY6427 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK11_SY6427 @ B @ A ) @ ( sK12_SY6429 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK12_SY6429 @ 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)],[462]) ).
thf(632,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(633,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_reflexive_in @ A @ ( relation_field @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(634,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( function @ ( function_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( relation @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(635,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(636,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(637,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(638,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(640,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(641,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(642,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(643,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(644,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(645,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(646,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(647,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(649,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( function @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(651,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( function @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(652,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(653,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(654,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(655,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(656,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(657,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(658,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(659,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(660,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(661,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(662,plain,
( ( ( function @ sK6_A )
& ( relation @ sK6_A )
& ( one_to_one @ sK6_A )
& ( empty @ sK6_A )
& ( epsilon_transitive @ sK6_A )
& ( epsilon_connected @ sK6_A )
& ( ordinal @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(663,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(664,plain,
( ( ( function @ sK4_A )
& ( relation @ sK4_A )
& ( one_to_one @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(665,plain,
( ( ( relation @ sK3_A )
& ( relation_empty_yielding @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(666,plain,
( ( ( relation @ sK2_A )
& ( relation_empty_yielding @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(667,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(668,plain,
( ( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
& ~ ( well_ordering @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(669,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY6444 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK32_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 @ ( sK31_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(670,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK30_SY6442 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY6442 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SX1 @ SX0 ) @ ( sK29_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= ( sK30_SY6442 @ 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)],[621]) ).
thf(671,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(672,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(673,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)],[594]) ).
thf(674,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(675,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ 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)],[549]) ).
thf(676,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(677,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(678,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(679,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY6434 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ 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 @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(680,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(681,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(682,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX2 ) @ ( sK35_C @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK35_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SX1 @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( is_well_founded_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_well_founded_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK34_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ( SX2 = empty_set )
| ~ ( subset @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(683,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(684,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(686,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ 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)],[606]) ).
thf(688,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(689,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( apply @ SX0 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( apply @ SX0 @ SX3 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(690,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(691,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(692,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK11_SY6427 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK12_SY6429 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY6427 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SX1 @ SX0 ) @ ( sK12_SY6429 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK12_SY6429 @ 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)],[631]) ).
thf(693,plain,
( ( ~ ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(694,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_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)],[547]) ).
thf(695,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) )
| ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ ( relation_rng @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(696,plain,
( ( ~ ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(697,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(698,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
| ~ ( function @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(699,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(700,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( relation_rng @ SX0 ) )
| ( SX1
= ( function_inverse @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( SX2
= ( apply @ SX0 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX3
= ( apply @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ ( relation_rng @ SX0 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( relation_rng @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(701,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(702,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ 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)],[615]) ).
thf(703,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY6436 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SX1 @ SX0 ) @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY6436 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SX1 @ SX0 ) @ ( sK19_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)],[628]) ).
thf(704,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ 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)],[548]) ).
thf(705,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ 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)],[604]) ).
thf(706,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK24_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SX1 @ SX0 ) @ ( sK24_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK24_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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(707,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
| ~ ( one_to_one @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(708,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ 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)],[603]) ).
thf(709,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)],[597]) ).
thf(710,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(711,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(712,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(713,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(714,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SX2 @ SX1 @ SX0 ) @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK51_SY6455 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK50_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 @ ( sK49_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK49_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(715,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(716,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 @ ( sK68_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK68_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK68_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(717,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(718,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 )
| ~ ( is_connected_in @ SX0 @ SX1 )
| ~ ( is_well_founded_in @ SX0 @ SX1 )
| ( well_orders @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_reflexive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_transitive_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_antisymmetric_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_connected_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_well_founded_in @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(719,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(720,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)],[576]) ).
thf(721,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SX1 @ SX0 ) @ ( sK42_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)],[614]) ).
thf(722,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(723,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(724,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(725,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)],[570]) ).
thf(726,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
| ~ ( ordinal @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(727,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(728,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(729,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 @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(730,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ ( sK48_SY6453 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK48_SY6453 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK47_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 @ ( sK46_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK46_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(731,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(732,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(733,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(734,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK27_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK28_SY6441 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ( SX2
!= ( apply @ SX0 @ ( sK26_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( in @ ( sK62_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( ( ( apply @ SX1 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) )
!= ( apply @ SX2 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ( SX1
= ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(736,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( ( sK56_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX3 ) ) )
| ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK56_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ SX4 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX4 @ SX1 )
| ( SX3
!= ( apply @ SX0 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( apply @ SX0 @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(737,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(738,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY6446 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY6446 @ 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)],[617]) ).
thf(739,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_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)],[550]) ).
thf(740,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(741,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= ( sK22_SY6437 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK22_SY6437 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SX1 @ SX0 ) @ ( sK22_SY6437 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SX1 @ SX0 ) @ ( sK21_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)],[627]) ).
thf(742,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(743,plain,
( ( ~ ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
| ~ ~ ( well_ordering @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(744,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)],[619]) ).
thf(745,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(746,plain,
! [SV1: $i] :
( ( ! [SY6468: $i] :
( ~ ( relation @ SY6468 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SY6468 ) ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(747,plain,
! [SV2: $i] :
( ( ! [SY6469: $i] :
( ~ ( relation @ SY6469 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SY6469 ) @ SY6469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(748,plain,
! [SV3: $i] :
( ( ! [SY6470: $i] :
( ~ ( relation @ SY6470 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SY6470 ) ) @ ( relation_rng @ SY6470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(749,plain,
! [SV4: $i] :
( ( ! [SY6471: $i] :
( ~ ( relation @ SY6471 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY6471 ) )
= ( set_intersection2 @ ( relation_rng @ SY6471 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(750,plain,
! [SV5: $i] :
( ( ! [SY6472: $i,SY6473: $i] :
( ~ ( relation @ SY6473 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY6473 ) @ SY6472 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY6473 @ SY6472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(751,plain,
! [SV6: $i] :
( ( ! [SY6474: $i] :
( ~ ( relation @ SY6474 )
| ( subset @ ( relation_image @ SY6474 @ SV6 ) @ ( relation_rng @ SY6474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(752,plain,
! [SV7: $i] :
( ( ! [SY6475: $i] :
( ~ ( function @ SY6475 )
| ~ ( relation @ SY6475 )
| ( subset @ ( relation_image @ SY6475 @ ( relation_inverse_image @ SY6475 @ SV7 ) ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(753,plain,
! [SV8: $i] :
( ( ! [SY6476: $i] :
( ~ ( relation @ SY6476 )
| ( ( relation_image @ SY6476 @ SV8 )
= ( relation_image @ SY6476 @ ( set_intersection2 @ ( relation_dom @ SY6476 ) @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(754,plain,
! [SV9: $i] :
( ( ! [SY6477: $i] :
( ~ ( relation @ SY6477 )
| ~ ( subset @ SV9 @ ( relation_dom @ SY6477 ) )
| ( subset @ SV9 @ ( relation_inverse_image @ SY6477 @ ( relation_image @ SY6477 @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(755,plain,
! [SV10: $i] :
( ( ~ ( relation @ SV10 )
| ( ( relation_image @ SV10 @ ( relation_dom @ SV10 ) )
= ( relation_rng @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(756,plain,
! [SV11: $i] :
( ( ! [SY6478: $i] :
( ~ ( function @ SY6478 )
| ~ ( relation @ SY6478 )
| ~ ( subset @ SV11 @ ( relation_rng @ SY6478 ) )
| ( ( relation_image @ SY6478 @ ( relation_inverse_image @ SY6478 @ SV11 ) )
= SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(757,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ! [SY6479: $i] :
( ~ ( relation @ SY6479 )
| ( ( relation_rng @ ( relation_composition @ SV12 @ SY6479 ) )
= ( relation_image @ SY6479 @ ( relation_rng @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(758,plain,
! [SV13: $i] :
( ( ! [SY6480: $i] :
( ~ ( relation @ SY6480 )
| ( subset @ ( relation_inverse_image @ SY6480 @ SV13 ) @ ( relation_dom @ SY6480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(759,plain,
! [SV14: $i] :
( ( ! [SY6481: $i] :
( ~ ( relation @ SY6481 )
| ( SV14 = empty_set )
| ~ ( subset @ SV14 @ ( relation_rng @ SY6481 ) )
| ( ( relation_inverse_image @ SY6481 @ SV14 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(760,plain,
! [SV15: $i] :
( ( ! [SY6482: $i,SY6483: $i] :
( ~ ( relation @ SY6483 )
| ~ ( subset @ SV15 @ SY6482 )
| ( subset @ ( relation_inverse_image @ SY6483 @ SV15 ) @ ( relation_inverse_image @ SY6483 @ SY6482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(761,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(762,plain,
! [SV17: $i] :
( ( ! [SY6484: $i] :
( ~ ( function @ SY6484 )
| ~ ( relation @ SY6484 )
| ! [SY6485: $i] :
( ~ ( function @ SY6485 )
| ~ ( relation @ SY6485 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6485 @ SY6484 ) ) )
| ( ( apply @ ( relation_composition @ SY6485 @ SY6484 ) @ SV17 )
= ( apply @ SY6484 @ ( apply @ SY6485 @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(763,plain,
! [SV18: $i] :
( ( ! [SY6486: $i] :
( ~ ( function @ SY6486 )
| ~ ( relation @ SY6486 )
| ! [SY6487: $i] :
( ~ ( function @ SY6487 )
| ~ ( relation @ SY6487 )
| ~ ( in @ SV18 @ ( relation_dom @ SY6486 ) )
| ( ( apply @ ( relation_composition @ SY6486 @ SY6487 ) @ SV18 )
= ( apply @ SY6487 @ ( apply @ SY6486 @ SV18 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(764,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ! [SY6488: $i] :
( ~ ( relation @ SY6488 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SY6488 ) ) @ ( relation_dom @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(765,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ! [SY6489: $i] :
( ~ ( relation @ SY6489 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SY6489 ) ) @ ( relation_rng @ SY6489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(766,plain,
! [SV21: $i] :
( ( ~ ( relation @ SV21 )
| ! [SY6490: $i] :
( ~ ( relation @ SY6490 )
| ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SY6490 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SY6490 ) )
= ( relation_dom @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(767,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ! [SY6491: $i] :
( ~ ( relation @ SY6491 )
| ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SY6491 ) )
| ( ( relation_rng @ ( relation_composition @ SY6491 @ SV22 ) )
= ( relation_rng @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(768,plain,
! [SV23: $i] :
( ( ~ ( relation @ SV23 )
| ( in @ ( ordered_pair @ ( sK63_B @ SV23 ) @ ( sK64_SY6461 @ SV23 ) ) @ SV23 )
| ( SV23 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(769,plain,
! [SV24: $i] :
( ( ~ ( function @ SV24 )
| ~ ( relation @ SV24 )
| ~ ( one_to_one @ SV24 )
| ( one_to_one @ ( function_inverse @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(770,plain,
! [SV25: $i] :
( ( ! [SY6492: $i,SY6493: $i] :
( ~ ( function @ SY6493 )
| ~ ( relation @ SY6493 )
| ~ ( in @ SY6492 @ ( relation_dom @ ( relation_dom_restriction @ SY6493 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY6493 @ SV25 ) @ SY6492 )
= ( apply @ SY6493 @ SY6492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(771,plain,
! [SV26: $i] :
( ( ! [SY6494: $i,SY6495: $i] :
( ~ ( function @ SY6495 )
| ~ ( relation @ SY6495 )
| ~ ( in @ SY6494 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SY6495 @ SV26 ) @ SY6494 )
= ( apply @ SY6495 @ SY6494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(772,plain,
! [SV27: $i] :
( ( ! [SY6496: $i] :
( ~ ( relation @ SY6496 )
| ( subset @ ( relation_dom_restriction @ SY6496 @ SV27 ) @ SY6496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(773,plain,
! [SV28: $i] :
( ( ! [SY6497: $i] :
( ~ ( relation @ SY6497 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY6497 @ SV28 ) )
= ( set_intersection2 @ ( relation_dom @ SY6497 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(774,plain,
! [SV29: $i] :
( ( ! [SY6498: $i] :
( ~ ( relation @ SY6498 )
| ( ( relation_dom_restriction @ SY6498 @ SV29 )
= ( relation_composition @ ( identity_relation @ SV29 ) @ SY6498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(775,plain,
! [SV30: $i] :
( ( ! [SY6499: $i] :
( ~ ( relation @ SY6499 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY6499 @ SV30 ) ) @ ( relation_rng @ SY6499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(776,plain,
! [SV31: $i] :
( ( ~ ( empty @ SV31 )
| ( relation @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(777,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ( ( relation_field @ SV32 )
= ( set_union2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(778,plain,
! [SV33: $i] :
( ( ~ ( function @ SV33 )
| ~ ( relation @ SV33 )
| ~ ( one_to_one @ SV33 )
| ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(779,plain,
! [SV34: $i] :
( ( ~ ( relation @ SV34 )
| ( relation @ ( relation_inverse @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(780,plain,
! [SV35: $i] :
( ( ! [SY6500: $i] :
( ~ ( relation @ SV35 )
| ~ ( relation @ SY6500 )
| ( relation @ ( relation_composition @ SV35 @ SY6500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(781,plain,
! [SV36: $i] :
( ( relation @ ( identity_relation @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(782,plain,
! [SV37: $i] :
( ( ~ ( relation @ SV37 )
| ! [SY6501: $i] : ( relation @ ( relation_dom_restriction @ SV37 @ SY6501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(783,plain,
! [SV38: $i] :
( ( ! [SY6502: $i] :
( ~ ( relation @ SY6502 )
| ( relation @ ( relation_rng_restriction @ SV38 @ SY6502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(784,plain,
! [SV39: $i] :
( ( ! [SY6503: $i] :
( ~ ( relation @ SV39 )
| ~ ( relation @ SY6503 )
| ( relation @ ( set_intersection2 @ SV39 @ SY6503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(785,plain,
! [SV40: $i] :
( ( ! [SY6504: $i] :
( ~ ( relation @ SV40 )
| ~ ( relation @ SY6504 )
| ( relation @ ( set_union2 @ SV40 @ SY6504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(786,plain,
! [SV41: $i] :
( ( ! [SY6505: $i] :
( ~ ( relation @ SV41 )
| ~ ( relation @ SY6505 )
| ( relation @ ( set_difference @ SV41 @ SY6505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(787,plain,
! [SV42: $i] :
( ( ( empty @ SV42 )
| ~ ( relation @ SV42 )
| ~ ( empty @ ( relation_dom @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(788,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
| ~ ( relation @ SV43 )
| ~ ( empty @ ( relation_rng @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(789,plain,
! [SV44: $i] :
( ( ~ ( relation @ SV44 )
| ( ( relation_inverse @ ( relation_inverse @ SV44 ) )
= SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(790,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ~ ( ~ ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(791,plain,
! [SV46: $i] :
( ( ~ ( relation @ SV46 )
| ~ ( ~ ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) )
| ~ ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(792,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(793,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(794,plain,
! [SV47: $i] :
( ( ! [SY6516: $i] :
~ ( ~ ! [SY6517: $i,SY6518: $i] :
( ~ ( relation @ SY6518 )
| ~ ( in @ SV47 @ SY6517 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY6516 ) @ SY6518 )
| ( in @ ( ordered_pair @ SV47 @ SY6516 ) @ ( relation_composition @ ( identity_relation @ SY6517 ) @ SY6518 ) ) )
| ~ ~ ( ~ ! [SY6519: $i,SY6520: $i] :
( ~ ( relation @ SY6520 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY6516 ) @ ( relation_composition @ ( identity_relation @ SY6519 ) @ SY6520 ) )
| ( in @ SV47 @ SY6519 ) )
| ~ ! [SY6521: $i,SY6522: $i] :
( ~ ( relation @ SY6522 )
| ~ ( in @ ( ordered_pair @ SV47 @ SY6516 ) @ ( relation_composition @ ( identity_relation @ SY6521 ) @ SY6522 ) )
| ( in @ ( ordered_pair @ SV47 @ SY6516 ) @ SY6522 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(795,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY6523: $i,SY6524: $i] :
( ~ ( relation @ SY6524 )
| ~ ( in @ SV48 @ SY6523 )
| ~ ( in @ SV48 @ ( relation_dom @ SY6524 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6524 @ SY6523 ) ) ) )
| ~ ~ ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) )
| ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(796,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ 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)],[675]) ).
thf(797,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(798,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(799,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(800,plain,
! [SV49: $i] :
( ( ~ ( relation @ SV49 )
| ! [SY6529: $i] :
( ~ ( relation @ SY6529 )
| ~ ( ~ ! [SY6530: $i] :
( ~ ( relation @ SY6530 )
| ~ ( ~ ( ! [SY6531: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ SY6531 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6531 @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) ) )
| ( SY6530
= ( relation_composition @ SV49 @ SY6529 ) ) )
| ~ ! [SY6532: $i] :
( ~ ( relation @ SY6532 )
| ( SY6532
!= ( relation_composition @ SV49 @ SY6529 ) )
| ~ ( ~ ! [SY6533: $i,SY6534: $i] :
( ! [SY6535: $i] :
( ~ ( in @ ( ordered_pair @ SY6533 @ SY6535 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6535 @ SY6534 ) @ SY6529 ) )
| ( in @ ( ordered_pair @ SY6533 @ SY6534 ) @ SY6532 ) )
| ~ ! [SY6536: $i,SY6537: $i] :
( ~ ( in @ ( ordered_pair @ SY6536 @ SY6537 ) @ SY6532 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6536 @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) @ SY6537 ) @ SY6529 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(801,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(802,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(803,plain,
! [SV50: $i] :
( ( ~ ( relation @ SV50 )
| ~ ( ~ ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) )
| ~ ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(804,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(805,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(806,plain,
! [SV51: $i] :
( ( ! [SY6542: $i] :
( ~ ( function @ SY6542 )
| ~ ( relation @ SY6542 )
| ~ ( ~ ! [SY6543: $i] :
( ~ ( function @ SY6543 )
| ~ ( relation @ SY6543 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6543 ) )
| ~ ( in @ ( apply @ SY6543 @ SV51 ) @ ( relation_dom @ SY6542 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6543 @ SY6542 ) ) ) )
| ~ ~ ( ~ ! [SY6544: $i] :
( ~ ( function @ SY6544 )
| ~ ( relation @ SY6544 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6544 @ SY6542 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6544 ) ) )
| ~ ! [SY6545: $i] :
( ~ ( function @ SY6545 )
| ~ ( relation @ SY6545 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6545 @ SY6542 ) ) )
| ( in @ ( apply @ SY6545 @ SV51 ) @ ( relation_dom @ SY6542 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(807,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(808,plain,
! [SV52: $i] :
( ( ! [SY6546: $i] :
( ~ ( relation @ SY6546 )
| ~ ( ~ ! [SY6547: $i] :
( ~ ( relation @ SY6547 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6547 @ SY6546 @ SV52 ) @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) ) @ SY6546 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6547 @ SY6546 @ SV52 ) @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) ) @ SY6547 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6547 @ SY6546 @ SV52 ) @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) ) @ SY6547 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6547 @ SY6546 @ SV52 ) @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) ) @ SY6546 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6547 @ SY6546 @ SV52 ) @ ( sK54_SY6456 @ SY6547 @ SY6546 @ SV52 ) ) @ SY6547 ) ) ) )
| ( SY6547
= ( relation_rng_restriction @ SV52 @ SY6546 ) ) )
| ~ ! [SY6548: $i] :
( ~ ( relation @ SY6548 )
| ( SY6548
!= ( relation_rng_restriction @ SV52 @ SY6546 ) )
| ~ ( ~ ! [SY6549: $i,SY6550: $i] :
( ~ ( in @ SY6550 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6549 @ SY6550 ) @ SY6546 )
| ( in @ ( ordered_pair @ SY6549 @ SY6550 ) @ SY6548 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6548 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6548 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6546 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(809,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(810,plain,
! [SV53: $i] :
( ( ~ ( function @ SV53 )
| ~ ( relation @ SV53 )
| ~ ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(811,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(812,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(813,plain,
! [SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( ~ ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) )
| ~ ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(814,plain,
( ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(815,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_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)],[694]) ).
thf(816,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY6567: $i,SY6568: $i] :
( ~ ( relation @ SY6568 )
| ~ ( in @ SV55 @ SY6567 )
| ~ ( in @ SV55 @ ( relation_rng @ SY6568 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6567 @ SY6568 ) ) ) )
| ~ ~ ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) )
| ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(817,plain,
( ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(818,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(819,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
| ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(820,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(821,plain,
! [SV56: $i] :
( ( ~ ( function @ SV56 )
| ~ ( relation @ SV56 )
| ~ ( one_to_one @ SV56 )
| ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(822,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(823,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ~ ( ~ ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) )
| ~ ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(824,plain,
! [SV58: $i] :
( ( ~ ( relation @ SV58 )
| ~ ( ~ ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) )
| ~ ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(825,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ 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)],[704]) ).
thf(826,plain,
! [SV59: $i] :
( ( ~ ( relation @ SV59 )
| ~ ( ~ ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) )
| ~ ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(827,plain,
! [SV60: $i] :
( ( ~ ( relation @ SV60 )
| ~ ( ~ ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) )
| ~ ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(828,plain,
( ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
| ~ ( one_to_one @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(829,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ 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)],[708]) ).
thf(830,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY6612: $i,SY6613: $i] :
( ~ ( function @ SY6613 )
| ~ ( relation @ SY6613 )
| ( SY6612
!= ( apply @ SY6613 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SY6613 ) )
| ( in @ ( ordered_pair @ SV61 @ SY6612 ) @ SY6613 ) )
| ~ ~ ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) )
| ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(831,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(832,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(833,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(834,plain,
! [SV62: $i] :
( ( ~ ( relation @ SV62 )
| ~ ( ~ ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) )
| ~ ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(835,plain,
! [SV63: $i] :
( ( ~ ( relation @ SV63 )
| ~ ( ~ ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) )
| ~ ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(836,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(837,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY6628: $i,SY6629: $i] :
( ~ ( relation @ SY6629 )
| ! [SY6630: $i] :
( ~ ( in @ SY6630 @ ( relation_rng @ SY6629 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6630 ) @ SY6629 )
| ~ ( in @ SY6630 @ SY6628 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SY6629 @ SY6628 ) ) )
| ~ ! [SY6631: $i,SY6632: $i] :
( ~ ( relation @ SY6632 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SY6632 @ SY6631 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ ( relation_rng @ SY6632 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) ) @ SY6632 ) )
| ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ SY6631 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(838,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(839,plain,
! [SV65: $i] :
( ( ~ ( relation @ SV65 )
| ~ ( ~ ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(840,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(841,plain,
! [SV66: $i] :
( ( ~ ( ~ ! [SY6639: $i,SY6640: $i] :
( ~ ( relation @ SY6640 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6639 ) @ SY6640 )
| ( in @ SV66 @ ( relation_field @ SY6640 ) ) )
| ~ ! [SY6641: $i,SY6642: $i] :
( ~ ( relation @ SY6642 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6641 ) @ SY6642 )
| ( in @ SY6641 @ ( relation_field @ SY6642 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(842,plain,
! [SV67: $i] :
( ( ~ ( relation @ SV67 )
| ~ ( ~ ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) )
| ~ ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(843,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(844,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(845,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(846,plain,
! [SV68: $i] :
( ( ~ ( ~ ! [SY6646: $i,SY6647: $i] :
( ~ ( relation @ SY6647 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6646 ) @ SY6647 )
| ( in @ SV68 @ ( relation_dom @ SY6647 ) ) )
| ~ ! [SY6648: $i,SY6649: $i] :
( ~ ( relation @ SY6649 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6648 ) @ SY6649 )
| ( in @ SY6648 @ ( relation_rng @ SY6649 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(847,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
| ~ ( ordinal @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(848,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(849,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(850,plain,
! [SV69: $i] :
( ( ~ ( ~ ! [SY6650: $i,SY6651: $i] :
( ~ ( relation @ SY6651 )
| ! [SY6652: $i] :
( ~ ( in @ SY6652 @ ( relation_dom @ SY6651 ) )
| ~ ( in @ ( ordered_pair @ SY6652 @ SV69 ) @ SY6651 )
| ~ ( in @ SY6652 @ SY6650 ) )
| ( in @ SV69 @ ( relation_image @ SY6651 @ SY6650 ) ) )
| ~ ! [SY6653: $i,SY6654: $i] :
( ~ ( relation @ SY6654 )
| ~ ( in @ SV69 @ ( relation_image @ SY6654 @ SY6653 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ ( relation_dom @ SY6654 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SV69 ) @ SY6654 ) )
| ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SY6653 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(851,plain,
! [SV70: $i] :
( ( ~ ( relation @ SV70 )
| ~ ( ~ ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) )
| ~ ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(852,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(853,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(854,plain,
! [SV71: $i] :
( ( ~ ( ~ ! [SY6663: $i,SY6664: $i] :
( ~ ( function @ SY6664 )
| ~ ( relation @ SY6664 )
| ~ ( in @ SY6663 @ ( relation_dom @ SY6664 ) )
| ~ ( in @ SY6663 @ SV71 )
| ( in @ SY6663 @ ( relation_dom @ ( relation_dom_restriction @ SY6664 @ SV71 ) ) ) )
| ~ ~ ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) )
| ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(855,plain,
! [SV72: $i] :
( ( ~ ( function @ SV72 )
| ~ ( relation @ SV72 )
| ~ ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(856,plain,
! [SV73: $i] :
( ( ! [SY6675: $i] :
( ~ ( function @ SY6675 )
| ~ ( relation @ SY6675 )
| ~ ( ~ ! [SY6676: $i] :
( ~ ( function @ SY6676 )
| ~ ( relation @ SY6676 )
| ~ ( ~ ( in @ ( sK62_D @ SY6676 @ SY6675 @ SV73 ) @ ( relation_dom @ SY6675 ) )
| ~ ( ( ( apply @ SY6675 @ ( sK62_D @ SY6676 @ SY6675 @ SV73 ) )
!= ( apply @ SY6676 @ ( sK62_D @ SY6676 @ SY6675 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SY6675 )
!= ( set_intersection2 @ ( relation_dom @ SY6676 ) @ SV73 ) )
| ( SY6675
= ( relation_dom_restriction @ SY6676 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6677: $i] :
( ~ ( function @ SY6677 )
| ~ ( relation @ SY6677 )
| ( SY6675
!= ( relation_dom_restriction @ SY6677 @ SV73 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY6675 ) )
| ( ( apply @ SY6675 @ SX3 )
= ( apply @ SY6677 @ SX3 ) ) ) )
| ~ ! [SY6679: $i] :
( ~ ( function @ SY6679 )
| ~ ( relation @ SY6679 )
| ( SY6675
!= ( relation_dom_restriction @ SY6679 @ SV73 ) )
| ( ( relation_dom @ SY6675 )
= ( set_intersection2 @ ( relation_dom @ SY6679 ) @ SV73 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(857,plain,
! [SV74: $i] :
( ( ~ ( function @ SV74 )
| ~ ( relation @ SV74 )
| ~ ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(858,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(859,plain,
! [SV75: $i] :
( ( ~ ( relation @ SV75 )
| ~ ( ~ ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) )
| ~ ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(860,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_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)],[739]) ).
thf(861,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(862,plain,
! [SV76: $i] :
( ( ~ ( relation @ SV76 )
| ~ ( ~ ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) )
| ~ ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(863,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(864,plain,
( ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
| ~ ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(865,plain,
! [SV77: $i] :
( ( ~ ( function @ SV77 )
| ~ ( relation @ SV77 )
| ~ ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(866,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(867,plain,
! [SV1: $i,SV78: $i] :
( ( ~ ( relation @ SV78 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV78 ) ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(868,plain,
! [SV2: $i,SV79: $i] :
( ( ~ ( relation @ SV79 )
| ( subset @ ( relation_rng_restriction @ SV2 @ SV79 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(869,plain,
! [SV3: $i,SV80: $i] :
( ( ~ ( relation @ SV80 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV80 ) ) @ ( relation_rng @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(870,plain,
! [SV4: $i,SV81: $i] :
( ( ~ ( relation @ SV81 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV81 ) )
= ( set_intersection2 @ ( relation_rng @ SV81 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(871,plain,
! [SV82: $i,SV5: $i] :
( ( ! [SY6704: $i] :
( ~ ( relation @ SY6704 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SY6704 ) @ SV82 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SY6704 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(872,plain,
! [SV6: $i,SV83: $i] :
( ( ~ ( relation @ SV83 )
| ( subset @ ( relation_image @ SV83 @ SV6 ) @ ( relation_rng @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(873,plain,
! [SV7: $i,SV84: $i] :
( ( ~ ( function @ SV84 )
| ~ ( relation @ SV84 )
| ( subset @ ( relation_image @ SV84 @ ( relation_inverse_image @ SV84 @ SV7 ) ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(874,plain,
! [SV8: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ( ( relation_image @ SV85 @ SV8 )
= ( relation_image @ SV85 @ ( set_intersection2 @ ( relation_dom @ SV85 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(875,plain,
! [SV9: $i,SV86: $i] :
( ( ~ ( relation @ SV86 )
| ~ ( subset @ SV9 @ ( relation_dom @ SV86 ) )
| ( subset @ SV9 @ ( relation_inverse_image @ SV86 @ ( relation_image @ SV86 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(876,plain,
! [SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ( relation_image @ SV10 @ ( relation_dom @ SV10 ) )
= ( relation_rng @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(877,plain,
! [SV11: $i,SV87: $i] :
( ( ~ ( function @ SV87 )
| ~ ( relation @ SV87 )
| ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) )
| ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(878,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ! [SY6479: $i] :
( ~ ( relation @ SY6479 )
| ( ( relation_rng @ ( relation_composition @ SV12 @ SY6479 ) )
= ( relation_image @ SY6479 @ ( relation_rng @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(879,plain,
! [SV13: $i,SV88: $i] :
( ( ~ ( relation @ SV88 )
| ( subset @ ( relation_inverse_image @ SV88 @ SV13 ) @ ( relation_dom @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(880,plain,
! [SV14: $i,SV89: $i] :
( ( ~ ( relation @ SV89 )
| ( SV14 = empty_set )
| ~ ( subset @ SV14 @ ( relation_rng @ SV89 ) )
| ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(881,plain,
! [SV90: $i,SV15: $i] :
( ( ! [SY6705: $i] :
( ~ ( relation @ SY6705 )
| ~ ( subset @ SV15 @ SV90 )
| ( subset @ ( relation_inverse_image @ SY6705 @ SV15 ) @ ( relation_inverse_image @ SY6705 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(882,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(883,plain,
! [SV17: $i,SV91: $i] :
( ( ~ ( function @ SV91 )
| ~ ( relation @ SV91 )
| ! [SY6706: $i] :
( ~ ( function @ SY6706 )
| ~ ( relation @ SY6706 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6706 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SY6706 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SY6706 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(884,plain,
! [SV18: $i,SV92: $i] :
( ( ~ ( function @ SV92 )
| ~ ( relation @ SV92 )
| ! [SY6707: $i] :
( ~ ( function @ SY6707 )
| ~ ( relation @ SY6707 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SY6707 ) @ SV18 )
= ( apply @ SY6707 @ ( apply @ SV92 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(885,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ! [SY6488: $i] :
( ~ ( relation @ SY6488 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SY6488 ) ) @ ( relation_dom @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(886,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ! [SY6489: $i] :
( ~ ( relation @ SY6489 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SY6489 ) ) @ ( relation_rng @ SY6489 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(887,plain,
! [SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ! [SY6490: $i] :
( ~ ( relation @ SY6490 )
| ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SY6490 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SY6490 ) )
= ( relation_dom @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(888,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ! [SY6491: $i] :
( ~ ( relation @ SY6491 )
| ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SY6491 ) )
| ( ( relation_rng @ ( relation_composition @ SY6491 @ SV22 ) )
= ( relation_rng @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(889,plain,
! [SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK63_B @ SV23 ) @ ( sK64_SY6461 @ SV23 ) ) @ SV23 )
| ( SV23 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(890,plain,
! [SV24: $i] :
( ( ( ~ ( function @ SV24 )
| ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( one_to_one @ SV24 )
| ( one_to_one @ ( function_inverse @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(891,plain,
! [SV25: $i,SV93: $i] :
( ( ! [SY6708: $i] :
( ~ ( function @ SY6708 )
| ~ ( relation @ SY6708 )
| ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SY6708 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY6708 @ SV25 ) @ SV93 )
= ( apply @ SY6708 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(892,plain,
! [SV26: $i,SV94: $i] :
( ( ! [SY6709: $i] :
( ~ ( function @ SY6709 )
| ~ ( relation @ SY6709 )
| ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SY6709 @ SV26 ) @ SV94 )
= ( apply @ SY6709 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(893,plain,
! [SV27: $i,SV95: $i] :
( ( ~ ( relation @ SV95 )
| ( subset @ ( relation_dom_restriction @ SV95 @ SV27 ) @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(894,plain,
! [SV28: $i,SV96: $i] :
( ( ~ ( relation @ SV96 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV96 @ SV28 ) )
= ( set_intersection2 @ ( relation_dom @ SV96 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(895,plain,
! [SV29: $i,SV97: $i] :
( ( ~ ( relation @ SV97 )
| ( ( relation_dom_restriction @ SV97 @ SV29 )
= ( relation_composition @ ( identity_relation @ SV29 ) @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(896,plain,
! [SV30: $i,SV98: $i] :
( ( ~ ( relation @ SV98 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV98 @ SV30 ) ) @ ( relation_rng @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(897,plain,
! [SV31: $i] :
( ( ( ~ ( empty @ SV31 ) )
= $true )
| ( ( relation @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(898,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ( relation_field @ SV32 )
= ( set_union2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(899,plain,
! [SV33: $i] :
( ( ( ~ ( function @ SV33 )
| ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( one_to_one @ SV33 )
| ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(900,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(901,plain,
! [SV99: $i,SV35: $i] :
( ( ~ ( relation @ SV35 )
| ~ ( relation @ SV99 )
| ( relation @ ( relation_composition @ SV35 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(902,plain,
! [SV37: $i] :
( ( ( ~ ( relation @ SV37 ) )
= $true )
| ( ( ! [SY6501: $i] : ( relation @ ( relation_dom_restriction @ SV37 @ SY6501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(903,plain,
! [SV38: $i,SV100: $i] :
( ( ~ ( relation @ SV100 )
| ( relation @ ( relation_rng_restriction @ SV38 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(904,plain,
! [SV101: $i,SV39: $i] :
( ( ~ ( relation @ SV39 )
| ~ ( relation @ SV101 )
| ( relation @ ( set_intersection2 @ SV39 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(905,plain,
! [SV102: $i,SV40: $i] :
( ( ~ ( relation @ SV40 )
| ~ ( relation @ SV102 )
| ( relation @ ( set_union2 @ SV40 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(906,plain,
! [SV103: $i,SV41: $i] :
( ( ~ ( relation @ SV41 )
| ~ ( relation @ SV103 )
| ( relation @ ( set_difference @ SV41 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(907,plain,
! [SV42: $i] :
( ( ( ( empty @ SV42 )
| ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(908,plain,
! [SV43: $i] :
( ( ( ( empty @ SV43 )
| ~ ( relation @ SV43 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(909,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV44 ) )
= SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(910,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( ~ ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(911,plain,
! [SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( ~ ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) )
| ~ ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(912,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(913,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(914,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(915,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(916,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ( ~ ! [SY6710: $i,SY6711: $i] :
( ~ ( relation @ SY6711 )
| ~ ( in @ SV47 @ SY6710 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6711 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6710 ) @ SY6711 ) ) )
| ~ ~ ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) )
| ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(917,plain,
! [SV48: $i] :
( ( ~ ! [SY6523: $i,SY6524: $i] :
( ~ ( relation @ SY6524 )
| ~ ( in @ SV48 @ SY6523 )
| ~ ( in @ SV48 @ ( relation_dom @ SY6524 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6524 @ SY6523 ) ) ) )
| ~ ~ ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) )
| ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(918,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(919,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)],[796]) ).
thf(920,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(921,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(922,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(923,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(924,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(925,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(926,plain,
! [SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ! [SY6529: $i] :
( ~ ( relation @ SY6529 )
| ~ ( ~ ! [SY6530: $i] :
( ~ ( relation @ SY6530 )
| ~ ( ~ ( ! [SY6531: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ SY6531 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6531 @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) ) )
| ( SY6530
= ( relation_composition @ SV49 @ SY6529 ) ) )
| ~ ! [SY6532: $i] :
( ~ ( relation @ SY6532 )
| ( SY6532
!= ( relation_composition @ SV49 @ SY6529 ) )
| ~ ( ~ ! [SY6533: $i,SY6534: $i] :
( ! [SY6535: $i] :
( ~ ( in @ ( ordered_pair @ SY6533 @ SY6535 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6535 @ SY6534 ) @ SY6529 ) )
| ( in @ ( ordered_pair @ SY6533 @ SY6534 ) @ SY6532 ) )
| ~ ! [SY6536: $i,SY6537: $i] :
( ~ ( in @ ( ordered_pair @ SY6536 @ SY6537 ) @ SY6532 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6536 @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) @ SY6537 ) @ SY6529 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(927,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(928,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(929,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[802]) ).
thf(930,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[802]) ).
thf(931,plain,
! [SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( ~ ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) )
| ~ ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(932,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(933,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[804]) ).
thf(934,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(935,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(936,plain,
! [SV51: $i,SV105: $i] :
( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 )
| ~ ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(937,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(938,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(939,plain,
! [SV52: $i,SV106: $i] :
( ( ~ ( relation @ SV106 )
| ~ ( ~ ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
| ~ ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(940,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(941,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(942,plain,
! [SV53: $i] :
( ( ( ~ ( function @ SV53 )
| ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(943,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(944,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(945,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(946,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(947,plain,
! [SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( ~ ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) )
| ~ ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(948,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(949,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(950,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(951,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)],[815]) ).
thf(952,plain,
! [SV55: $i] :
( ( ~ ! [SY6567: $i,SY6568: $i] :
( ~ ( relation @ SY6568 )
| ~ ( in @ SV55 @ SY6567 )
| ~ ( in @ SV55 @ ( relation_rng @ SY6568 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6567 @ SY6568 ) ) ) )
| ~ ~ ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) )
| ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(953,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(954,plain,
( ( ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(955,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(956,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[818]) ).
thf(957,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(958,plain,
( ( ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(959,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(960,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[820]) ).
thf(961,plain,
! [SV56: $i] :
( ( ( ~ ( function @ SV56 )
| ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( one_to_one @ SV56 )
| ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(962,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(963,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(964,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( ~ ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) )
| ~ ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(965,plain,
! [SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( ~ ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) )
| ~ ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(966,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(967,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)],[825]) ).
thf(968,plain,
! [SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) )
| ~ ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(969,plain,
! [SV60: $i] :
( ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( ~ ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) )
| ~ ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(970,plain,
( ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(971,plain,
( ( ~ ( one_to_one @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(972,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(973,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)],[829]) ).
thf(974,plain,
! [SV61: $i] :
( ( ~ ! [SY6612: $i,SY6613: $i] :
( ~ ( function @ SY6613 )
| ~ ( relation @ SY6613 )
| ( SY6612
!= ( apply @ SY6613 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SY6613 ) )
| ( in @ ( ordered_pair @ SV61 @ SY6612 ) @ SY6613 ) )
| ~ ~ ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) )
| ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(975,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(976,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(977,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(978,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(979,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(980,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(981,plain,
! [SV62: $i] :
( ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( ~ ( ~ ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) )
| ~ ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(982,plain,
! [SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( ~ ( ~ ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) )
| ~ ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(983,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[836]) ).
thf(984,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[836]) ).
thf(985,plain,
! [SV64: $i] :
( ( ~ ! [SY6628: $i,SY6629: $i] :
( ~ ( relation @ SY6629 )
| ! [SY6630: $i] :
( ~ ( in @ SY6630 @ ( relation_rng @ SY6629 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6630 ) @ SY6629 )
| ~ ( in @ SY6630 @ SY6628 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SY6629 @ SY6628 ) ) )
| ~ ! [SY6631: $i,SY6632: $i] :
( ~ ( relation @ SY6632 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SY6632 @ SY6631 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ ( relation_rng @ SY6632 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) ) @ SY6632 ) )
| ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ SY6631 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(986,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(987,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(988,plain,
! [SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(989,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(990,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(991,plain,
! [SV66: $i] :
( ( ~ ! [SY6639: $i,SY6640: $i] :
( ~ ( relation @ SY6640 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6639 ) @ SY6640 )
| ( in @ SV66 @ ( relation_field @ SY6640 ) ) )
| ~ ! [SY6641: $i,SY6642: $i] :
( ~ ( relation @ SY6642 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6641 ) @ SY6642 )
| ( in @ SY6641 @ ( relation_field @ SY6642 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(992,plain,
! [SV67: $i] :
( ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) )
| ~ ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(993,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(994,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(995,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(996,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(997,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(998,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[845]) ).
thf(999,plain,
! [SV68: $i] :
( ( ~ ! [SY6646: $i,SY6647: $i] :
( ~ ( relation @ SY6647 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6646 ) @ SY6647 )
| ( in @ SV68 @ ( relation_dom @ SY6647 ) ) )
| ~ ! [SY6648: $i,SY6649: $i] :
( ~ ( relation @ SY6649 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6648 ) @ SY6649 )
| ( in @ SY6648 @ ( relation_rng @ SY6649 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(1000,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(1001,plain,
( ( ~ ( ordinal @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(1002,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(1003,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(1004,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(1005,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(1006,plain,
! [SV69: $i] :
( ( ~ ! [SY6650: $i,SY6651: $i] :
( ~ ( relation @ SY6651 )
| ! [SY6652: $i] :
( ~ ( in @ SY6652 @ ( relation_dom @ SY6651 ) )
| ~ ( in @ ( ordered_pair @ SY6652 @ SV69 ) @ SY6651 )
| ~ ( in @ SY6652 @ SY6650 ) )
| ( in @ SV69 @ ( relation_image @ SY6651 @ SY6650 ) ) )
| ~ ! [SY6653: $i,SY6654: $i] :
( ~ ( relation @ SY6654 )
| ~ ( in @ SV69 @ ( relation_image @ SY6654 @ SY6653 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ ( relation_dom @ SY6654 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SV69 ) @ SY6654 ) )
| ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SY6653 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(1007,plain,
! [SV70: $i] :
( ( ( ~ ( relation @ SV70 ) )
= $true )
| ( ( ~ ( ~ ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) )
| ~ ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(1008,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(1009,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(1010,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(1011,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(1012,plain,
! [SV71: $i] :
( ( ~ ! [SY6663: $i,SY6664: $i] :
( ~ ( function @ SY6664 )
| ~ ( relation @ SY6664 )
| ~ ( in @ SY6663 @ ( relation_dom @ SY6664 ) )
| ~ ( in @ SY6663 @ SV71 )
| ( in @ SY6663 @ ( relation_dom @ ( relation_dom_restriction @ SY6664 @ SV71 ) ) ) )
| ~ ~ ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) )
| ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(1013,plain,
! [SV72: $i] :
( ( ( ~ ( function @ SV72 )
| ~ ( relation @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(1014,plain,
! [SV73: $i,SV107: $i] :
( ( ~ ( function @ SV107 )
| ~ ( relation @ SV107 )
| ~ ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1015,plain,
! [SV74: $i] :
( ( ( ~ ( function @ SV74 )
| ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(1016,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(1017,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(1018,plain,
! [SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) )
| ~ ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(1019,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(1020,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)],[860]) ).
thf(1021,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(1022,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(1023,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ~ ( ~ ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) )
| ~ ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(1024,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(1025,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(1026,plain,
( ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(1027,plain,
( ( ~ ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(1028,plain,
! [SV77: $i] :
( ( ( ~ ( function @ SV77 )
| ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(1029,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(1030,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(1031,plain,
! [SV1: $i,SV78: $i] :
( ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV78 ) ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(1032,plain,
! [SV2: $i,SV79: $i] :
( ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(1033,plain,
! [SV3: $i,SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV80 ) ) @ ( relation_rng @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1034,plain,
! [SV4: $i,SV81: $i] :
( ( ( ~ ( relation @ SV81 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV81 ) )
= ( set_intersection2 @ ( relation_rng @ SV81 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(1035,plain,
! [SV82: $i,SV5: $i,SV108: $i] :
( ( ~ ( relation @ SV108 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV108 ) @ SV82 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV108 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1036,plain,
! [SV6: $i,SV83: $i] :
( ( ( ~ ( relation @ SV83 ) )
= $true )
| ( ( subset @ ( relation_image @ SV83 @ SV6 ) @ ( relation_rng @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1037,plain,
! [SV7: $i,SV84: $i] :
( ( ( ~ ( function @ SV84 )
| ~ ( relation @ SV84 ) )
= $true )
| ( ( subset @ ( relation_image @ SV84 @ ( relation_inverse_image @ SV84 @ SV7 ) ) @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1038,plain,
! [SV8: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ( relation_image @ SV85 @ SV8 )
= ( relation_image @ SV85 @ ( set_intersection2 @ ( relation_dom @ SV85 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1039,plain,
! [SV9: $i,SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( subset @ SV9 @ ( relation_dom @ SV86 ) )
| ( subset @ SV9 @ ( relation_inverse_image @ SV86 @ ( relation_image @ SV86 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1040,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ( relation_image @ SV10 @ ( relation_dom @ SV10 ) )
= ( relation_rng @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(1041,plain,
! [SV11: $i,SV87: $i] :
( ( ( ~ ( function @ SV87 )
| ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) )
| ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1042,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ! [SY6479: $i] :
( ~ ( relation @ SY6479 )
| ( ( relation_rng @ ( relation_composition @ SV12 @ SY6479 ) )
= ( relation_image @ SY6479 @ ( relation_rng @ SV12 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1043,plain,
! [SV13: $i,SV88: $i] :
( ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV88 @ SV13 ) @ ( relation_dom @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1044,plain,
! [SV14: $i,SV89: $i] :
( ( ( ~ ( relation @ SV89 ) )
= $true )
| ( ( ( SV14 = empty_set )
| ~ ( subset @ SV14 @ ( relation_rng @ SV89 ) )
| ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1045,plain,
! [SV90: $i,SV15: $i,SV109: $i] :
( ( ~ ( relation @ SV109 )
| ~ ( subset @ SV15 @ SV90 )
| ( subset @ ( relation_inverse_image @ SV109 @ SV15 ) @ ( relation_inverse_image @ SV109 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1046,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( subset @ SV16 @ ( cartesian_product2 @ ( relation_dom @ SV16 ) @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1047,plain,
! [SV17: $i,SV91: $i] :
( ( ( ~ ( function @ SV91 )
| ~ ( relation @ SV91 ) )
= $true )
| ( ( ! [SY6706: $i] :
( ~ ( function @ SY6706 )
| ~ ( relation @ SY6706 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6706 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SY6706 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SY6706 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(1048,plain,
! [SV18: $i,SV92: $i] :
( ( ( ~ ( function @ SV92 )
| ~ ( relation @ SV92 ) )
= $true )
| ( ( ! [SY6707: $i] :
( ~ ( function @ SY6707 )
| ~ ( relation @ SY6707 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SY6707 ) @ SV18 )
= ( apply @ SY6707 @ ( apply @ SV92 @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1049,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ! [SY6488: $i] :
( ~ ( relation @ SY6488 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SY6488 ) ) @ ( relation_dom @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1050,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ! [SY6489: $i] :
( ~ ( relation @ SY6489 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SY6489 ) ) @ ( relation_rng @ SY6489 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(1051,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ! [SY6490: $i] :
( ~ ( relation @ SY6490 )
| ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SY6490 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SY6490 ) )
= ( relation_dom @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(1052,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ! [SY6491: $i] :
( ~ ( relation @ SY6491 )
| ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SY6491 ) )
| ( ( relation_rng @ ( relation_composition @ SY6491 @ SV22 ) )
= ( relation_rng @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1053,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK63_B @ SV23 ) @ ( sK64_SY6461 @ SV23 ) ) @ SV23 )
| ( SV23 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(1054,plain,
! [SV24: $i] :
( ( ( ~ ( function @ SV24 ) )
= $true )
| ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( one_to_one @ SV24 )
| ( one_to_one @ ( function_inverse @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(1055,plain,
! [SV25: $i,SV93: $i,SV110: $i] :
( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 )
| ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1056,plain,
! [SV26: $i,SV94: $i,SV111: $i] :
( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 )
| ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1057,plain,
! [SV27: $i,SV95: $i] :
( ( ( ~ ( relation @ SV95 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV95 @ SV27 ) @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1058,plain,
! [SV28: $i,SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV96 @ SV28 ) )
= ( set_intersection2 @ ( relation_dom @ SV96 ) @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(1059,plain,
! [SV29: $i,SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV97 @ SV29 )
= ( relation_composition @ ( identity_relation @ SV29 ) @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(1060,plain,
! [SV30: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV98 @ SV30 ) ) @ ( relation_rng @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1061,plain,
! [SV31: $i] :
( ( ( empty @ SV31 )
= $false )
| ( ( relation @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1062,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ( relation_field @ SV32 )
= ( set_union2 @ ( relation_dom @ SV32 ) @ ( relation_rng @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1063,plain,
! [SV33: $i] :
( ( ( ~ ( function @ SV33 ) )
= $true )
| ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( one_to_one @ SV33 )
| ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1064,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( relation @ ( relation_inverse @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1065,plain,
! [SV99: $i,SV35: $i] :
( ( ( ~ ( relation @ SV35 )
| ~ ( relation @ SV99 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV35 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1066,plain,
! [SV37: $i] :
( ( ( relation @ SV37 )
= $false )
| ( ( ! [SY6501: $i] : ( relation @ ( relation_dom_restriction @ SV37 @ SY6501 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1067,plain,
! [SV38: $i,SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV38 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(1068,plain,
! [SV101: $i,SV39: $i] :
( ( ( ~ ( relation @ SV39 )
| ~ ( relation @ SV101 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV39 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(1069,plain,
! [SV102: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 )
| ~ ( relation @ SV102 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV40 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1070,plain,
! [SV103: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 )
| ~ ( relation @ SV103 ) )
= $true )
| ( ( relation @ ( set_difference @ SV41 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1071,plain,
! [SV42: $i] :
( ( ( empty @ SV42 )
= $true )
| ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1072,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
= $true )
| ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1073,plain,
! [SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV44 ) )
= SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1074,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ~ ( ~ ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1075,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ~ ( ~ ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) )
| ~ ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1076,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(1077,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(1078,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(1079,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(1080,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ! [SY6710: $i,SY6711: $i] :
( ~ ( relation @ SY6711 )
| ~ ( in @ SV47 @ SY6710 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6711 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6710 ) @ SY6711 ) ) )
| ~ ~ ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) )
| ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(1081,plain,
! [SV48: $i] :
( ( ~ ! [SY6523: $i,SY6524: $i] :
( ~ ( relation @ SY6524 )
| ~ ( in @ SV48 @ SY6523 )
| ~ ( in @ SV48 @ ( relation_dom @ SY6524 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6524 @ SY6523 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(1082,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) )
| ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(1083,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(1084,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)],[919]) ).
thf(1085,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(1086,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(1087,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(1088,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(1089,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(1090,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(1091,plain,
! [SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( ! [SY6529: $i] :
( ~ ( relation @ SY6529 )
| ~ ( ~ ! [SY6530: $i] :
( ~ ( relation @ SY6530 )
| ~ ( ~ ( ! [SY6531: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ SY6531 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6531 @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6529 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6530 @ SY6529 @ SV49 ) @ ( sK15_SY6430 @ SY6530 @ SY6529 @ SV49 ) ) @ SY6530 ) ) )
| ( SY6530
= ( relation_composition @ SV49 @ SY6529 ) ) )
| ~ ! [SY6532: $i] :
( ~ ( relation @ SY6532 )
| ( SY6532
!= ( relation_composition @ SV49 @ SY6529 ) )
| ~ ( ~ ! [SY6533: $i,SY6534: $i] :
( ! [SY6535: $i] :
( ~ ( in @ ( ordered_pair @ SY6533 @ SY6535 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6535 @ SY6534 ) @ SY6529 ) )
| ( in @ ( ordered_pair @ SY6533 @ SY6534 ) @ SY6532 ) )
| ~ ! [SY6536: $i,SY6537: $i] :
( ~ ( in @ ( ordered_pair @ SY6536 @ SY6537 ) @ SY6532 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6536 @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6537 @ SY6536 @ SY6532 @ SY6529 @ SV49 ) @ SY6537 ) @ SY6529 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1092,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(1093,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(1094,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1095,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1096,plain,
! [SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( ~ ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) )
| ~ ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1097,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(1098,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(1099,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(1100,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(1101,plain,
! [SV51: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1102,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(1103,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(1104,plain,
! [SV52: $i,SV106: $i] :
( ( ( ~ ( relation @ SV106 ) )
= $true )
| ( ( ~ ( ~ ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
| ~ ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1105,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(1106,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1107,plain,
! [SV53: $i] :
( ( ( ~ ( function @ SV53 ) )
= $true )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1108,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1109,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(1110,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1111,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1112,plain,
! [SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( ~ ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) )
| ~ ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1113,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1114,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1115,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1116,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)],[951]) ).
thf(1117,plain,
! [SV55: $i] :
( ( ~ ! [SY6567: $i,SY6568: $i] :
( ~ ( relation @ SY6568 )
| ~ ( in @ SV55 @ SY6567 )
| ~ ( in @ SV55 @ ( relation_rng @ SY6568 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6567 @ SY6568 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1118,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) )
| ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1119,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1120,plain,
( ( relation_empty_yielding @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1121,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1122,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1123,plain,
( ( ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(1124,plain,
( ( function @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1126,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1127,plain,
! [SV56: $i] :
( ( ( ~ ( function @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( one_to_one @ SV56 )
| ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1128,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1129,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1130,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ~ ( ~ ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) )
| ~ ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1131,plain,
! [SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ~ ( ~ ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) )
| ~ ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1132,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1133,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)],[967]) ).
thf(1134,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( ~ ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) )
| ~ ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1135,plain,
! [SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( ~ ( ~ ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) )
| ~ ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1136,plain,
( ( ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1137,plain,
( ( one_to_one @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1138,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1139,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)],[973]) ).
thf(1140,plain,
! [SV61: $i] :
( ( ~ ! [SY6612: $i,SY6613: $i] :
( ~ ( function @ SY6613 )
| ~ ( relation @ SY6613 )
| ( SY6612
!= ( apply @ SY6613 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SY6613 ) )
| ( in @ ( ordered_pair @ SV61 @ SY6612 ) @ SY6613 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1141,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) )
| ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1142,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1143,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1144,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(1145,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1146,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1147,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1148,plain,
! [SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( ~ ( ~ ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) )
| ~ ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1149,plain,
! [SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( ~ ( ~ ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) )
| ~ ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1150,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1152,plain,
! [SV64: $i] :
( ( ~ ! [SY6628: $i,SY6629: $i] :
( ~ ( relation @ SY6629 )
| ! [SY6630: $i] :
( ~ ( in @ SY6630 @ ( relation_rng @ SY6629 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6630 ) @ SY6629 )
| ~ ( in @ SY6630 @ SY6628 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SY6629 @ SY6628 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1153,plain,
! [SV64: $i] :
( ( ~ ! [SY6631: $i,SY6632: $i] :
( ~ ( relation @ SY6632 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SY6632 @ SY6631 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ ( relation_rng @ SY6632 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) ) @ SY6632 ) )
| ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ SY6631 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1154,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1155,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1156,plain,
! [SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ~ ( ~ ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1157,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1158,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1159,plain,
! [SV66: $i] :
( ( ~ ! [SY6639: $i,SY6640: $i] :
( ~ ( relation @ SY6640 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6639 ) @ SY6640 )
| ( in @ SV66 @ ( relation_field @ SY6640 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1160,plain,
! [SV66: $i] :
( ( ~ ! [SY6641: $i,SY6642: $i] :
( ~ ( relation @ SY6642 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6641 ) @ SY6642 )
| ( in @ SY6641 @ ( relation_field @ SY6642 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1161,plain,
! [SV67: $i] :
( ( ( relation @ SV67 )
= $false )
| ( ( ~ ( ~ ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) )
| ~ ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1162,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1163,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1164,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1166,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1167,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1168,plain,
! [SV68: $i] :
( ( ~ ! [SY6646: $i,SY6647: $i] :
( ~ ( relation @ SY6647 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6646 ) @ SY6647 )
| ( in @ SV68 @ ( relation_dom @ SY6647 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1169,plain,
! [SV68: $i] :
( ( ~ ! [SY6648: $i,SY6649: $i] :
( ~ ( relation @ SY6649 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6648 ) @ SY6649 )
| ( in @ SY6648 @ ( relation_rng @ SY6649 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1170,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1171,plain,
( ( ordinal @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1172,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1173,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1174,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1175,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1176,plain,
! [SV69: $i] :
( ( ~ ! [SY6650: $i,SY6651: $i] :
( ~ ( relation @ SY6651 )
| ! [SY6652: $i] :
( ~ ( in @ SY6652 @ ( relation_dom @ SY6651 ) )
| ~ ( in @ ( ordered_pair @ SY6652 @ SV69 ) @ SY6651 )
| ~ ( in @ SY6652 @ SY6650 ) )
| ( in @ SV69 @ ( relation_image @ SY6651 @ SY6650 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1177,plain,
! [SV69: $i] :
( ( ~ ! [SY6653: $i,SY6654: $i] :
( ~ ( relation @ SY6654 )
| ~ ( in @ SV69 @ ( relation_image @ SY6654 @ SY6653 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ ( relation_dom @ SY6654 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SV69 ) @ SY6654 ) )
| ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SY6653 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1006]) ).
thf(1178,plain,
! [SV70: $i] :
( ( ( relation @ SV70 )
= $false )
| ( ( ~ ( ~ ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) )
| ~ ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1179,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1180,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1181,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1182,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1183,plain,
! [SV71: $i] :
( ( ~ ! [SY6663: $i,SY6664: $i] :
( ~ ( function @ SY6664 )
| ~ ( relation @ SY6664 )
| ~ ( in @ SY6663 @ ( relation_dom @ SY6664 ) )
| ~ ( in @ SY6663 @ SV71 )
| ( in @ SY6663 @ ( relation_dom @ ( relation_dom_restriction @ SY6664 @ SV71 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1184,plain,
! [SV71: $i] :
( ( ~ ~ ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) )
| ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1012]) ).
thf(1185,plain,
! [SV72: $i] :
( ( ( ~ ( function @ SV72 ) )
= $true )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1186,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ( function @ SV107 )
| ~ ( relation @ SV107 ) )
= $true )
| ( ( ~ ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1187,plain,
! [SV74: $i] :
( ( ( ~ ( function @ SV74 ) )
= $true )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1188,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1189,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1190,plain,
! [SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( ~ ( ~ ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) )
| ~ ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1191,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1192,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)],[1020]) ).
thf(1193,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1194,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1195,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ~ ( ~ ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) )
| ~ ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1196,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1197,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1198,plain,
( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1199,plain,
( ( ~ ( well_ordering @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1200,plain,
! [SV77: $i] :
( ( ( ~ ( function @ SV77 ) )
= $true )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1201,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1202,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1203,plain,
! [SV1: $i,SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV1 @ SV78 ) ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1204,plain,
! [SV2: $i,SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV2 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1205,plain,
! [SV3: $i,SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV3 @ SV80 ) ) @ ( relation_rng @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1206,plain,
! [SV4: $i,SV81: $i] :
( ( ( relation @ SV81 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV81 ) )
= ( set_intersection2 @ ( relation_rng @ SV81 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1207,plain,
! [SV82: $i,SV5: $i,SV108: $i] :
( ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV108 ) @ SV82 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV108 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1208,plain,
! [SV6: $i,SV83: $i] :
( ( ( relation @ SV83 )
= $false )
| ( ( subset @ ( relation_image @ SV83 @ SV6 ) @ ( relation_rng @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1209,plain,
! [SV7: $i,SV84: $i] :
( ( ( ~ ( function @ SV84 ) )
= $true )
| ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( subset @ ( relation_image @ SV84 @ ( relation_inverse_image @ SV84 @ SV7 ) ) @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1210,plain,
! [SV8: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( ( relation_image @ SV85 @ SV8 )
= ( relation_image @ SV85 @ ( set_intersection2 @ ( relation_dom @ SV85 ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1211,plain,
! [SV9: $i,SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ~ ( subset @ SV9 @ ( relation_dom @ SV86 ) )
| ( subset @ SV9 @ ( relation_inverse_image @ SV86 @ ( relation_image @ SV86 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1212,plain,
! [SV11: $i,SV87: $i] :
( ( ( ~ ( function @ SV87 ) )
= $true )
| ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) )
| ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1213,plain,
! [SV12: $i,SV112: $i] :
( ( ( ~ ( relation @ SV112 )
| ( ( relation_rng @ ( relation_composition @ SV12 @ SV112 ) )
= ( relation_image @ SV112 @ ( relation_rng @ SV12 ) ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1214,plain,
! [SV13: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV88 @ SV13 ) @ ( relation_dom @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1215,plain,
! [SV14: $i,SV89: $i] :
( ( ( relation @ SV89 )
= $false )
| ( ( ( SV14 = empty_set )
| ~ ( subset @ SV14 @ ( relation_rng @ SV89 ) )
| ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1216,plain,
! [SV90: $i,SV15: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( ~ ( subset @ SV15 @ SV90 )
| ( subset @ ( relation_inverse_image @ SV109 @ SV15 ) @ ( relation_inverse_image @ SV109 @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1217,plain,
! [SV17: $i,SV91: $i] :
( ( ( ~ ( function @ SV91 ) )
= $true )
| ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ! [SY6706: $i] :
( ~ ( function @ SY6706 )
| ~ ( relation @ SY6706 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6706 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SY6706 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SY6706 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1218,plain,
! [SV18: $i,SV92: $i] :
( ( ( ~ ( function @ SV92 ) )
= $true )
| ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ! [SY6707: $i] :
( ~ ( function @ SY6707 )
| ~ ( relation @ SY6707 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SY6707 ) @ SV18 )
= ( apply @ SY6707 @ ( apply @ SV92 @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1219,plain,
! [SV19: $i,SV113: $i] :
( ( ( ~ ( relation @ SV113 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SV113 ) ) @ ( relation_dom @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1220,plain,
! [SV20: $i,SV114: $i] :
( ( ( ~ ( relation @ SV114 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SV114 ) ) @ ( relation_rng @ SV114 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1221,plain,
! [SV21: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 )
| ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SV115 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SV115 ) )
= ( relation_dom @ SV21 ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1222,plain,
! [SV22: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 )
| ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV116 ) )
| ( ( relation_rng @ ( relation_composition @ SV116 @ SV22 ) )
= ( relation_rng @ SV22 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1223,plain,
! [SV23: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_B @ SV23 ) @ ( sK64_SY6461 @ SV23 ) ) @ SV23 )
= $true )
| ( ( SV23 = empty_set )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1224,plain,
! [SV24: $i] :
( ( ( function @ SV24 )
= $false )
| ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( one_to_one @ SV24 )
| ( one_to_one @ ( function_inverse @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1225,plain,
! [SV25: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 )
| ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1226,plain,
! [SV26: $i,SV94: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 )
| ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1227,plain,
! [SV27: $i,SV95: $i] :
( ( ( relation @ SV95 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV95 @ SV27 ) @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1228,plain,
! [SV28: $i,SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV96 @ SV28 ) )
= ( set_intersection2 @ ( relation_dom @ SV96 ) @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1229,plain,
! [SV29: $i,SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ( relation_dom_restriction @ SV97 @ SV29 )
= ( relation_composition @ ( identity_relation @ SV29 ) @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1230,plain,
! [SV30: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV98 @ SV30 ) ) @ ( relation_rng @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1231,plain,
! [SV33: $i] :
( ( ( function @ SV33 )
= $false )
| ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( one_to_one @ SV33 )
| ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1232,plain,
! [SV99: $i,SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV35 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1233,plain,
! [SV117: $i,SV37: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV37 @ SV117 ) )
= $true )
| ( ( relation @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1234,plain,
! [SV38: $i,SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV38 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1235,plain,
! [SV101: $i,SV39: $i] :
( ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV39 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1236,plain,
! [SV102: $i,SV40: $i] :
( ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV40 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1237,plain,
! [SV103: $i,SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( relation @ ( set_difference @ SV41 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1238,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( empty @ SV42 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1239,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( empty @ SV43 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1240,plain,
! [SV45: $i] :
( ( ( ~ ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) )
| ~ ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1241,plain,
! [SV46: $i] :
( ( ( ~ ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) )
| ~ ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1242,plain,
! [SV118: $i] :
( ( ~ ( relation @ SV118 )
| ~ ( relation_empty_yielding @ SV118 )
| ! [SY6731: $i] : ( relation @ ( relation_dom_restriction @ SV118 @ SY6731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1243,plain,
! [SV119: $i] :
( ( ~ ( relation @ SV119 )
| ~ ( relation_empty_yielding @ SV119 )
| ! [SY6732: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SY6732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1244,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ! [SY6710: $i,SY6711: $i] :
( ~ ( relation @ SY6711 )
| ~ ( in @ SV47 @ SY6710 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6711 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6710 ) @ SY6711 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1245,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ~ ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) )
| ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1246,plain,
! [SV48: $i] :
( ( ! [SY6523: $i,SY6524: $i] :
( ~ ( relation @ SY6524 )
| ~ ( in @ SV48 @ SY6523 )
| ~ ( in @ SV48 @ ( relation_dom @ SY6524 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6524 @ SY6523 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1247,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) )
| ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1248,plain,
! [SV120: $i] :
( ( ~ ( relation @ SV120 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
| ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) )
| ( antisymmetric @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1249,plain,
! [SV121: $i] :
( ( ~ ( relation @ SV121 )
| ~ ( antisymmetric @ SV121 )
| ! [SY6733: $i,SY6734: $i] :
( ~ ( in @ ( ordered_pair @ SY6733 @ SY6734 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6734 @ SY6733 ) @ SV121 )
| ( SY6733 = SY6734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1250,plain,
! [SV122: $i] :
( ( ~ ( relation @ SV122 )
| ~ ( connected @ SV122 )
| ( is_connected_in @ SV122 @ ( relation_field @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1251,plain,
! [SV123: $i] :
( ( ~ ( relation @ SV123 )
| ~ ( is_connected_in @ SV123 @ ( relation_field @ SV123 ) )
| ( connected @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1252,plain,
! [SV124: $i] :
( ( ~ ( relation @ SV124 )
| ~ ( is_transitive_in @ SV124 @ ( relation_field @ SV124 ) )
| ( transitive @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1253,plain,
! [SV125: $i] :
( ( ~ ( relation @ SV125 )
| ~ ( transitive @ SV125 )
| ( is_transitive_in @ SV125 @ ( relation_field @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1254,plain,
! [SV49: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 )
| ~ ( ~ ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) )
| ~ ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1255,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1256,plain,
! [SV127: $i] :
( ( function @ ( identity_relation @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1257,plain,
! [SV128: $i] :
( ( relation @ ( identity_relation @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1258,plain,
! [SV50: $i] :
( ( ( ~ ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) )
| ~ ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1259,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1260,plain,
! [SV129: $i] :
( ( ~ ( relation @ SV129 )
| ~ ( is_reflexive_in @ SV129 @ ( relation_field @ SV129 ) )
| ( reflexive @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1261,plain,
! [SV130: $i] :
( ( ~ ( relation @ SV130 )
| ~ ( reflexive @ SV130 )
| ( is_reflexive_in @ SV130 @ ( relation_field @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1262,plain,
! [SV51: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 ) )
= $true )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1263,plain,
! [SV131: $i] :
( ( ~ ( relation @ SV131 )
| ~ ( antisymmetric @ SV131 )
| ( is_antisymmetric_in @ SV131 @ ( relation_field @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1264,plain,
! [SV132: $i] :
( ( ~ ( relation @ SV132 )
| ~ ( is_antisymmetric_in @ SV132 @ ( relation_field @ SV132 ) )
| ( antisymmetric @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1265,plain,
! [SV52: $i,SV106: $i] :
( ( ( relation @ SV106 )
= $false )
| ( ( ~ ( ~ ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
| ~ ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1266,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1267,plain,
! [SV133: $i] :
( ( ~ ( empty @ SV133 )
| ~ ( relation @ SV133 )
| ~ ( function @ SV133 )
| ( one_to_one @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1268,plain,
! [SV53: $i] :
( ( ( function @ SV53 )
= $false )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1269,plain,
! [SV134: $i] :
( ( ~ ( empty @ SV134 )
| ( empty @ ( relation_rng @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1270,plain,
! [SV135: $i] :
( ( ~ ( empty @ SV135 )
| ( relation @ ( relation_rng @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1271,plain,
! [SV136: $i] :
( ( ~ ( relation @ SV136 )
| ( ( relation_dom @ SV136 )
!= empty_set )
| ( SV136 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1272,plain,
! [SV137: $i] :
( ( ~ ( relation @ SV137 )
| ( ( relation_rng @ SV137 )
!= empty_set )
| ( SV137 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1273,plain,
! [SV54: $i] :
( ( ( ~ ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) )
| ~ ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1274,plain,
! [SV138: $i] :
( ( ~ ( relation @ SV138 )
| ~ ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
| ( reflexive @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1275,plain,
! [SV139: $i] :
( ( ~ ( relation @ SV139 )
| ~ ( reflexive @ SV139 )
| ! [SY6743: $i] :
( ~ ( in @ SY6743 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SY6743 @ SY6743 ) @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1276,plain,
! [SV55: $i] :
( ( ! [SY6567: $i,SY6568: $i] :
( ~ ( relation @ SY6568 )
| ~ ( in @ SV55 @ SY6567 )
| ~ ( in @ SV55 @ ( relation_rng @ SY6568 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6567 @ SY6568 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1277,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) )
| ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1278,plain,
! [SV140: $i] :
( ( ~ ( relation @ SV140 )
| ( ( relation_dom @ SV140 )
!= empty_set )
| ( ( relation_rng @ SV140 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1279,plain,
! [SV141: $i] :
( ( ~ ( relation @ SV141 )
| ( ( relation_rng @ SV141 )
!= empty_set )
| ( ( relation_dom @ SV141 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1280,plain,
( ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1281,plain,
! [SV142: $i] :
( ( ! [SY6744: $i] :
( ~ ( function @ SY6744 )
| ~ ( relation @ SY6744 )
| ~ ( ~ ( in @ ( sK67_C @ SY6744 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SY6744 @ ( sK67_C @ SY6744 @ SV142 ) )
!= ( sK67_C @ SY6744 @ SV142 ) ) ) )
| ( ( relation_dom @ SY6744 )
!= SV142 )
| ( SY6744
= ( identity_relation @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1282,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1283,plain,
! [SV56: $i] :
( ( ( function @ SV56 )
= $false )
| ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( one_to_one @ SV56 )
| ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1284,plain,
! [SV143: $i] :
( ( ~ ( relation @ SV143 )
| ~ ( is_well_founded_in @ SV143 @ ( relation_field @ SV143 ) )
| ( well_founded_relation @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1285,plain,
! [SV144: $i] :
( ( ~ ( relation @ SV144 )
| ~ ( well_founded_relation @ SV144 )
| ( is_well_founded_in @ SV144 @ ( relation_field @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1286,plain,
! [SV57: $i] :
( ( ( ~ ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) )
| ~ ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1287,plain,
! [SV58: $i] :
( ( ( ~ ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) )
| ~ ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1288,plain,
! [SV145: $i] :
( ( ~ ( relation @ SV145 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ( transitive @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1289,plain,
! [SV146: $i] :
( ( ~ ( relation @ SV146 )
| ~ ( transitive @ SV146 )
| ! [SY6745: $i,SY6746: $i,SY6747: $i] :
( ~ ( in @ ( ordered_pair @ SY6745 @ SY6746 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6746 @ SY6747 ) @ SV146 )
| ( in @ ( ordered_pair @ SY6745 @ SY6747 ) @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1290,plain,
! [SV59: $i] :
( ( ( ~ ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) )
| ~ ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1291,plain,
! [SV60: $i] :
( ( ( ~ ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) )
| ~ ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1292,plain,
( ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1293,plain,
! [SV147: $i] :
( ( ! [SY6748: $i] :
( ~ ( relation @ SY6748 )
| ~ ( ~ ( ( ( sK60_C @ SY6748 @ SV147 )
!= ( sK61_SY6460 @ SY6748 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SY6748 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SY6748 @ SV147 ) @ ( sK61_SY6460 @ SY6748 @ SV147 ) ) @ SY6748 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SY6748 @ SV147 )
= ( sK61_SY6460 @ SY6748 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SY6748 @ SV147 ) @ ( sK61_SY6460 @ SY6748 @ SV147 ) ) @ SY6748 ) )
| ~ ( ( in @ ( sK60_C @ SY6748 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SY6748 @ SV147 ) @ ( sK61_SY6460 @ SY6748 @ SV147 ) ) @ SY6748 ) ) ) )
| ( SY6748
= ( identity_relation @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1294,plain,
! [SV148: $i] :
( ( ! [SY6749: $i] :
( ~ ( relation @ SY6749 )
| ( SY6749
!= ( identity_relation @ SV148 ) )
| ~ ( ~ ! [SY6750: $i,SY6751: $i] :
( ( SY6750 != SY6751 )
| ~ ( in @ SY6750 @ SV148 )
| ( in @ ( ordered_pair @ SY6750 @ SY6751 ) @ SY6749 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY6749 )
| ( SX2 = SX3 ) )
| ~ ! [SY6754: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY6754 @ SX3 ) @ SY6749 )
| ( in @ SY6754 @ SV148 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1295,plain,
! [SV61: $i] :
( ( ! [SY6612: $i,SY6613: $i] :
( ~ ( function @ SY6613 )
| ~ ( relation @ SY6613 )
| ( SY6612
!= ( apply @ SY6613 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SY6613 ) )
| ( in @ ( ordered_pair @ SV61 @ SY6612 ) @ SY6613 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1296,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) )
| ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1297,plain,
! [SV149: $i] :
( ( ~ ( empty @ SV149 )
| ( empty @ ( relation_inverse @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1298,plain,
! [SV150: $i] :
( ( ~ ( empty @ SV150 )
| ( relation @ ( relation_inverse @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1299,plain,
! [SV151: $i] :
( ( ! [SY6756: $i] :
( ~ ( function @ SY6756 )
| ~ ( relation @ SY6756 )
| ~ ( in @ SV151 @ ( relation_rng @ SY6756 ) )
| ~ ( one_to_one @ SY6756 )
| ( SV151
= ( apply @ SY6756 @ ( apply @ ( function_inverse @ SY6756 ) @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1300,plain,
! [SV152: $i] :
( ( ! [SY6757: $i] :
( ~ ( function @ SY6757 )
| ~ ( relation @ SY6757 )
| ~ ( in @ SV152 @ ( relation_rng @ SY6757 ) )
| ~ ( one_to_one @ SY6757 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SY6757 ) @ SY6757 ) @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1301,plain,
! [SV153: $i] :
( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 )
| ~ ( one_to_one @ SV153 )
| ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1302,plain,
! [SV154: $i] :
( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 )
| ~ ( one_to_one @ SV154 )
| ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1303,plain,
! [SV62: $i] :
( ( ( ~ ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) )
| ~ ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1304,plain,
! [SV63: $i] :
( ( ( ~ ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) )
| ~ ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1305,plain,
! [SV155: $i] :
( ( ! [SY6758: $i] :
( ~ ( empty @ SV155 )
| ~ ( relation @ SY6758 )
| ( empty @ ( relation_composition @ SV155 @ SY6758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1306,plain,
! [SV156: $i] :
( ( ! [SY6759: $i] :
( ~ ( empty @ SV156 )
| ~ ( relation @ SY6759 )
| ( relation @ ( relation_composition @ SV156 @ SY6759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1307,plain,
! [SV64: $i] :
( ( ! [SY6628: $i,SY6629: $i] :
( ~ ( relation @ SY6629 )
| ! [SY6630: $i] :
( ~ ( in @ SY6630 @ ( relation_rng @ SY6629 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6630 ) @ SY6629 )
| ~ ( in @ SY6630 @ SY6628 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SY6629 @ SY6628 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1308,plain,
! [SV64: $i] :
( ( ! [SY6631: $i,SY6632: $i] :
( ~ ( relation @ SY6632 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SY6632 @ SY6631 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ ( relation_rng @ SY6632 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) ) @ SY6632 ) )
| ~ ( in @ ( sK68_D @ SY6632 @ SY6631 @ SV64 ) @ SY6631 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1309,plain,
! [SV157: $i] :
( ( ~ ( relation @ SV157 )
| ~ ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
| ( well_founded_relation @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1310,plain,
! [SV158: $i] :
( ( ~ ( relation @ SV158 )
| ~ ( well_founded_relation @ SV158 )
| ! [SY6761: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SY6761 @ SV158 ) ) @ SY6761 )
| ~ ( in @ ( sK38_C @ SY6761 @ SV158 ) @ SY6761 ) )
| ( SY6761 = empty_set )
| ~ ( subset @ SY6761 @ ( relation_field @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1311,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1312,plain,
! [SV159: $i] :
( ( ~ ( empty @ SV159 )
| ( empty @ ( relation_dom @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1313,plain,
! [SV160: $i] :
( ( ~ ( empty @ SV160 )
| ( relation @ ( relation_dom @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1314,plain,
! [SV66: $i] :
( ( ! [SY6639: $i,SY6640: $i] :
( ~ ( relation @ SY6640 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6639 ) @ SY6640 )
| ( in @ SV66 @ ( relation_field @ SY6640 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1315,plain,
! [SV66: $i] :
( ( ! [SY6641: $i,SY6642: $i] :
( ~ ( relation @ SY6642 )
| ~ ( in @ ( ordered_pair @ SV66 @ SY6641 ) @ SY6642 )
| ( in @ SY6641 @ ( relation_field @ SY6642 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1316,plain,
! [SV67: $i] :
( ( ( ~ ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) )
| ~ ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1317,plain,
! [SV161: $i] :
( ( ~ ( function @ SV161 )
| ~ ( relation @ SV161 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
| ( one_to_one @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1318,plain,
! [SV162: $i] :
( ( ~ ( function @ SV162 )
| ~ ( relation @ SV162 )
| ~ ( one_to_one @ SV162 )
| ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1319,plain,
! [SV163: $i] :
( ( ! [SY6764: $i] :
( ~ ( function @ SV163 )
| ~ ( relation @ SV163 )
| ~ ( relation @ SY6764 )
| ~ ( function @ SY6764 )
| ( function @ ( relation_composition @ SV163 @ SY6764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1320,plain,
! [SV164: $i] :
( ( ! [SY6765: $i] :
( ~ ( function @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( relation @ SY6765 )
| ~ ( function @ SY6765 )
| ( relation @ ( relation_composition @ SV164 @ SY6765 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1321,plain,
! [SV165: $i] :
( ( ~ ( ~ ! [SY6766: $i,SY6767: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SY6766 @ SY6767 ) )
| ~ ( in @ ( sK45_B @ SV165 ) @ SV165 ) )
| ( relation @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1322,plain,
! [SV166: $i] :
( ( ~ ( relation @ SV166 )
| ! [SY6768: $i] :
( ( SY6768
= ( ordered_pair @ ( sK43_C @ SY6768 @ SV166 ) @ ( sK44_SY6449 @ SY6768 @ SV166 ) ) )
| ~ ( in @ SY6768 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1323,plain,
! [SV68: $i] :
( ( ! [SY6646: $i,SY6647: $i] :
( ~ ( relation @ SY6647 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6646 ) @ SY6647 )
| ( in @ SV68 @ ( relation_dom @ SY6647 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1324,plain,
! [SV68: $i] :
( ( ! [SY6648: $i,SY6649: $i] :
( ~ ( relation @ SY6649 )
| ~ ( in @ ( ordered_pair @ SV68 @ SY6648 ) @ SY6649 )
| ( in @ SY6648 @ ( relation_rng @ SY6649 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1325,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1326,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1327,plain,
! [SV167: $i] :
( ( ~ ( function @ SV167 )
| ~ ( relation @ SV167 )
| ~ ( one_to_one @ SV167 )
| ( function @ ( relation_inverse @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1328,plain,
! [SV168: $i] :
( ( ~ ( function @ SV168 )
| ~ ( relation @ SV168 )
| ~ ( one_to_one @ SV168 )
| ( relation @ ( relation_inverse @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1329,plain,
! [SV69: $i] :
( ( ! [SY6650: $i,SY6651: $i] :
( ~ ( relation @ SY6651 )
| ! [SY6652: $i] :
( ~ ( in @ SY6652 @ ( relation_dom @ SY6651 ) )
| ~ ( in @ ( ordered_pair @ SY6652 @ SV69 ) @ SY6651 )
| ~ ( in @ SY6652 @ SY6650 ) )
| ( in @ SV69 @ ( relation_image @ SY6651 @ SY6650 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1330,plain,
! [SV69: $i] :
( ( ! [SY6653: $i,SY6654: $i] :
( ~ ( relation @ SY6654 )
| ~ ( in @ SV69 @ ( relation_image @ SY6654 @ SY6653 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ ( relation_dom @ SY6654 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SV69 ) @ SY6654 ) )
| ~ ( in @ ( sK69_D @ SY6654 @ SY6653 @ SV69 ) @ SY6653 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1331,plain,
! [SV70: $i] :
( ( ( ~ ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) )
| ~ ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1332,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1333,plain,
! [SV169: $i] :
( ( ~ ( relation @ SV169 )
| ( ( relation_rng @ SV169 )
= ( relation_dom @ ( relation_inverse @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1334,plain,
! [SV170: $i] :
( ( ~ ( relation @ SV170 )
| ( ( relation_dom @ SV170 )
= ( relation_rng @ ( relation_inverse @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1335,plain,
! [SV71: $i] :
( ( ! [SY6663: $i,SY6664: $i] :
( ~ ( function @ SY6664 )
| ~ ( relation @ SY6664 )
| ~ ( in @ SY6663 @ ( relation_dom @ SY6664 ) )
| ~ ( in @ SY6663 @ SV71 )
| ( in @ SY6663 @ ( relation_dom @ ( relation_dom_restriction @ SY6664 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1336,plain,
! [SV71: $i] :
( ( ~ ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) )
| ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1337,plain,
! [SV72: $i] :
( ( ( function @ SV72 )
= $false )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ~ ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1338,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ( function @ SV107 ) )
= $true )
| ( ( ~ ( relation @ SV107 ) )
= $true )
| ( ( ~ ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1339,plain,
! [SV74: $i] :
( ( ( function @ SV74 )
= $false )
| ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1340,plain,
! [SV171: $i] :
( ( ~ ( function @ SV171 )
| ~ ( relation @ SV171 )
| ! [SY6769: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY6769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1341,plain,
! [SV172: $i] :
( ( ~ ( function @ SV172 )
| ~ ( relation @ SV172 )
| ! [SY6770: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY6770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1342,plain,
! [SV75: $i] :
( ( ( ~ ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) )
| ~ ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1343,plain,
! [SV173: $i] :
( ( ~ ( relation @ SV173 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
| ( connected @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1344,plain,
! [SV174: $i] :
( ( ~ ( relation @ SV174 )
| ~ ( connected @ SV174 )
| ! [SY6771: $i,SY6772: $i] :
( ( SY6771 = SY6772 )
| ~ ( in @ SY6771 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6772 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SY6771 @ SY6772 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6772 @ SY6771 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1345,plain,
! [SV175: $i] :
( ( ! [SY6773: $i] :
( ~ ( empty @ SV175 )
| ~ ( relation @ SY6773 )
| ( empty @ ( relation_composition @ SY6773 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1346,plain,
! [SV176: $i] :
( ( ! [SY6774: $i] :
( ~ ( empty @ SV176 )
| ~ ( relation @ SY6774 )
| ( relation @ ( relation_composition @ SY6774 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1347,plain,
! [SV76: $i] :
( ( ( ~ ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) )
| ~ ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1348,plain,
! [SV177: $i] :
( ( ~ ( function @ SV177 )
| ~ ( relation @ SV177 )
| ( function @ ( function_inverse @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1349,plain,
! [SV178: $i] :
( ( ~ ( function @ SV178 )
| ~ ( relation @ SV178 )
| ( relation @ ( function_inverse @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1350,plain,
( ( well_ordering @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1351,plain,
! [SV77: $i] :
( ( ( function @ SV77 )
= $false )
| ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1352,plain,
! [SV179: $i] :
( ( ~ ( relation @ SV179 )
| ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 )
| ~ ( connected @ SV179 )
| ~ ( well_founded_relation @ SV179 )
| ( well_ordering @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1353,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1354,plain,
! [SV82: $i,SV5: $i,SV108: $i] :
( ( ( relation @ SV108 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV5 @ SV108 ) @ SV82 )
= ( relation_rng_restriction @ SV5 @ ( relation_dom_restriction @ SV108 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1355,plain,
! [SV7: $i,SV84: $i] :
( ( ( function @ SV84 )
= $false )
| ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( subset @ ( relation_image @ SV84 @ ( relation_inverse_image @ SV84 @ SV7 ) ) @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1356,plain,
! [SV86: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( subset @ SV9 @ ( relation_inverse_image @ SV86 @ ( relation_image @ SV86 @ SV9 ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1357,plain,
! [SV11: $i,SV87: $i] :
( ( ( function @ SV87 )
= $false )
| ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) )
| ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1358,plain,
! [SV12: $i,SV112: $i] :
( ( ( ~ ( relation @ SV112 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV12 @ SV112 ) )
= ( relation_image @ SV112 @ ( relation_rng @ SV12 ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1359,plain,
! [SV89: $i,SV14: $i] :
( ( ( ( SV14 = empty_set )
| ~ ( subset @ SV14 @ ( relation_rng @ SV89 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1360,plain,
! [SV90: $i,SV15: $i,SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( ~ ( subset @ SV15 @ SV90 )
| ( subset @ ( relation_inverse_image @ SV109 @ SV15 ) @ ( relation_inverse_image @ SV109 @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1361,plain,
! [SV17: $i,SV91: $i] :
( ( ( function @ SV91 )
= $false )
| ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ! [SY6706: $i] :
( ~ ( function @ SY6706 )
| ~ ( relation @ SY6706 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6706 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SY6706 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SY6706 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1362,plain,
! [SV18: $i,SV92: $i] :
( ( ( function @ SV92 )
= $false )
| ( ( ~ ( relation @ SV92 ) )
= $true )
| ( ( ! [SY6707: $i] :
( ~ ( function @ SY6707 )
| ~ ( relation @ SY6707 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SY6707 ) @ SV18 )
= ( apply @ SY6707 @ ( apply @ SV92 @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1363,plain,
! [SV19: $i,SV113: $i] :
( ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SV113 ) ) @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1364,plain,
! [SV20: $i,SV114: $i] :
( ( ( ~ ( relation @ SV114 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SV114 ) ) @ ( relation_rng @ SV114 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1365,plain,
! [SV21: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SV115 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SV115 ) )
= ( relation_dom @ SV21 ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1366,plain,
! [SV22: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV116 ) )
| ( ( relation_rng @ ( relation_composition @ SV116 @ SV22 ) )
= ( relation_rng @ SV22 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1367,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( ~ ( one_to_one @ SV24 )
| ( one_to_one @ ( function_inverse @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1368,plain,
! [SV25: $i,SV93: $i,SV110: $i] :
( ( ( ~ ( function @ SV110 ) )
= $true )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1369,plain,
! [SV26: $i,SV94: $i,SV111: $i] :
( ( ( ~ ( function @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1370,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( function @ SV33 )
= $false )
| ( ( ~ ( one_to_one @ SV33 )
| ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1371,plain,
! [SV99: $i,SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV35 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1372,plain,
! [SV101: $i,SV39: $i] :
( ( ( relation @ SV39 )
= $false )
| ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV39 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1373,plain,
! [SV102: $i,SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV40 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1374,plain,
! [SV103: $i,SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( relation @ ( set_difference @ SV41 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1375,plain,
! [SV42: $i] :
( ( ( empty @ ( relation_dom @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1376,plain,
! [SV43: $i] :
( ( ( empty @ ( relation_rng @ SV43 ) )
= $false )
| ( ( empty @ SV43 )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1377,plain,
! [SV45: $i] :
( ( ( ~ ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1378,plain,
! [SV45: $i] :
( ( ( ~ ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1240]) ).
thf(1379,plain,
! [SV46: $i] :
( ( ( ~ ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) ) )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1380,plain,
! [SV46: $i] :
( ( ( ~ ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1241]) ).
thf(1381,plain,
! [SV118: $i] :
( ( ( ~ ( relation @ SV118 )
| ~ ( relation_empty_yielding @ SV118 ) )
= $true )
| ( ( ! [SY6731: $i] : ( relation @ ( relation_dom_restriction @ SV118 @ SY6731 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1382,plain,
! [SV119: $i] :
( ( ( ~ ( relation @ SV119 )
| ~ ( relation_empty_yielding @ SV119 ) )
= $true )
| ( ( ! [SY6732: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SY6732 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1383,plain,
! [SV104: $i,SV47: $i] :
( ( ! [SY6710: $i,SY6711: $i] :
( ~ ( relation @ SY6711 )
| ~ ( in @ SV47 @ SY6710 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6711 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6710 ) @ SY6711 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1384,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) )
| ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1385,plain,
! [SV180: $i,SV48: $i] :
( ( ! [SY6775: $i] :
( ~ ( relation @ SY6775 )
| ~ ( in @ SV48 @ SV180 )
| ~ ( in @ SV48 @ ( relation_dom @ SY6775 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6775 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1386,plain,
! [SV48: $i] :
( ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) )
| ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1387,plain,
! [SV120: $i] :
( ( ( ~ ( relation @ SV120 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
| ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) )
| ( antisymmetric @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1388,plain,
! [SV121: $i] :
( ( ( ~ ( relation @ SV121 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV121 )
| ! [SY6733: $i,SY6734: $i] :
( ~ ( in @ ( ordered_pair @ SY6733 @ SY6734 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6734 @ SY6733 ) @ SV121 )
| ( SY6733 = SY6734 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1389,plain,
! [SV122: $i] :
( ( ( ~ ( relation @ SV122 ) )
= $true )
| ( ( ~ ( connected @ SV122 )
| ( is_connected_in @ SV122 @ ( relation_field @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1390,plain,
! [SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV123 @ ( relation_field @ SV123 ) )
| ( connected @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1391,plain,
! [SV124: $i] :
( ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV124 @ ( relation_field @ SV124 ) )
| ( transitive @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1392,plain,
! [SV125: $i] :
( ( ( ~ ( relation @ SV125 ) )
= $true )
| ( ( ~ ( transitive @ SV125 )
| ( is_transitive_in @ SV125 @ ( relation_field @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1393,plain,
! [SV49: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 ) )
= $true )
| ( ( ~ ( ~ ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) )
| ~ ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1394,plain,
! [SV50: $i] :
( ( ( ~ ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1395,plain,
! [SV50: $i] :
( ( ( ~ ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1258]) ).
thf(1396,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1397,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1398,plain,
! [SV129: $i] :
( ( ( ~ ( relation @ SV129 ) )
= $true )
| ( ( ~ ( is_reflexive_in @ SV129 @ ( relation_field @ SV129 ) )
| ( reflexive @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1399,plain,
! [SV130: $i] :
( ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( ~ ( reflexive @ SV130 )
| ( is_reflexive_in @ SV130 @ ( relation_field @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1400,plain,
! [SV51: $i,SV105: $i] :
( ( ( function @ SV105 )
= $false )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( ~ ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1401,plain,
! [SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV131 )
| ( is_antisymmetric_in @ SV131 @ ( relation_field @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1402,plain,
! [SV132: $i] :
( ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV132 @ ( relation_field @ SV132 ) )
| ( antisymmetric @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1403,plain,
! [SV52: $i,SV106: $i] :
( ( ( ~ ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
| ~ ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1404,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1405,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1406,plain,
! [SV133: $i] :
( ( ( ~ ( empty @ SV133 )
| ~ ( relation @ SV133 )
| ~ ( function @ SV133 ) )
= $true )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1407,plain,
! [SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( ~ ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1408,plain,
! [SV134: $i] :
( ( ( ~ ( empty @ SV134 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1409,plain,
! [SV135: $i] :
( ( ( ~ ( empty @ SV135 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1410,plain,
! [SV136: $i] :
( ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( ( ( relation_dom @ SV136 )
!= empty_set )
| ( SV136 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1411,plain,
! [SV137: $i] :
( ( ( ~ ( relation @ SV137 ) )
= $true )
| ( ( ( ( relation_rng @ SV137 )
!= empty_set )
| ( SV137 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1412,plain,
! [SV54: $i] :
( ( ( ~ ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1413,plain,
! [SV54: $i] :
( ( ( ~ ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1273]) ).
thf(1414,plain,
! [SV138: $i] :
( ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
| ( reflexive @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1415,plain,
! [SV139: $i] :
( ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( reflexive @ SV139 )
| ! [SY6743: $i] :
( ~ ( in @ SY6743 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SY6743 @ SY6743 ) @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1416,plain,
! [SV181: $i,SV55: $i] :
( ( ! [SY6776: $i] :
( ~ ( relation @ SY6776 )
| ~ ( in @ SV55 @ SV181 )
| ~ ( in @ SV55 @ ( relation_rng @ SY6776 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SY6776 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1417,plain,
! [SV55: $i] :
( ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) )
| ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1418,plain,
! [SV140: $i] :
( ( ( ~ ( relation @ SV140 ) )
= $true )
| ( ( ( ( relation_dom @ SV140 )
!= empty_set )
| ( ( relation_rng @ SV140 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1419,plain,
! [SV141: $i] :
( ( ( ~ ( relation @ SV141 ) )
= $true )
| ( ( ( ( relation_rng @ SV141 )
!= empty_set )
| ( ( relation_dom @ SV141 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1420,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1421,plain,
( ( ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1280]) ).
thf(1422,plain,
! [SV142: $i,SV182: $i] :
( ( ~ ( function @ SV182 )
| ~ ( relation @ SV182 )
| ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 )
| ( SV182
= ( identity_relation @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1423,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1424,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1282]) ).
thf(1425,plain,
! [SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( ~ ( one_to_one @ SV56 )
| ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1426,plain,
! [SV143: $i] :
( ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV143 @ ( relation_field @ SV143 ) )
| ( well_founded_relation @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1427,plain,
! [SV144: $i] :
( ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV144 )
| ( is_well_founded_in @ SV144 @ ( relation_field @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1428,plain,
! [SV57: $i] :
( ( ( ~ ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1429,plain,
! [SV57: $i] :
( ( ( ~ ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1430,plain,
! [SV58: $i] :
( ( ( ~ ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1431,plain,
! [SV58: $i] :
( ( ( ~ ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1287]) ).
thf(1432,plain,
! [SV145: $i] :
( ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ( transitive @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1433,plain,
! [SV146: $i] :
( ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( ~ ( transitive @ SV146 )
| ! [SY6745: $i,SY6746: $i,SY6747: $i] :
( ~ ( in @ ( ordered_pair @ SY6745 @ SY6746 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6746 @ SY6747 ) @ SV146 )
| ( in @ ( ordered_pair @ SY6745 @ SY6747 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1434,plain,
! [SV59: $i] :
( ( ( ~ ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1435,plain,
! [SV59: $i] :
( ( ( ~ ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1436,plain,
! [SV60: $i] :
( ( ( ~ ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1437,plain,
! [SV60: $i] :
( ( ( ~ ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1438,plain,
( ( ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1439,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1292]) ).
thf(1440,plain,
! [SV147: $i,SV183: $i] :
( ( ~ ( relation @ SV183 )
| ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
| ( SV183
= ( identity_relation @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1441,plain,
! [SV148: $i,SV184: $i] :
( ( ~ ( relation @ SV184 )
| ( SV184
!= ( identity_relation @ SV148 ) )
| ~ ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1442,plain,
! [SV61: $i,SV185: $i] :
( ( ! [SY6783: $i] :
( ~ ( function @ SY6783 )
| ~ ( relation @ SY6783 )
| ( SV185
!= ( apply @ SY6783 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SY6783 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SY6783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1443,plain,
! [SV61: $i] :
( ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) )
| ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1444,plain,
! [SV149: $i] :
( ( ( ~ ( empty @ SV149 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1445,plain,
! [SV150: $i] :
( ( ( ~ ( empty @ SV150 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1446,plain,
! [SV151: $i,SV186: $i] :
( ( ~ ( function @ SV186 )
| ~ ( relation @ SV186 )
| ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 )
| ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1447,plain,
! [SV152: $i,SV187: $i] :
( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 )
| ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1448,plain,
! [SV153: $i] :
( ( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( one_to_one @ SV153 )
| ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1449,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1450,plain,
! [SV62: $i] :
( ( ( ~ ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1451,plain,
! [SV62: $i] :
( ( ( ~ ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1452,plain,
! [SV63: $i] :
( ( ( ~ ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1453,plain,
! [SV63: $i] :
( ( ( ~ ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1454,plain,
! [SV188: $i,SV155: $i] :
( ( ~ ( empty @ SV155 )
| ~ ( relation @ SV188 )
| ( empty @ ( relation_composition @ SV155 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1455,plain,
! [SV189: $i,SV156: $i] :
( ( ~ ( empty @ SV156 )
| ~ ( relation @ SV189 )
| ( relation @ ( relation_composition @ SV156 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1456,plain,
! [SV190: $i,SV64: $i] :
( ( ! [SY6784: $i] :
( ~ ( relation @ SY6784 )
| ! [SY6785: $i] :
( ~ ( in @ SY6785 @ ( relation_rng @ SY6784 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6785 ) @ SY6784 )
| ~ ( in @ SY6785 @ SV190 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SY6784 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1457,plain,
! [SV191: $i,SV64: $i] :
( ( ! [SY6786: $i] :
( ~ ( relation @ SY6786 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SY6786 @ SV191 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY6786 @ SV191 @ SV64 ) @ ( relation_rng @ SY6786 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SY6786 @ SV191 @ SV64 ) ) @ SY6786 ) )
| ~ ( in @ ( sK68_D @ SY6786 @ SV191 @ SV64 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1458,plain,
! [SV157: $i] :
( ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
| ( well_founded_relation @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1459,plain,
! [SV158: $i] :
( ( ( ~ ( relation @ SV158 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV158 )
| ! [SY6761: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SY6761 @ SV158 ) ) @ SY6761 )
| ~ ( in @ ( sK38_C @ SY6761 @ SV158 ) @ SY6761 ) )
| ( SY6761 = empty_set )
| ~ ( subset @ SY6761 @ ( relation_field @ SV158 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1460,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1461,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1462,plain,
! [SV159: $i] :
( ( ( ~ ( empty @ SV159 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1463,plain,
! [SV160: $i] :
( ( ( ~ ( empty @ SV160 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1464,plain,
! [SV192: $i,SV66: $i] :
( ( ! [SY6787: $i] :
( ~ ( relation @ SY6787 )
| ~ ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SY6787 )
| ( in @ SV66 @ ( relation_field @ SY6787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1465,plain,
! [SV193: $i,SV66: $i] :
( ( ! [SY6788: $i] :
( ~ ( relation @ SY6788 )
| ~ ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SY6788 )
| ( in @ SV193 @ ( relation_field @ SY6788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1466,plain,
! [SV67: $i] :
( ( ( ~ ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) ) )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1467,plain,
! [SV67: $i] :
( ( ( ~ ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1316]) ).
thf(1468,plain,
! [SV161: $i] :
( ( ( ~ ( function @ SV161 )
| ~ ( relation @ SV161 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
| ( one_to_one @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1469,plain,
! [SV162: $i] :
( ( ( ~ ( function @ SV162 )
| ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( one_to_one @ SV162 )
| ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1470,plain,
! [SV194: $i,SV163: $i] :
( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 )
| ~ ( relation @ SV194 )
| ~ ( function @ SV194 )
| ( function @ ( relation_composition @ SV163 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1471,plain,
! [SV195: $i,SV164: $i] :
( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( relation @ SV195 )
| ~ ( function @ SV195 )
| ( relation @ ( relation_composition @ SV164 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1472,plain,
! [SV165: $i] :
( ( ( ~ ( ~ ! [SY6766: $i,SY6767: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SY6766 @ SY6767 ) )
| ~ ( in @ ( sK45_B @ SV165 ) @ SV165 ) ) )
= $true )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1473,plain,
! [SV166: $i] :
( ( ( ~ ( relation @ SV166 ) )
= $true )
| ( ( ! [SY6768: $i] :
( ( SY6768
= ( ordered_pair @ ( sK43_C @ SY6768 @ SV166 ) @ ( sK44_SY6449 @ SY6768 @ SV166 ) ) )
| ~ ( in @ SY6768 @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1474,plain,
! [SV196: $i,SV68: $i] :
( ( ! [SY6789: $i] :
( ~ ( relation @ SY6789 )
| ~ ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SY6789 )
| ( in @ SV68 @ ( relation_dom @ SY6789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1475,plain,
! [SV197: $i,SV68: $i] :
( ( ! [SY6790: $i] :
( ~ ( relation @ SY6790 )
| ~ ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SY6790 )
| ( in @ SV197 @ ( relation_rng @ SY6790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1476,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1477,plain,
( ( ~ ( epsilon_connected @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1325]) ).
thf(1478,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1479,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1480,plain,
! [SV167: $i] :
( ( ( ~ ( function @ SV167 )
| ~ ( relation @ SV167 )
| ~ ( one_to_one @ SV167 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1481,plain,
! [SV168: $i] :
( ( ( ~ ( function @ SV168 )
| ~ ( relation @ SV168 )
| ~ ( one_to_one @ SV168 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1482,plain,
! [SV198: $i,SV69: $i] :
( ( ! [SY6791: $i] :
( ~ ( relation @ SY6791 )
| ! [SY6792: $i] :
( ~ ( in @ SY6792 @ ( relation_dom @ SY6791 ) )
| ~ ( in @ ( ordered_pair @ SY6792 @ SV69 ) @ SY6791 )
| ~ ( in @ SY6792 @ SV198 ) )
| ( in @ SV69 @ ( relation_image @ SY6791 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1483,plain,
! [SV199: $i,SV69: $i] :
( ( ! [SY6793: $i] :
( ~ ( relation @ SY6793 )
| ~ ( in @ SV69 @ ( relation_image @ SY6793 @ SV199 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY6793 @ SV199 @ SV69 ) @ ( relation_dom @ SY6793 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY6793 @ SV199 @ SV69 ) @ SV69 ) @ SY6793 ) )
| ~ ( in @ ( sK69_D @ SY6793 @ SV199 @ SV69 ) @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1484,plain,
! [SV70: $i] :
( ( ( ~ ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1485,plain,
! [SV70: $i] :
( ( ( ~ ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1486,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1487,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1332]) ).
thf(1488,plain,
! [SV169: $i] :
( ( ( ~ ( relation @ SV169 ) )
= $true )
| ( ( ( relation_rng @ SV169 )
= ( relation_dom @ ( relation_inverse @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1489,plain,
! [SV170: $i] :
( ( ( ~ ( relation @ SV170 ) )
= $true )
| ( ( ( relation_dom @ SV170 )
= ( relation_rng @ ( relation_inverse @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1490,plain,
! [SV71: $i,SV200: $i] :
( ( ! [SY6794: $i] :
( ~ ( function @ SY6794 )
| ~ ( relation @ SY6794 )
| ~ ( in @ SV200 @ ( relation_dom @ SY6794 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SY6794 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1491,plain,
! [SV71: $i] :
( ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) )
| ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1492,plain,
! [SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( ~ ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1493,plain,
! [SV73: $i,SV107: $i] :
( ( ( function @ SV107 )
= $false )
| ( ( ~ ( relation @ SV107 ) )
= $true )
| ( ( ~ ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1494,plain,
! [SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( ~ ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1495,plain,
! [SV171: $i] :
( ( ( ~ ( function @ SV171 )
| ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY6769: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY6769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1496,plain,
! [SV172: $i] :
( ( ( ~ ( function @ SV172 )
| ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY6770: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY6770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1497,plain,
! [SV75: $i] :
( ( ( ~ ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) ) )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1498,plain,
! [SV75: $i] :
( ( ( ~ ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1499,plain,
! [SV173: $i] :
( ( ( ~ ( relation @ SV173 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
| ( connected @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1500,plain,
! [SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( connected @ SV174 )
| ! [SY6771: $i,SY6772: $i] :
( ( SY6771 = SY6772 )
| ~ ( in @ SY6771 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6772 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SY6771 @ SY6772 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6772 @ SY6771 ) @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1501,plain,
! [SV201: $i,SV175: $i] :
( ( ~ ( empty @ SV175 )
| ~ ( relation @ SV201 )
| ( empty @ ( relation_composition @ SV201 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1502,plain,
! [SV202: $i,SV176: $i] :
( ( ~ ( empty @ SV176 )
| ~ ( relation @ SV202 )
| ( relation @ ( relation_composition @ SV202 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1503,plain,
! [SV76: $i] :
( ( ( ~ ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1504,plain,
! [SV76: $i] :
( ( ( ~ ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1505,plain,
! [SV177: $i] :
( ( ( ~ ( function @ SV177 )
| ~ ( relation @ SV177 ) )
= $true )
| ( ( function @ ( function_inverse @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1506,plain,
! [SV178: $i] :
( ( ( ~ ( function @ SV178 )
| ~ ( relation @ SV178 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1507,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1508,plain,
! [SV179: $i] :
( ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 )
| ~ ( connected @ SV179 )
| ~ ( well_founded_relation @ SV179 )
| ( well_ordering @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1509,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1510,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1353]) ).
thf(1511,plain,
! [SV7: $i,SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( function @ SV84 )
= $false )
| ( ( subset @ ( relation_image @ SV84 @ ( relation_inverse_image @ SV84 @ SV7 ) ) @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1512,plain,
! [SV86: $i,SV9: $i] :
( ( ( subset @ SV9 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( subset @ SV9 @ ( relation_inverse_image @ SV86 @ ( relation_image @ SV86 @ SV9 ) ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1513,plain,
! [SV11: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( function @ SV87 )
= $false )
| ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) )
| ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1514,plain,
! [SV12: $i,SV112: $i] :
( ( ( relation @ SV112 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV12 @ SV112 ) )
= ( relation_image @ SV112 @ ( relation_rng @ SV12 ) ) )
= $true )
| ( ( relation @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1515,plain,
! [SV89: $i,SV14: $i] :
( ( ( SV14 = empty_set )
= $true )
| ( ( ~ ( subset @ SV14 @ ( relation_rng @ SV89 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1516,plain,
! [SV109: $i,SV90: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV90 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV109 @ SV15 ) @ ( relation_inverse_image @ SV109 @ SV90 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1517,plain,
! [SV17: $i,SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( ! [SY6706: $i] :
( ~ ( function @ SY6706 )
| ~ ( relation @ SY6706 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SY6706 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SY6706 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SY6706 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1518,plain,
! [SV18: $i,SV92: $i] :
( ( ( relation @ SV92 )
= $false )
| ( ( function @ SV92 )
= $false )
| ( ( ! [SY6707: $i] :
( ~ ( function @ SY6707 )
| ~ ( relation @ SY6707 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SY6707 ) @ SV18 )
= ( apply @ SY6707 @ ( apply @ SV92 @ SV18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1519,plain,
! [SV19: $i,SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV19 @ SV113 ) ) @ ( relation_dom @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1520,plain,
! [SV20: $i,SV114: $i] :
( ( ( relation @ SV114 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV20 @ SV114 ) ) @ ( relation_rng @ SV114 ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1521,plain,
! [SV21: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SV115 ) )
| ( ( relation_dom @ ( relation_composition @ SV21 @ SV115 ) )
= ( relation_dom @ SV21 ) ) )
= $true )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1522,plain,
! [SV22: $i,SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV116 ) )
| ( ( relation_rng @ ( relation_composition @ SV116 @ SV22 ) )
= ( relation_rng @ SV22 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1523,plain,
! [SV24: $i] :
( ( ( ~ ( one_to_one @ SV24 ) )
= $true )
| ( ( one_to_one @ ( function_inverse @ SV24 ) )
= $true )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1524,plain,
! [SV25: $i,SV93: $i,SV110: $i] :
( ( ( function @ SV110 )
= $false )
| ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1525,plain,
! [SV26: $i,SV94: $i,SV111: $i] :
( ( ( function @ SV111 )
= $false )
| ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1526,plain,
! [SV33: $i] :
( ( ( ~ ( one_to_one @ SV33 ) )
= $true )
| ( ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) )
= $true )
| ( ( function @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1527,plain,
! [SV35: $i,SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV35 )
= $false )
| ( ( relation @ ( relation_composition @ SV35 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1528,plain,
! [SV39: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( relation @ SV39 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV39 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1529,plain,
! [SV40: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( relation @ ( set_union2 @ SV40 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1530,plain,
! [SV41: $i,SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( relation @ SV41 )
= $false )
| ( ( relation @ ( set_difference @ SV41 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1531,plain,
! [SV45: $i] :
( ( ( ! [SY6506: $i] :
( ~ ( ~ ( ! [SY6507: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ SY6507 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY6506 @ SV45 ) @ ( sK33_SY6444 @ SY6506 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SY6506 @ SV45 ) @ SY6506 ) ) )
| ( SY6506
= ( relation_dom @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1532,plain,
! [SV45: $i] :
( ( ( ! [SY6508: $i] :
( ( SY6508
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6509: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6509 @ SY6510 ) @ SV45 )
| ( in @ SY6509 @ SY6508 ) )
| ~ ! [SY6511: $i] :
( ~ ( in @ SY6511 @ SY6508 )
| ( in @ ( ordered_pair @ SY6511 @ ( sK31_D @ SY6511 @ SY6508 @ SV45 ) ) @ SV45 ) ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1533,plain,
! [SV46: $i] :
( ( ( ! [SY6512: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY6512 @ SV46 ) @ SY6512 )
| ~ ( in @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ SY6512 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY6512 @ SV46 ) @ ( sK30_SY6442 @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY6512 @ SV46 ) @ ( sK29_C @ SY6512 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SY6512 @ SV46 )
!= ( sK30_SY6442 @ SY6512 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SY6512 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1379]) ).
thf(1534,plain,
! [SV46: $i] :
( ( ( ! [SY6513: $i] :
( ~ ( is_antisymmetric_in @ SV46 @ SY6513 )
| ! [SY6514: $i,SY6515: $i] :
( ~ ( in @ SY6514 @ SY6513 )
| ~ ( in @ SY6515 @ SY6513 )
| ~ ( in @ ( ordered_pair @ SY6514 @ SY6515 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6515 @ SY6514 ) @ SV46 )
| ( SY6514 = SY6515 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1380]) ).
thf(1535,plain,
! [SV118: $i] :
( ( ( ~ ( relation @ SV118 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV118 ) )
= $true )
| ( ( ! [SY6731: $i] : ( relation @ ( relation_dom_restriction @ SV118 @ SY6731 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1536,plain,
! [SV119: $i] :
( ( ( ~ ( relation @ SV119 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV119 ) )
= $true )
| ( ( ! [SY6732: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SY6732 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1537,plain,
! [SV104: $i,SV203: $i,SV47: $i] :
( ( ! [SY6795: $i] :
( ~ ( relation @ SY6795 )
| ~ ( in @ SV47 @ SV203 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6795 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SY6795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1538,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) )
| ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1539,plain,
! [SV180: $i,SV48: $i,SV204: $i] :
( ( ~ ( relation @ SV204 )
| ~ ( in @ SV48 @ SV180 )
| ~ ( in @ SV48 @ ( relation_dom @ SV204 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1540,plain,
! [SV48: $i] :
( ( ~ ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1541,plain,
! [SV48: $i] :
( ( ~ ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1542,plain,
! [SV120: $i] :
( ( ( relation @ SV120 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
| ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) )
| ( antisymmetric @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1543,plain,
! [SV121: $i] :
( ( ( relation @ SV121 )
= $false )
| ( ( ~ ( antisymmetric @ SV121 )
| ! [SY6733: $i,SY6734: $i] :
( ~ ( in @ ( ordered_pair @ SY6733 @ SY6734 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6734 @ SY6733 ) @ SV121 )
| ( SY6733 = SY6734 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1544,plain,
! [SV122: $i] :
( ( ( relation @ SV122 )
= $false )
| ( ( ~ ( connected @ SV122 )
| ( is_connected_in @ SV122 @ ( relation_field @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1545,plain,
! [SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( is_connected_in @ SV123 @ ( relation_field @ SV123 ) )
| ( connected @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1546,plain,
! [SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( ~ ( is_transitive_in @ SV124 @ ( relation_field @ SV124 ) )
| ( transitive @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1547,plain,
! [SV125: $i] :
( ( ( relation @ SV125 )
= $false )
| ( ( ~ ( transitive @ SV125 )
| ( is_transitive_in @ SV125 @ ( relation_field @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1548,plain,
! [SV49: $i,SV126: $i] :
( ( ( relation @ SV126 )
= $false )
| ( ( ~ ( ~ ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) )
| ~ ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1549,plain,
! [SV50: $i] :
( ( ( ! [SY6538: $i] :
( ~ ( ~ ! [SY6539: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6539 ) @ ( sK35_C @ SY6538 @ SV50 ) )
| ~ ( in @ SY6539 @ ( sK35_C @ SY6538 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY6538 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY6538 @ SV50 ) @ SY6538 ) ) )
| ( is_well_founded_in @ SV50 @ SY6538 ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1394]) ).
thf(1550,plain,
! [SV50: $i] :
( ( ( ! [SY6540: $i] :
( ~ ( is_well_founded_in @ SV50 @ SY6540 )
| ! [SY6541: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) ) @ SY6541 )
| ~ ( in @ ( sK34_D @ SY6541 @ SY6540 @ SV50 ) @ SY6541 ) )
| ( SY6541 = empty_set )
| ~ ( subset @ SY6541 @ SY6540 ) ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1551,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1552,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1553,plain,
! [SV129: $i] :
( ( ( relation @ SV129 )
= $false )
| ( ( ~ ( is_reflexive_in @ SV129 @ ( relation_field @ SV129 ) )
| ( reflexive @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1554,plain,
! [SV130: $i] :
( ( ( relation @ SV130 )
= $false )
| ( ( ~ ( reflexive @ SV130 )
| ( is_reflexive_in @ SV130 @ ( relation_field @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1555,plain,
! [SV51: $i,SV105: $i] :
( ( ( relation @ SV105 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( ~ ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1556,plain,
! [SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( ~ ( antisymmetric @ SV131 )
| ( is_antisymmetric_in @ SV131 @ ( relation_field @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1557,plain,
! [SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV132 @ ( relation_field @ SV132 ) )
| ( antisymmetric @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1558,plain,
! [SV52: $i,SV106: $i] :
( ( ( ~ ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) ) )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1559,plain,
! [SV106: $i,SV52: $i] :
( ( ( ~ ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1560,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1561,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1405]) ).
thf(1562,plain,
! [SV133: $i] :
( ( ( ~ ( empty @ SV133 )
| ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1563,plain,
! [SV53: $i] :
( ( ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) )
| ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1564,plain,
! [SV134: $i] :
( ( ( empty @ SV134 )
= $false )
| ( ( empty @ ( relation_rng @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1565,plain,
! [SV135: $i] :
( ( ( empty @ SV135 )
= $false )
| ( ( relation @ ( relation_rng @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1566,plain,
! [SV136: $i] :
( ( ( relation @ SV136 )
= $false )
| ( ( ( ( relation_dom @ SV136 )
!= empty_set )
| ( SV136 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1567,plain,
! [SV137: $i] :
( ( ( relation @ SV137 )
= $false )
| ( ( ( ( relation_rng @ SV137 )
!= empty_set )
| ( SV137 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1568,plain,
! [SV54: $i] :
( ( ( ! [SY6562: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY6562 @ SV54 ) @ SY6562 )
| ~ ( in @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( sK12_SY6429 @ SY6562 @ SV54 ) @ SY6562 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK11_SY6427 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY6562 @ SV54 ) @ ( sK12_SY6429 @ SY6562 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SY6562 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1569,plain,
! [SV54: $i] :
( ( ( ! [SY6563: $i] :
( ~ ( is_transitive_in @ SV54 @ SY6563 )
| ! [SY6564: $i,SY6565: $i,SY6566: $i] :
( ~ ( in @ SY6564 @ SY6563 )
| ~ ( in @ SY6565 @ SY6563 )
| ~ ( in @ SY6566 @ SY6563 )
| ~ ( in @ ( ordered_pair @ SY6564 @ SY6565 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6565 @ SY6566 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6564 @ SY6566 ) @ SV54 ) ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1570,plain,
! [SV138: $i] :
( ( ( relation @ SV138 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
| ( reflexive @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1571,plain,
! [SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( ~ ( reflexive @ SV139 )
| ! [SY6743: $i] :
( ~ ( in @ SY6743 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SY6743 @ SY6743 ) @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1572,plain,
! [SV181: $i,SV55: $i,SV205: $i] :
( ( ~ ( relation @ SV205 )
| ~ ( in @ SV55 @ SV181 )
| ~ ( in @ SV55 @ ( relation_rng @ SV205 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1573,plain,
! [SV55: $i] :
( ( ~ ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1574,plain,
! [SV55: $i] :
( ( ~ ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1575,plain,
! [SV140: $i] :
( ( ( relation @ SV140 )
= $false )
| ( ( ( ( relation_dom @ SV140 )
!= empty_set )
| ( ( relation_rng @ SV140 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1576,plain,
! [SV141: $i] :
( ( ( relation @ SV141 )
= $false )
| ( ( ( ( relation_rng @ SV141 )
!= empty_set )
| ( ( relation_dom @ SV141 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1577,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1578,plain,
( ( relation_empty_yielding @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1579,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( function @ SV182 )
| ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 )
| ( SV182
= ( identity_relation @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1423]) ).
thf(1581,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1424]) ).
thf(1582,plain,
! [SV56: $i] :
( ( ( ~ ( one_to_one @ SV56 ) )
= $true )
| ( ( ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1583,plain,
! [SV143: $i] :
( ( ( relation @ SV143 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV143 @ ( relation_field @ SV143 ) )
| ( well_founded_relation @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1584,plain,
! [SV144: $i] :
( ( ( relation @ SV144 )
= $false )
| ( ( ~ ( well_founded_relation @ SV144 )
| ( is_well_founded_in @ SV144 @ ( relation_field @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1585,plain,
! [SV57: $i] :
( ( ( ! [SY6584: $i] :
( ~ ( relation @ SY6584 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY6584 @ SV57 ) @ ( sK41_SY6448 @ SY6584 @ SV57 ) ) @ SY6584 ) ) )
| ( SV57 = SY6584 ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1586,plain,
! [SV57: $i] :
( ( ( ! [SY6585: $i] :
( ~ ( relation @ SY6585 )
| ( SV57 != SY6585 )
| ~ ( ~ ! [SY6586: $i,SY6587: $i] :
( ~ ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6586 @ SY6587 ) @ SY6585 ) )
| ~ ! [SY6588: $i,SY6589: $i] :
( ~ ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SY6585 )
| ( in @ ( ordered_pair @ SY6588 @ SY6589 ) @ SV57 ) ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1587,plain,
! [SV58: $i] :
( ( ( ! [SY6590: $i] :
( ~ ( relation @ SY6590 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY6590 @ SV58 ) @ ( sK20_SY6436 @ SY6590 @ SV58 ) ) @ SY6590 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY6590 @ SV58 ) @ ( sK19_C @ SY6590 @ SV58 ) ) @ SV58 ) ) )
| ( SY6590
= ( relation_inverse @ SV58 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1588,plain,
! [SV58: $i] :
( ( ( ! [SY6591: $i] :
( ~ ( relation @ SY6591 )
| ( SY6591
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6592: $i,SY6593: $i] :
( ~ ( in @ ( ordered_pair @ SY6592 @ SY6593 ) @ SY6591 )
| ( in @ ( ordered_pair @ SY6593 @ SY6592 ) @ SV58 ) )
| ~ ! [SY6594: $i,SY6595: $i] :
( ~ ( in @ ( ordered_pair @ SY6595 @ SY6594 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6594 @ SY6595 ) @ SY6591 ) ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1589,plain,
! [SV145: $i] :
( ( ( relation @ SV145 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ( transitive @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1590,plain,
! [SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( ~ ( transitive @ SV146 )
| ! [SY6745: $i,SY6746: $i,SY6747: $i] :
( ~ ( in @ ( ordered_pair @ SY6745 @ SY6746 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6746 @ SY6747 ) @ SV146 )
| ( in @ ( ordered_pair @ SY6745 @ SY6747 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1591,plain,
! [SV59: $i] :
( ( ( ! [SY6596: $i,SY6597: $i] :
( ~ ( relation @ SY6597 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ SY6596 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6597 @ SY6596 @ SV59 ) @ ( sK59_SY6459 @ SY6597 @ SY6596 @ SV59 ) ) @ SY6597 ) ) ) )
| ( SY6597
= ( relation_dom_restriction @ SV59 @ SY6596 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1592,plain,
! [SV59: $i] :
( ( ( ! [SY6598: $i,SY6599: $i] :
( ~ ( relation @ SY6599 )
| ( SY6599
!= ( relation_dom_restriction @ SV59 @ SY6598 ) )
| ~ ( ~ ! [SY6600: $i,SY6601: $i] :
( ~ ( in @ SY6600 @ SY6598 )
| ~ ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6600 @ SY6601 ) @ SY6599 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY6599 )
| ( in @ SX3 @ SY6598 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6599 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1593,plain,
! [SV60: $i] :
( ( ( ! [SY6606: $i] :
( ~ ( ~ ( ! [SY6607: $i] :
~ ( in @ ( ordered_pair @ SY6607 @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY6606 @ SV60 ) @ ( sK24_C @ SY6606 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SY6606 @ SV60 ) @ SY6606 ) ) )
| ( SY6606
= ( relation_rng @ SV60 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1594,plain,
! [SV60: $i] :
( ( ( ! [SY6608: $i] :
( ( SY6608
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6609: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6609 ) @ SV60 )
| ( in @ SY6609 @ SY6608 ) )
| ~ ! [SY6611: $i] :
( ~ ( in @ SY6611 @ SY6608 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6611 @ SY6608 @ SV60 ) @ SY6611 ) @ SV60 ) ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1437]) ).
thf(1595,plain,
( ( function @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1596,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1597,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( relation @ SV183 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
| ( SV183
= ( identity_relation @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1598,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ( relation @ SV184 ) )
= $true )
| ( ( ( SV184
!= ( identity_relation @ SV148 ) )
| ~ ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1599,plain,
! [SV61: $i,SV185: $i,SV206: $i] :
( ( ~ ( function @ SV206 )
| ~ ( relation @ SV206 )
| ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1600,plain,
! [SV61: $i] :
( ( ~ ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1601,plain,
! [SV61: $i] :
( ( ~ ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1602,plain,
! [SV149: $i] :
( ( ( empty @ SV149 )
= $false )
| ( ( empty @ ( relation_inverse @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1603,plain,
! [SV150: $i] :
( ( ( empty @ SV150 )
= $false )
| ( ( relation @ ( relation_inverse @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1604,plain,
! [SV151: $i,SV186: $i] :
( ( ( ~ ( function @ SV186 )
| ~ ( relation @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 )
| ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1605,plain,
! [SV152: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1606,plain,
! [SV153: $i] :
( ( ( ~ ( function @ SV153 ) )
= $true )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( one_to_one @ SV153 )
| ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1607,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 ) )
= $true )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1608,plain,
! [SV62: $i] :
( ( ( ! [SY6618: $i] :
( ~ ( relation @ SY6618 )
| ~ ( subset @ SV62 @ SY6618 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SY6618 ) ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1609,plain,
! [SV62: $i] :
( ( ( ! [SY6619: $i] :
( ~ ( relation @ SY6619 )
| ~ ( subset @ SV62 @ SY6619 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SY6619 ) ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1610,plain,
! [SV63: $i] :
( ( ( ! [SY6620: $i,SY6621: $i] :
( ~ ( ~ ( ! [SY6622: $i] :
( ~ ( in @ ( ordered_pair @ SY6622 @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6622 @ SY6620 ) )
| ~ ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6621 @ SY6620 @ SV63 ) @ SY6620 ) )
| ( in @ ( sK50_D @ SY6621 @ SY6620 @ SV63 ) @ SY6621 ) ) )
| ( SY6621
= ( relation_image @ SV63 @ SY6620 ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1611,plain,
! [SV63: $i] :
( ( ( ! [SY6623: $i,SY6624: $i] :
( ( SY6624
!= ( relation_image @ SV63 @ SY6623 ) )
| ~ ( ~ ! [SY6625: $i] :
( ! [SY6626: $i] :
( ~ ( in @ ( ordered_pair @ SY6626 @ SY6625 ) @ SV63 )
| ~ ( in @ SY6626 @ SY6623 ) )
| ( in @ SY6625 @ SY6624 ) )
| ~ ! [SY6627: $i] :
( ~ ( in @ SY6627 @ SY6624 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6627 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6627 @ SY6624 @ SY6623 @ SV63 ) @ SY6623 ) ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1612,plain,
! [SV188: $i,SV155: $i] :
( ( ( ~ ( empty @ SV155 )
| ~ ( relation @ SV188 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV155 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1613,plain,
! [SV189: $i,SV156: $i] :
( ( ( ~ ( empty @ SV156 )
| ~ ( relation @ SV189 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV156 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1614,plain,
! [SV190: $i,SV64: $i,SV207: $i] :
( ( ~ ( relation @ SV207 )
| ! [SY6796: $i] :
( ~ ( in @ SY6796 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6796 ) @ SV207 )
| ~ ( in @ SY6796 @ SV190 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1615,plain,
! [SV191: $i,SV64: $i,SV208: $i] :
( ( ~ ( relation @ SV208 )
| ~ ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1616,plain,
! [SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( ~ ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
| ( well_founded_relation @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1617,plain,
! [SV158: $i] :
( ( ( relation @ SV158 )
= $false )
| ( ( ~ ( well_founded_relation @ SV158 )
| ! [SY6761: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SY6761 @ SV158 ) ) @ SY6761 )
| ~ ( in @ ( sK38_C @ SY6761 @ SV158 ) @ SY6761 ) )
| ( SY6761 = empty_set )
| ~ ( subset @ SY6761 @ ( relation_field @ SV158 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1618,plain,
! [SV65: $i] :
( ( ( ! [SY6633: $i] :
( ~ ( is_reflexive_in @ SV65 @ SY6633 )
| ~ ( is_transitive_in @ SV65 @ SY6633 )
| ~ ( is_antisymmetric_in @ SV65 @ SY6633 )
| ~ ( is_connected_in @ SV65 @ SY6633 )
| ~ ( is_well_founded_in @ SV65 @ SY6633 )
| ( well_orders @ SV65 @ SY6633 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1619,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1620,plain,
! [SV159: $i] :
( ( ( empty @ SV159 )
= $false )
| ( ( empty @ ( relation_dom @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1621,plain,
! [SV160: $i] :
( ( ( empty @ SV160 )
= $false )
| ( ( relation @ ( relation_dom @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1622,plain,
! [SV192: $i,SV66: $i,SV209: $i] :
( ( ~ ( relation @ SV209 )
| ~ ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SV209 )
| ( in @ SV66 @ ( relation_field @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1623,plain,
! [SV193: $i,SV66: $i,SV210: $i] :
( ( ~ ( relation @ SV210 )
| ~ ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SV210 )
| ( in @ SV193 @ ( relation_field @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1624,plain,
! [SV67: $i] :
( ( ( ! [SY6643: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY6643 @ SV67 ) @ SY6643 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY6643 @ SV67 ) @ ( sK42_C @ SY6643 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SY6643 ) ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1625,plain,
! [SV67: $i] :
( ( ( ! [SY6644: $i] :
( ~ ( is_reflexive_in @ SV67 @ SY6644 )
| ! [SY6645: $i] :
( ~ ( in @ SY6645 @ SY6644 )
| ( in @ ( ordered_pair @ SY6645 @ SY6645 ) @ SV67 ) ) ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1626,plain,
! [SV161: $i] :
( ( ( ~ ( function @ SV161 ) )
= $true )
| ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
| ( one_to_one @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1627,plain,
! [SV162: $i] :
( ( ( ~ ( function @ SV162 ) )
= $true )
| ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( one_to_one @ SV162 )
| ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1628,plain,
! [SV194: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 )
| ~ ( relation @ SV194 )
| ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1629,plain,
! [SV195: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( relation @ SV195 )
| ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1471]) ).
thf(1630,plain,
! [SV165: $i] :
( ( ( ~ ! [SY6766: $i,SY6767: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SY6766 @ SY6767 ) )
| ~ ( in @ ( sK45_B @ SV165 ) @ SV165 ) )
= $false )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1631,plain,
! [SV166: $i] :
( ( ( relation @ SV166 )
= $false )
| ( ( ! [SY6768: $i] :
( ( SY6768
= ( ordered_pair @ ( sK43_C @ SY6768 @ SV166 ) @ ( sK44_SY6449 @ SY6768 @ SV166 ) ) )
| ~ ( in @ SY6768 @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1632,plain,
! [SV196: $i,SV68: $i,SV211: $i] :
( ( ~ ( relation @ SV211 )
| ~ ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SV211 )
| ( in @ SV68 @ ( relation_dom @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1633,plain,
! [SV197: $i,SV68: $i,SV212: $i] :
( ( ~ ( relation @ SV212 )
| ~ ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SV212 )
| ( in @ SV197 @ ( relation_rng @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1634,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1635,plain,
( ( epsilon_connected @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1636,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1637,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1638,plain,
! [SV167: $i] :
( ( ( ~ ( function @ SV167 )
| ~ ( relation @ SV167 ) )
= $true )
| ( ( ~ ( one_to_one @ SV167 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1639,plain,
! [SV168: $i] :
( ( ( ~ ( function @ SV168 )
| ~ ( relation @ SV168 ) )
= $true )
| ( ( ~ ( one_to_one @ SV168 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1640,plain,
! [SV198: $i,SV69: $i,SV213: $i] :
( ( ~ ( relation @ SV213 )
| ! [SY6797: $i] :
( ~ ( in @ SY6797 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SY6797 @ SV69 ) @ SV213 )
| ~ ( in @ SY6797 @ SV198 ) )
| ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1641,plain,
! [SV199: $i,SV69: $i,SV214: $i] :
( ( ~ ( relation @ SV214 )
| ~ ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1642,plain,
! [SV70: $i] :
( ( ( ! [SY6655: $i,SY6656: $i] :
( ~ ( ~ ( ! [SY6657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6657 ) @ SV70 )
| ~ ( in @ SY6657 @ SY6655 ) )
| ~ ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6656 @ SY6655 @ SV70 ) @ SY6655 ) )
| ( in @ ( sK47_D @ SY6656 @ SY6655 @ SV70 ) @ SY6656 ) ) )
| ( SY6656
= ( relation_inverse_image @ SV70 @ SY6655 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1643,plain,
! [SV70: $i] :
( ( ( ! [SY6658: $i,SY6659: $i] :
( ( SY6659
!= ( relation_inverse_image @ SV70 @ SY6658 ) )
| ~ ( ~ ! [SY6660: $i] :
( ! [SY6661: $i] :
( ~ ( in @ ( ordered_pair @ SY6660 @ SY6661 ) @ SV70 )
| ~ ( in @ SY6661 @ SY6658 ) )
| ( in @ SY6660 @ SY6659 ) )
| ~ ! [SY6662: $i] :
( ~ ( in @ SY6662 @ SY6659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6662 @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6662 @ SY6659 @ SY6658 @ SV70 ) @ SY6658 ) ) ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1644,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1645,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1646,plain,
! [SV169: $i] :
( ( ( relation @ SV169 )
= $false )
| ( ( ( relation_rng @ SV169 )
= ( relation_dom @ ( relation_inverse @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1647,plain,
! [SV170: $i] :
( ( ( relation @ SV170 )
= $false )
| ( ( ( relation_dom @ SV170 )
= ( relation_rng @ ( relation_inverse @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1648,plain,
! [SV71: $i,SV200: $i,SV215: $i] :
( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 )
| ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1649,plain,
! [SV71: $i] :
( ( ~ ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1650,plain,
! [SV71: $i] :
( ( ~ ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1651,plain,
! [SV72: $i] :
( ( ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) )
| ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1652,plain,
! [SV73: $i,SV107: $i] :
( ( ( relation @ SV107 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( ~ ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1653,plain,
! [SV74: $i] :
( ( ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) )
| ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1654,plain,
! [SV171: $i] :
( ( ( ~ ( function @ SV171 ) )
= $true )
| ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY6769: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY6769 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1655,plain,
! [SV172: $i] :
( ( ( ~ ( function @ SV172 ) )
= $true )
| ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY6770: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY6770 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1656,plain,
! [SV75: $i] :
( ( ( ! [SY6688: $i] :
( ~ ( relation @ SY6688 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY6688 @ SV75 ) @ ( sK37_SY6446 @ SY6688 @ SV75 ) ) @ SY6688 ) )
| ( subset @ SV75 @ SY6688 ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1657,plain,
! [SV75: $i] :
( ( ( ! [SY6689: $i] :
( ~ ( relation @ SY6689 )
| ~ ( subset @ SV75 @ SY6689 )
| ! [SY6690: $i,SY6691: $i] :
( ~ ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6690 @ SY6691 ) @ SY6689 ) ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1658,plain,
! [SV173: $i] :
( ( ( relation @ SV173 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
| ( connected @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1659,plain,
! [SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ~ ( connected @ SV174 )
| ! [SY6771: $i,SY6772: $i] :
( ( SY6771 = SY6772 )
| ~ ( in @ SY6771 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6772 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SY6771 @ SY6772 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6772 @ SY6771 ) @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1660,plain,
! [SV201: $i,SV175: $i] :
( ( ( ~ ( empty @ SV175 )
| ~ ( relation @ SV201 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV201 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1661,plain,
! [SV202: $i,SV176: $i] :
( ( ( ~ ( empty @ SV176 )
| ~ ( relation @ SV202 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV202 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1662,plain,
! [SV76: $i] :
( ( ( ! [SY6692: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY6692 @ SV76 )
!= ( sK22_SY6437 @ SY6692 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY6692 @ SV76 ) @ SY6692 )
| ~ ( in @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ SY6692 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY6692 @ SV76 ) @ ( sK22_SY6437 @ SY6692 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY6692 @ SV76 ) @ ( sK21_C @ SY6692 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SY6692 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1663,plain,
! [SV76: $i] :
( ( ( ! [SY6693: $i] :
( ~ ( is_connected_in @ SV76 @ SY6693 )
| ! [SY6694: $i,SY6695: $i] :
( ( SY6694 = SY6695 )
| ~ ( in @ SY6694 @ SY6693 )
| ~ ( in @ SY6695 @ SY6693 )
| ( in @ ( ordered_pair @ SY6694 @ SY6695 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6695 @ SY6694 ) @ SV76 ) ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1664,plain,
! [SV177: $i] :
( ( ( ~ ( function @ SV177 ) )
= $true )
| ( ( ~ ( relation @ SV177 ) )
= $true )
| ( ( function @ ( function_inverse @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1665,plain,
! [SV178: $i] :
( ( ( ~ ( function @ SV178 ) )
= $true )
| ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1666,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
| ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1667,plain,
! [SV179: $i] :
( ( ( relation @ SV179 )
= $false )
| ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 )
| ~ ( connected @ SV179 )
| ~ ( well_founded_relation @ SV179 )
| ( well_ordering @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1668,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1669,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1670,plain,
! [SV87: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ ( relation_rng @ SV87 ) ) )
= $true )
| ( ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 )
= $true )
| ( ( function @ SV87 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1671,plain,
! [SV89: $i,SV14: $i] :
( ( ( subset @ SV14 @ ( relation_rng @ SV89 ) )
= $false )
| ( ( SV14 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV89 @ SV14 )
!= empty_set ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1672,plain,
! [SV109: $i,SV90: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV90 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV109 @ SV15 ) @ ( relation_inverse_image @ SV109 @ SV90 ) )
= $true )
| ( ( relation @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1673,plain,
! [SV91: $i,SV17: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 )
| ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1674,plain,
! [SV92: $i,SV18: $i,SV217: $i] :
( ( ( ~ ( function @ SV217 )
| ~ ( relation @ SV217 )
| ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) ) )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1675,plain,
! [SV115: $i,SV21: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SV115 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV21 @ SV115 ) )
= ( relation_dom @ SV21 ) )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1676,plain,
! [SV116: $i,SV22: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV116 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV116 @ SV22 ) )
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1677,plain,
! [SV24: $i] :
( ( ( one_to_one @ SV24 )
= $false )
| ( ( one_to_one @ ( function_inverse @ SV24 ) )
= $true )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1678,plain,
! [SV25: $i,SV93: $i,SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( function @ SV110 )
= $false )
| ( ( ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1679,plain,
! [SV26: $i,SV94: $i,SV111: $i] :
( ( ( relation @ SV111 )
= $false )
| ( ( function @ SV111 )
= $false )
| ( ( ~ ( in @ SV94 @ SV26 )
| ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1680,plain,
! [SV33: $i] :
( ( ( one_to_one @ SV33 )
= $false )
| ( ( ( function_inverse @ SV33 )
= ( relation_inverse @ SV33 ) )
= $true )
| ( ( function @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1681,plain,
! [SV45: $i,SV218: $i] :
( ( ( ~ ( ~ ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) ) )
| ( SV218
= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1682,plain,
! [SV45: $i,SV219: $i] :
( ( ( ( SV219
!= ( relation_dom @ SV45 ) )
| ~ ( ~ ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) )
| ~ ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1683,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SV220 @ SV46 )
!= ( sK30_SY6442 @ SV220 @ SV46 ) ) ) )
| ( is_antisymmetric_in @ SV46 @ SV220 ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1684,plain,
! [SV221: $i,SV46: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV46 @ SV221 )
| ! [SY6802: $i,SY6803: $i] :
( ~ ( in @ SY6802 @ SV221 )
| ~ ( in @ SY6803 @ SV221 )
| ~ ( in @ ( ordered_pair @ SY6802 @ SY6803 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6803 @ SY6802 ) @ SV46 )
| ( SY6802 = SY6803 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1685,plain,
! [SV118: $i] :
( ( ( relation @ SV118 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV118 ) )
= $true )
| ( ( ! [SY6731: $i] : ( relation @ ( relation_dom_restriction @ SV118 @ SY6731 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1686,plain,
! [SV119: $i] :
( ( ( relation @ SV119 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV119 ) )
= $true )
| ( ( ! [SY6732: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SY6732 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1687,plain,
! [SV104: $i,SV203: $i,SV47: $i,SV222: $i] :
( ( ~ ( relation @ SV222 )
| ~ ( in @ SV47 @ SV203 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1688,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1689,plain,
! [SV104: $i,SV47: $i] :
( ( ~ ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1690,plain,
! [SV180: $i,SV48: $i,SV204: $i] :
( ( ( ~ ( relation @ SV204 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV180 )
| ~ ( in @ SV48 @ ( relation_dom @ SV204 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1691,plain,
! [SV48: $i] :
( ( ! [SY6525: $i,SY6526: $i] :
( ~ ( relation @ SY6526 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6526 @ SY6525 ) ) )
| ( in @ SV48 @ SY6525 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1540]) ).
thf(1692,plain,
! [SV48: $i] :
( ( ! [SY6527: $i,SY6528: $i] :
( ~ ( relation @ SY6528 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6528 @ SY6527 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6528 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1693,plain,
! [SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
| ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1694,plain,
! [SV121: $i] :
( ( ( ~ ( antisymmetric @ SV121 ) )
= $true )
| ( ( ! [SY6733: $i,SY6734: $i] :
( ~ ( in @ ( ordered_pair @ SY6733 @ SY6734 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6734 @ SY6733 ) @ SV121 )
| ( SY6733 = SY6734 ) ) )
= $true )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1695,plain,
! [SV122: $i] :
( ( ( ~ ( connected @ SV122 ) )
= $true )
| ( ( is_connected_in @ SV122 @ ( relation_field @ SV122 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1696,plain,
! [SV123: $i] :
( ( ( ~ ( is_connected_in @ SV123 @ ( relation_field @ SV123 ) ) )
= $true )
| ( ( connected @ SV123 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1697,plain,
! [SV124: $i] :
( ( ( ~ ( is_transitive_in @ SV124 @ ( relation_field @ SV124 ) ) )
= $true )
| ( ( transitive @ SV124 )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1698,plain,
! [SV125: $i] :
( ( ( ~ ( transitive @ SV125 ) )
= $true )
| ( ( is_transitive_in @ SV125 @ ( relation_field @ SV125 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1699,plain,
! [SV49: $i,SV126: $i] :
( ( ( ~ ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) )
| ~ ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1700,plain,
! [SV223: $i,SV50: $i] :
( ( ( ~ ( ~ ! [SY6804: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6804 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SY6804 @ ( sK35_C @ SV223 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) ) )
| ( is_well_founded_in @ SV50 @ SV223 ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1701,plain,
! [SV224: $i,SV50: $i] :
( ( ( ~ ( is_well_founded_in @ SV50 @ SV224 )
| ! [SY6805: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) ) @ SY6805 )
| ~ ( in @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) @ SY6805 ) )
| ( SY6805 = empty_set )
| ~ ( subset @ SY6805 @ SV224 ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1702,plain,
! [SV129: $i] :
( ( ( ~ ( is_reflexive_in @ SV129 @ ( relation_field @ SV129 ) ) )
= $true )
| ( ( reflexive @ SV129 )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1703,plain,
! [SV130: $i] :
( ( ( ~ ( reflexive @ SV130 ) )
= $true )
| ( ( is_reflexive_in @ SV130 @ ( relation_field @ SV130 ) )
= $true )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1704,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) )
| ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1705,plain,
! [SV131: $i] :
( ( ( ~ ( antisymmetric @ SV131 ) )
= $true )
| ( ( is_antisymmetric_in @ SV131 @ ( relation_field @ SV131 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1706,plain,
! [SV132: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV132 @ ( relation_field @ SV132 ) ) )
= $true )
| ( ( antisymmetric @ SV132 )
= $true )
| ( ( relation @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1707,plain,
! [SV52: $i,SV106: $i] :
( ( ( ! [SY6719: $i] :
( ~ ( relation @ SY6719 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY6719 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SY6719 @ SV106 @ SV52 ) ) @ SY6719 ) ) ) )
| ( SY6719
= ( relation_rng_restriction @ SV52 @ SV106 ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1708,plain,
! [SV106: $i,SV52: $i] :
( ( ( ! [SY6720: $i] :
( ~ ( relation @ SY6720 )
| ( SY6720
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6721: $i,SY6722: $i] :
( ~ ( in @ SY6722 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6721 @ SY6722 ) @ SY6720 ) )
| ~ ~ ( ~ ! [SY6551: $i,SY6552: $i] :
( ~ ( in @ ( ordered_pair @ SY6551 @ SY6552 ) @ SY6720 )
| ( in @ SY6552 @ SV52 ) )
| ~ ! [SY6725: $i,SY6726: $i] :
( ~ ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SY6720 )
| ( in @ ( ordered_pair @ SY6725 @ SY6726 ) @ SV106 ) ) ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1709,plain,
! [SV225: $i] :
( ( ~ ( empty @ SV225 )
| ~ ( relation @ SV225 )
| ~ ( function @ SV225 )
| ( function @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1710,plain,
! [SV226: $i] :
( ( ~ ( empty @ SV226 )
| ~ ( relation @ SV226 )
| ~ ( function @ SV226 )
| ( relation @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1711,plain,
! [SV133: $i] :
( ( ( ~ ( empty @ SV133 ) )
= $true )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1712,plain,
! [SV53: $i] :
( ( ( ~ ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1713,plain,
! [SV53: $i] :
( ( ( ~ ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1714,plain,
! [SV136: $i] :
( ( ( ( ( relation_dom @ SV136 )
!= empty_set ) )
= $true )
| ( ( SV136 = empty_set )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1715,plain,
! [SV137: $i] :
( ( ( ( ( relation_rng @ SV137 )
!= empty_set ) )
= $true )
| ( ( SV137 = empty_set )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1716,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
| ( is_transitive_in @ SV54 @ SV227 ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1717,plain,
! [SV228: $i,SV54: $i] :
( ( ( ~ ( is_transitive_in @ SV54 @ SV228 )
| ! [SY6806: $i,SY6807: $i,SY6808: $i] :
( ~ ( in @ SY6806 @ SV228 )
| ~ ( in @ SY6807 @ SV228 )
| ~ ( in @ SY6808 @ SV228 )
| ~ ( in @ ( ordered_pair @ SY6806 @ SY6807 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6807 @ SY6808 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6806 @ SY6808 ) @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1718,plain,
! [SV138: $i] :
( ( ( ~ ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) ) )
= $true )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1719,plain,
! [SV139: $i] :
( ( ( ~ ( reflexive @ SV139 ) )
= $true )
| ( ( ! [SY6743: $i] :
( ~ ( in @ SY6743 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SY6743 @ SY6743 ) @ SV139 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1720,plain,
! [SV181: $i,SV55: $i,SV205: $i] :
( ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( ~ ( in @ SV55 @ SV181 )
| ~ ( in @ SV55 @ ( relation_rng @ SV205 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1721,plain,
! [SV55: $i] :
( ( ! [SY6569: $i,SY6570: $i] :
( ~ ( relation @ SY6570 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6569 @ SY6570 ) ) )
| ( in @ SV55 @ SY6569 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1722,plain,
! [SV55: $i] :
( ( ! [SY6571: $i,SY6572: $i] :
( ~ ( relation @ SY6572 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SY6571 @ SY6572 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6572 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1723,plain,
! [SV140: $i] :
( ( ( ( ( relation_dom @ SV140 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV140 )
= empty_set )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1724,plain,
! [SV141: $i] :
( ( ( ( ( relation_rng @ SV141 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV141 )
= empty_set )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1725,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( function @ SV182 ) )
= $true )
| ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 )
| ( SV182
= ( identity_relation @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1726,plain,
! [SV229: $i] :
( ( ! [SY6809: $i] :
( ~ ( function @ SY6809 )
| ~ ( relation @ SY6809 )
| ( SY6809
!= ( identity_relation @ SV229 ) )
| ! [SY6810: $i] :
( ~ ( in @ SY6810 @ SV229 )
| ( ( apply @ SY6809 @ SY6810 )
= SY6810 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1727,plain,
! [SV230: $i] :
( ( ! [SY6811: $i] :
( ~ ( function @ SY6811 )
| ~ ( relation @ SY6811 )
| ( SY6811
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SY6811 )
= SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1728,plain,
! [SV56: $i] :
( ( ( one_to_one @ SV56 )
= $false )
| ( ( ~ ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1729,plain,
! [SV143: $i] :
( ( ( ~ ( is_well_founded_in @ SV143 @ ( relation_field @ SV143 ) ) )
= $true )
| ( ( well_founded_relation @ SV143 )
= $true )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1730,plain,
! [SV144: $i] :
( ( ( ~ ( well_founded_relation @ SV144 ) )
= $true )
| ( ( is_well_founded_in @ SV144 @ ( relation_field @ SV144 ) )
= $true )
| ( ( relation @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1731,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( relation @ SV231 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
| ( SV57 = SV231 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1732,plain,
! [SV57: $i,SV232: $i] :
( ( ( ~ ( relation @ SV232 )
| ( SV57 != SV232 )
| ~ ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1733,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( relation @ SV233 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
| ( SV233
= ( relation_inverse @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1734,plain,
! [SV58: $i,SV234: $i] :
( ( ( ~ ( relation @ SV234 )
| ( SV234
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1735,plain,
! [SV145: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) ) )
= $true )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1736,plain,
! [SV146: $i] :
( ( ( ~ ( transitive @ SV146 ) )
= $true )
| ( ( ! [SY6745: $i,SY6746: $i,SY6747: $i] :
( ~ ( in @ ( ordered_pair @ SY6745 @ SY6746 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6746 @ SY6747 ) @ SV146 )
| ( in @ ( ordered_pair @ SY6745 @ SY6747 ) @ SV146 ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1737,plain,
! [SV59: $i,SV235: $i] :
( ( ( ! [SY6820: $i] :
( ~ ( relation @ SY6820 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SY6820 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SY6820 @ SV235 @ SV59 ) ) @ SY6820 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SY6820 @ SV235 @ SV59 ) ) @ SY6820 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SY6820 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY6820 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SY6820 @ SV235 @ SV59 ) ) @ SY6820 ) ) ) )
| ( SY6820
= ( relation_dom_restriction @ SV59 @ SV235 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1738,plain,
! [SV236: $i,SV59: $i] :
( ( ( ! [SY6821: $i] :
( ~ ( relation @ SY6821 )
| ( SY6821
!= ( relation_dom_restriction @ SV59 @ SV236 ) )
| ~ ( ~ ! [SY6822: $i,SY6823: $i] :
( ~ ( in @ SY6822 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6822 @ SY6823 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6822 @ SY6823 ) @ SY6821 ) )
| ~ ~ ( ~ ! [SY6824: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY6824 @ SX4 ) @ SY6821 )
| ( in @ SY6824 @ SV236 ) )
| ~ ! [SY6604: $i,SY6605: $i] :
( ~ ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SY6821 )
| ( in @ ( ordered_pair @ SY6604 @ SY6605 ) @ SV59 ) ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1739,plain,
! [SV60: $i,SV237: $i] :
( ( ( ~ ( ~ ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) ) )
| ( SV237
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1740,plain,
! [SV60: $i,SV238: $i] :
( ( ( ( SV238
!= ( relation_rng @ SV60 ) )
| ~ ( ~ ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) )
| ~ ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1741,plain,
! [SV147: $i,SV183: $i] :
( ( ( relation @ SV183 )
= $false )
| ( ( ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
| ( SV183
= ( identity_relation @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1742,plain,
! [SV148: $i,SV184: $i] :
( ( ( relation @ SV184 )
= $false )
| ( ( ( SV184
!= ( identity_relation @ SV148 ) )
| ~ ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1743,plain,
! [SV61: $i,SV185: $i,SV206: $i] :
( ( ( ~ ( function @ SV206 )
| ~ ( relation @ SV206 ) )
= $true )
| ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1744,plain,
! [SV61: $i] :
( ( ! [SY6614: $i,SY6615: $i] :
( ~ ( function @ SY6615 )
| ~ ( relation @ SY6615 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6614 ) @ SY6615 )
| ( SY6614
= ( apply @ SY6615 @ SV61 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1745,plain,
! [SV61: $i] :
( ( ! [SY6616: $i,SY6617: $i] :
( ~ ( function @ SY6617 )
| ~ ( relation @ SY6617 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY6616 ) @ SY6617 )
| ( in @ SV61 @ ( relation_dom @ SY6617 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1746,plain,
! [SV151: $i,SV186: $i] :
( ( ( ~ ( function @ SV186 ) )
= $true )
| ( ( ~ ( relation @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 )
| ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1747,plain,
! [SV152: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 ) )
= $true )
| ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1748,plain,
! [SV153: $i] :
( ( ( function @ SV153 )
= $false )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( one_to_one @ SV153 )
| ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1749,plain,
! [SV154: $i] :
( ( ( function @ SV154 )
= $false )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1750,plain,
! [SV62: $i,SV239: $i] :
( ( ( ~ ( relation @ SV239 )
| ~ ( subset @ SV62 @ SV239 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SV239 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1751,plain,
! [SV62: $i,SV240: $i] :
( ( ( ~ ( relation @ SV240 )
| ~ ( subset @ SV62 @ SV240 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SV240 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1752,plain,
! [SV63: $i,SV241: $i] :
( ( ( ! [SY6832: $i] :
( ~ ( ~ ( ! [SY6833: $i] :
( ~ ( in @ ( ordered_pair @ SY6833 @ ( sK50_D @ SY6832 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6833 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SY6832 @ SV241 @ SV63 ) @ SY6832 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY6832 @ SV241 @ SV63 ) @ ( sK50_D @ SY6832 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SY6832 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SY6832 @ SV241 @ SV63 ) @ SY6832 ) ) )
| ( SY6832
= ( relation_image @ SV63 @ SV241 ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1753,plain,
! [SV242: $i,SV63: $i] :
( ( ( ! [SY6834: $i] :
( ( SY6834
!= ( relation_image @ SV63 @ SV242 ) )
| ~ ( ~ ! [SY6835: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6835 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6835 @ SY6834 ) )
| ~ ! [SY6837: $i] :
( ~ ( in @ SY6837 @ SY6834 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6837 @ SY6834 @ SV242 @ SV63 ) @ SY6837 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6837 @ SY6834 @ SV242 @ SV63 ) @ SV242 ) ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1754,plain,
! [SV188: $i,SV155: $i] :
( ( ( ~ ( empty @ SV155 ) )
= $true )
| ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV155 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1755,plain,
! [SV189: $i,SV156: $i] :
( ( ( ~ ( empty @ SV156 ) )
= $true )
| ( ( ~ ( relation @ SV189 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV156 @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1756,plain,
! [SV190: $i,SV64: $i,SV207: $i] :
( ( ( ~ ( relation @ SV207 ) )
= $true )
| ( ( ! [SY6796: $i] :
( ~ ( in @ SY6796 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6796 ) @ SV207 )
| ~ ( in @ SY6796 @ SV190 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1757,plain,
! [SV191: $i,SV64: $i,SV208: $i] :
( ( ( ~ ( relation @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1758,plain,
! [SV157: $i] :
( ( ( ~ ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1759,plain,
! [SV158: $i] :
( ( ( ~ ( well_founded_relation @ SV158 ) )
= $true )
| ( ( ! [SY6761: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SY6761 @ SV158 ) ) @ SY6761 )
| ~ ( in @ ( sK38_C @ SY6761 @ SV158 ) @ SY6761 ) )
| ( SY6761 = empty_set )
| ~ ( subset @ SY6761 @ ( relation_field @ SV158 ) ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1760,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 )
| ~ ( is_transitive_in @ SV65 @ SV243 )
| ~ ( is_antisymmetric_in @ SV65 @ SV243 )
| ~ ( is_connected_in @ SV65 @ SV243 )
| ~ ( is_well_founded_in @ SV65 @ SV243 )
| ( well_orders @ SV65 @ SV243 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1761,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
| ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1762,plain,
! [SV192: $i,SV66: $i,SV209: $i] :
( ( ( ~ ( relation @ SV209 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SV209 )
| ( in @ SV66 @ ( relation_field @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1763,plain,
! [SV193: $i,SV66: $i,SV210: $i] :
( ( ( ~ ( relation @ SV210 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SV210 )
| ( in @ SV193 @ ( relation_field @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1764,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_C @ SV244 @ SV67 ) @ SV244 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 ) )
| ( is_reflexive_in @ SV67 @ SV244 ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1765,plain,
! [SV245: $i,SV67: $i] :
( ( ( ~ ( is_reflexive_in @ SV67 @ SV245 )
| ! [SY6838: $i] :
( ~ ( in @ SY6838 @ SV245 )
| ( in @ ( ordered_pair @ SY6838 @ SY6838 ) @ SV67 ) ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1766,plain,
! [SV161: $i] :
( ( ( function @ SV161 )
= $false )
| ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
| ( one_to_one @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1767,plain,
! [SV162: $i] :
( ( ( function @ SV162 )
= $false )
| ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( one_to_one @ SV162 )
| ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1768,plain,
! [SV194: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 )
| ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1769,plain,
! [SV195: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1770,plain,
! [SV165: $i] :
( ( ( ~ ! [SY6766: $i,SY6767: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SY6766 @ SY6767 ) ) )
= $false )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1771,plain,
! [SV165: $i] :
( ( ( ~ ( in @ ( sK45_B @ SV165 ) @ SV165 ) )
= $false )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1630]) ).
thf(1772,plain,
! [SV166: $i,SV246: $i] :
( ( ( ( SV246
= ( ordered_pair @ ( sK43_C @ SV246 @ SV166 ) @ ( sK44_SY6449 @ SV246 @ SV166 ) ) )
| ~ ( in @ SV246 @ SV166 ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1773,plain,
! [SV196: $i,SV68: $i,SV211: $i] :
( ( ( ~ ( relation @ SV211 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SV211 )
| ( in @ SV68 @ ( relation_dom @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1774,plain,
! [SV197: $i,SV68: $i,SV212: $i] :
( ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SV212 )
| ( in @ SV197 @ ( relation_rng @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1775,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1776,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1777,plain,
! [SV167: $i] :
( ( ( ~ ( function @ SV167 ) )
= $true )
| ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( ~ ( one_to_one @ SV167 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1778,plain,
! [SV168: $i] :
( ( ( ~ ( function @ SV168 ) )
= $true )
| ( ( ~ ( relation @ SV168 ) )
= $true )
| ( ( ~ ( one_to_one @ SV168 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1639]) ).
thf(1779,plain,
! [SV198: $i,SV69: $i,SV213: $i] :
( ( ( ~ ( relation @ SV213 ) )
= $true )
| ( ( ! [SY6797: $i] :
( ~ ( in @ SY6797 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SY6797 @ SV69 ) @ SV213 )
| ~ ( in @ SY6797 @ SV198 ) )
| ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1780,plain,
! [SV199: $i,SV69: $i,SV214: $i] :
( ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( ~ ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1781,plain,
! [SV70: $i,SV247: $i] :
( ( ( ! [SY6839: $i] :
( ~ ( ~ ( ! [SY6840: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6839 @ SV247 @ SV70 ) @ SY6840 ) @ SV70 )
| ~ ( in @ SY6840 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SY6839 @ SV247 @ SV70 ) @ SY6839 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY6839 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SY6839 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SY6839 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SY6839 @ SV247 @ SV70 ) @ SY6839 ) ) )
| ( SY6839
= ( relation_inverse_image @ SV70 @ SV247 ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1782,plain,
! [SV248: $i,SV70: $i] :
( ( ( ! [SY6841: $i] :
( ( SY6841
!= ( relation_inverse_image @ SV70 @ SV248 ) )
| ~ ( ~ ! [SY6842: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6842 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6842 @ SY6841 ) )
| ~ ! [SY6844: $i] :
( ~ ( in @ SY6844 @ SY6841 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6844 @ ( sK46_E @ SY6844 @ SY6841 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6844 @ SY6841 @ SV248 @ SV70 ) @ SV248 ) ) ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1783,plain,
! [SV71: $i,SV200: $i,SV215: $i] :
( ( ( ~ ( function @ SV215 )
| ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1784,plain,
! [SV71: $i] :
( ( ! [SY6665: $i,SY6666: $i] :
( ~ ( function @ SY6666 )
| ~ ( relation @ SY6666 )
| ~ ( in @ SY6665 @ ( relation_dom @ ( relation_dom_restriction @ SY6666 @ SV71 ) ) )
| ( in @ SY6665 @ ( relation_dom @ SY6666 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1785,plain,
! [SV71: $i] :
( ( ! [SY6667: $i,SY6668: $i] :
( ~ ( function @ SY6668 )
| ~ ( relation @ SY6668 )
| ~ ( in @ SY6667 @ ( relation_dom @ ( relation_dom_restriction @ SY6668 @ SV71 ) ) )
| ( in @ SY6667 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1786,plain,
! [SV72: $i] :
( ( ( ~ ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1787,plain,
! [SV72: $i] :
( ( ( ~ ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1788,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) )
| ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1789,plain,
! [SV74: $i] :
( ( ( ~ ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1790,plain,
! [SV74: $i] :
( ( ( ~ ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1791,plain,
! [SV171: $i] :
( ( ( function @ SV171 )
= $false )
| ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY6769: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY6769 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1792,plain,
! [SV172: $i] :
( ( ( function @ SV172 )
= $false )
| ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY6770: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY6770 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1793,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
| ( subset @ SV75 @ SV249 ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1794,plain,
! [SV75: $i,SV250: $i] :
( ( ( ~ ( relation @ SV250 )
| ~ ( subset @ SV75 @ SV250 )
| ! [SY6845: $i,SY6846: $i] :
( ~ ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV250 ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1795,plain,
! [SV173: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1796,plain,
! [SV174: $i] :
( ( ( ~ ( connected @ SV174 ) )
= $true )
| ( ( ! [SY6771: $i,SY6772: $i] :
( ( SY6771 = SY6772 )
| ~ ( in @ SY6771 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6772 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SY6771 @ SY6772 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6772 @ SY6771 ) @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1797,plain,
! [SV201: $i,SV175: $i] :
( ( ( ~ ( empty @ SV175 ) )
= $true )
| ( ( ~ ( relation @ SV201 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV201 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1798,plain,
! [SV202: $i,SV176: $i] :
( ( ( ~ ( empty @ SV176 ) )
= $true )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV202 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1799,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 ) )
| ( is_connected_in @ SV76 @ SV251 ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1800,plain,
! [SV252: $i,SV76: $i] :
( ( ( ~ ( is_connected_in @ SV76 @ SV252 )
| ! [SY6847: $i,SY6848: $i] :
( ( SY6847 = SY6848 )
| ~ ( in @ SY6847 @ SV252 )
| ~ ( in @ SY6848 @ SV252 )
| ( in @ ( ordered_pair @ SY6847 @ SY6848 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6848 @ SY6847 ) @ SV76 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1801,plain,
! [SV177: $i] :
( ( ( function @ SV177 )
= $false )
| ( ( ~ ( relation @ SV177 ) )
= $true )
| ( ( function @ ( function_inverse @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1802,plain,
! [SV178: $i] :
( ( ( function @ SV178 )
= $false )
| ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1803,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1804,plain,
! [SV77: $i] :
( ( ( ~ ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1666]) ).
thf(1805,plain,
! [SV179: $i] :
( ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 )
| ~ ( connected @ SV179 )
| ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1806,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1807,plain,
! [SV253: $i] :
( ( ~ ( relation @ SV253 )
| ~ ( well_ordering @ SV253 )
| ( well_founded_relation @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1808,plain,
! [SV87: $i,SV11: $i] :
( ( ( subset @ SV11 @ ( relation_rng @ SV87 ) )
= $false )
| ( ( ( relation_image @ SV87 @ ( relation_inverse_image @ SV87 @ SV11 ) )
= SV11 )
= $true )
| ( ( function @ SV87 )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1809,plain,
! [SV14: $i,SV89: $i] :
( ( ( ( relation_inverse_image @ SV89 @ SV14 )
= empty_set )
= $false )
| ( ( SV14 = empty_set )
= $true )
| ( ( subset @ SV14 @ ( relation_rng @ SV89 ) )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1810,plain,
! [SV91: $i,SV17: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 )
| ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1811,plain,
! [SV92: $i,SV18: $i,SV217: $i] :
( ( ( ~ ( function @ SV217 )
| ~ ( relation @ SV217 ) )
= $true )
| ( ( ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) ) )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1812,plain,
! [SV115: $i,SV21: $i] :
( ( ( subset @ ( relation_rng @ SV21 ) @ ( relation_dom @ SV115 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV21 @ SV115 ) )
= ( relation_dom @ SV21 ) )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1813,plain,
! [SV116: $i,SV22: $i] :
( ( ( subset @ ( relation_dom @ SV22 ) @ ( relation_rng @ SV116 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV116 @ SV22 ) )
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1814,plain,
! [SV25: $i,SV110: $i,SV93: $i] :
( ( ( ~ ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1815,plain,
! [SV111: $i,SV26: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV26 ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) )
= $true )
| ( ( function @ SV111 )
= $false )
| ( ( relation @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1816,plain,
! [SV45: $i,SV218: $i] :
( ( ( ~ ( ~ ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) ) ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1817,plain,
! [SV45: $i,SV219: $i] :
( ( ( ( SV219
!= ( relation_dom @ SV45 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) )
| ~ ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1818,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SV220 @ SV46 )
!= ( sK30_SY6442 @ SV220 @ SV46 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1819,plain,
! [SV221: $i,SV46: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV46 @ SV221 ) )
= $true )
| ( ( ! [SY6802: $i,SY6803: $i] :
( ~ ( in @ SY6802 @ SV221 )
| ~ ( in @ SY6803 @ SV221 )
| ~ ( in @ ( ordered_pair @ SY6802 @ SY6803 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6803 @ SY6802 ) @ SV46 )
| ( SY6802 = SY6803 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1820,plain,
! [SV118: $i] :
( ( ( relation_empty_yielding @ SV118 )
= $false )
| ( ( relation @ SV118 )
= $false )
| ( ( ! [SY6731: $i] : ( relation @ ( relation_dom_restriction @ SV118 @ SY6731 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1821,plain,
! [SV119: $i] :
( ( ( relation_empty_yielding @ SV119 )
= $false )
| ( ( relation @ SV119 )
= $false )
| ( ( ! [SY6732: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SY6732 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1822,plain,
! [SV104: $i,SV203: $i,SV47: $i,SV222: $i] :
( ( ( ~ ( relation @ SV222 ) )
= $true )
| ( ( ~ ( in @ SV47 @ SV203 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1823,plain,
! [SV104: $i,SV47: $i] :
( ( ! [SY6712: $i,SY6713: $i] :
( ~ ( relation @ SY6713 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6712 ) @ SY6713 ) )
| ( in @ SV47 @ SY6712 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1824,plain,
! [SV104: $i,SV47: $i] :
( ( ! [SY6714: $i,SY6715: $i] :
( ~ ( relation @ SY6715 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SY6714 ) @ SY6715 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6715 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1825,plain,
! [SV180: $i,SV48: $i,SV204: $i] :
( ( ( relation @ SV204 )
= $false )
| ( ( ~ ( in @ SV48 @ SV180 )
| ~ ( in @ SV48 @ ( relation_dom @ SV204 ) )
| ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1826,plain,
! [SV254: $i,SV48: $i] :
( ( ! [SY6849: $i] :
( ~ ( relation @ SY6849 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6849 @ SV254 ) ) )
| ( in @ SV48 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1827,plain,
! [SV255: $i,SV48: $i] :
( ( ! [SY6850: $i] :
( ~ ( relation @ SY6850 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SY6850 @ SV255 ) ) )
| ( in @ SV48 @ ( relation_dom @ SY6850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1828,plain,
! [SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
| ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1829,plain,
! [SV121: $i] :
( ( ( antisymmetric @ SV121 )
= $false )
| ( ( ! [SY6733: $i,SY6734: $i] :
( ~ ( in @ ( ordered_pair @ SY6733 @ SY6734 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6734 @ SY6733 ) @ SV121 )
| ( SY6733 = SY6734 ) ) )
= $true )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1830,plain,
! [SV122: $i] :
( ( ( connected @ SV122 )
= $false )
| ( ( is_connected_in @ SV122 @ ( relation_field @ SV122 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1831,plain,
! [SV123: $i] :
( ( ( is_connected_in @ SV123 @ ( relation_field @ SV123 ) )
= $false )
| ( ( connected @ SV123 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1832,plain,
! [SV124: $i] :
( ( ( is_transitive_in @ SV124 @ ( relation_field @ SV124 ) )
= $false )
| ( ( transitive @ SV124 )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1833,plain,
! [SV125: $i] :
( ( ( transitive @ SV125 )
= $false )
| ( ( is_transitive_in @ SV125 @ ( relation_field @ SV125 ) )
= $true )
| ( ( relation @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1834,plain,
! [SV49: $i,SV126: $i] :
( ( ( ~ ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) ) )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1835,plain,
! [SV126: $i,SV49: $i] :
( ( ( ~ ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1836,plain,
! [SV223: $i,SV50: $i] :
( ( ( ~ ( ~ ! [SY6804: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6804 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SY6804 @ ( sK35_C @ SV223 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1837,plain,
! [SV224: $i,SV50: $i] :
( ( ( ~ ( is_well_founded_in @ SV50 @ SV224 ) )
= $true )
| ( ( ! [SY6805: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) ) @ SY6805 )
| ~ ( in @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) @ SY6805 ) )
| ( SY6805 = empty_set )
| ~ ( subset @ SY6805 @ SV224 ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1838,plain,
! [SV129: $i] :
( ( ( is_reflexive_in @ SV129 @ ( relation_field @ SV129 ) )
= $false )
| ( ( reflexive @ SV129 )
= $true )
| ( ( relation @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1839,plain,
! [SV130: $i] :
( ( ( reflexive @ SV130 )
= $false )
| ( ( is_reflexive_in @ SV130 @ ( relation_field @ SV130 ) )
= $true )
| ( ( relation @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1840,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1841,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1842,plain,
! [SV131: $i] :
( ( ( antisymmetric @ SV131 )
= $false )
| ( ( is_antisymmetric_in @ SV131 @ ( relation_field @ SV131 ) )
= $true )
| ( ( relation @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1843,plain,
! [SV132: $i] :
( ( ( is_antisymmetric_in @ SV132 @ ( relation_field @ SV132 ) )
= $false )
| ( ( antisymmetric @ SV132 )
= $true )
| ( ( relation @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1844,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( relation @ SV256 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
| ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1845,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ( relation @ SV257 )
| ( SV257
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1846,plain,
! [SV225: $i] :
( ( ( ~ ( empty @ SV225 )
| ~ ( relation @ SV225 )
| ~ ( function @ SV225 ) )
= $true )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1847,plain,
! [SV226: $i] :
( ( ( ~ ( empty @ SV226 )
| ~ ( relation @ SV226 )
| ~ ( function @ SV226 ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1848,plain,
! [SV133: $i] :
( ( ( empty @ SV133 )
= $false )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1849,plain,
! [SV53: $i] :
( ( ( ! [SY6555: $i,SY6556: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ~ ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) ) @ SY6555 )
| ( in @ ( sK52_D @ SY6556 @ SY6555 @ SV53 ) @ SY6556 ) ) ) )
| ( SY6556
= ( relation_inverse_image @ SV53 @ SY6555 ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1850,plain,
! [SV53: $i] :
( ( ( ! [SY6557: $i,SY6558: $i] :
( ( SY6558
!= ( relation_inverse_image @ SV53 @ SY6557 ) )
| ~ ( ~ ! [SY6559: $i] :
( ~ ( in @ SY6559 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6559 ) @ SY6557 )
| ( in @ SY6559 @ SY6558 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6558 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6561: $i] :
( ~ ( in @ SY6561 @ SY6558 )
| ( in @ ( apply @ SV53 @ SY6561 ) @ SY6557 ) ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1851,plain,
! [SV136: $i] :
( ( ( ( relation_dom @ SV136 )
= empty_set )
= $false )
| ( ( SV136 = empty_set )
= $true )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1852,plain,
! [SV137: $i] :
( ( ( ( relation_rng @ SV137 )
= empty_set )
= $false )
| ( ( SV137 = empty_set )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1853,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1854,plain,
! [SV228: $i,SV54: $i] :
( ( ( ~ ( is_transitive_in @ SV54 @ SV228 ) )
= $true )
| ( ( ! [SY6806: $i,SY6807: $i,SY6808: $i] :
( ~ ( in @ SY6806 @ SV228 )
| ~ ( in @ SY6807 @ SV228 )
| ~ ( in @ SY6808 @ SV228 )
| ~ ( in @ ( ordered_pair @ SY6806 @ SY6807 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6807 @ SY6808 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6806 @ SY6808 ) @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1855,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
= $false )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1856,plain,
! [SV139: $i] :
( ( ( reflexive @ SV139 )
= $false )
| ( ( ! [SY6743: $i] :
( ~ ( in @ SY6743 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SY6743 @ SY6743 ) @ SV139 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1857,plain,
! [SV181: $i,SV55: $i,SV205: $i] :
( ( ( relation @ SV205 )
= $false )
| ( ( ~ ( in @ SV55 @ SV181 )
| ~ ( in @ SV55 @ ( relation_rng @ SV205 ) )
| ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1858,plain,
! [SV258: $i,SV55: $i] :
( ( ! [SY6857: $i] :
( ~ ( relation @ SY6857 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SY6857 ) ) )
| ( in @ SV55 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1859,plain,
! [SV259: $i,SV55: $i] :
( ( ! [SY6858: $i] :
( ~ ( relation @ SY6858 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SY6858 ) ) )
| ( in @ SV55 @ ( relation_rng @ SY6858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1860,plain,
! [SV140: $i] :
( ( ( ( relation_dom @ SV140 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV140 )
= empty_set )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1861,plain,
! [SV141: $i] :
( ( ( ( relation_rng @ SV141 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV141 )
= empty_set )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1862,plain,
! [SV142: $i,SV182: $i] :
( ( ( function @ SV182 )
= $false )
| ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 )
| ( SV182
= ( identity_relation @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1863,plain,
! [SV229: $i,SV260: $i] :
( ( ~ ( function @ SV260 )
| ~ ( relation @ SV260 )
| ( SV260
!= ( identity_relation @ SV229 ) )
| ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1864,plain,
! [SV230: $i,SV261: $i] :
( ( ~ ( function @ SV261 )
| ~ ( relation @ SV261 )
| ( SV261
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SV261 )
= SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1865,plain,
! [SV56: $i] :
( ( ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) )
| ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1866,plain,
! [SV143: $i] :
( ( ( is_well_founded_in @ SV143 @ ( relation_field @ SV143 ) )
= $false )
| ( ( well_founded_relation @ SV143 )
= $true )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1867,plain,
! [SV144: $i] :
( ( ( well_founded_relation @ SV144 )
= $false )
| ( ( is_well_founded_in @ SV144 @ ( relation_field @ SV144 ) )
= $true )
| ( ( relation @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1868,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( relation @ SV231 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
| ( SV57 = SV231 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1869,plain,
! [SV57: $i,SV232: $i] :
( ( ( ~ ( relation @ SV232 ) )
= $true )
| ( ( ( SV57 != SV232 )
| ~ ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1870,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( relation @ SV233 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
| ( SV233
= ( relation_inverse @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1871,plain,
! [SV58: $i,SV234: $i] :
( ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ( SV234
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(1872,plain,
! [SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1873,plain,
! [SV146: $i] :
( ( ( transitive @ SV146 )
= $false )
| ( ( ! [SY6745: $i,SY6746: $i,SY6747: $i] :
( ~ ( in @ ( ordered_pair @ SY6745 @ SY6746 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6746 @ SY6747 ) @ SV146 )
| ( in @ ( ordered_pair @ SY6745 @ SY6747 ) @ SV146 ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1874,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1875,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 )
| ( SV263
!= ( relation_dom_restriction @ SV59 @ SV236 ) )
| ~ ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1876,plain,
! [SV60: $i,SV237: $i] :
( ( ( ~ ( ~ ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) ) ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1877,plain,
! [SV60: $i,SV238: $i] :
( ( ( ( SV238
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) )
| ~ ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1878,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1741]) ).
thf(1879,plain,
! [SV148: $i,SV184: $i] :
( ( ( ( SV184
!= ( identity_relation @ SV148 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) ) )
= $true )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1880,plain,
! [SV61: $i,SV185: $i,SV206: $i] :
( ( ( ~ ( function @ SV206 ) )
= $true )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(1881,plain,
! [SV264: $i,SV61: $i] :
( ( ! [SY6866: $i] :
( ~ ( function @ SY6866 )
| ~ ( relation @ SY6866 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SY6866 )
| ( SV264
= ( apply @ SY6866 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1882,plain,
! [SV265: $i,SV61: $i] :
( ( ! [SY6867: $i] :
( ~ ( function @ SY6867 )
| ~ ( relation @ SY6867 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SY6867 )
| ( in @ SV61 @ ( relation_dom @ SY6867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(1883,plain,
! [SV151: $i,SV186: $i] :
( ( ( function @ SV186 )
= $false )
| ( ( ~ ( relation @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 )
| ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1884,plain,
! [SV152: $i,SV187: $i] :
( ( ( function @ SV187 )
= $false )
| ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1885,plain,
! [SV153: $i] :
( ( ( relation @ SV153 )
= $false )
| ( ( function @ SV153 )
= $false )
| ( ( ~ ( one_to_one @ SV153 )
| ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1886,plain,
! [SV154: $i] :
( ( ( relation @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( ~ ( one_to_one @ SV154 )
| ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1887,plain,
! [SV62: $i,SV239: $i] :
( ( ( ~ ( relation @ SV239 ) )
= $true )
| ( ( ~ ( subset @ SV62 @ SV239 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SV239 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1888,plain,
! [SV62: $i,SV240: $i] :
( ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ~ ( subset @ SV62 @ SV240 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SV240 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1889,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ~ ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) ) )
| ( SV266
= ( relation_image @ SV63 @ SV241 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1890,plain,
! [SV242: $i,SV63: $i,SV267: $i] :
( ( ( ( SV267
!= ( relation_image @ SV63 @ SV242 ) )
| ~ ( ~ ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) )
| ~ ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1891,plain,
! [SV188: $i,SV155: $i] :
( ( ( empty @ SV155 )
= $false )
| ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV155 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1892,plain,
! [SV189: $i,SV156: $i] :
( ( ( empty @ SV156 )
= $false )
| ( ( ~ ( relation @ SV189 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV156 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1893,plain,
! [SV190: $i,SV64: $i,SV207: $i] :
( ( ( relation @ SV207 )
= $false )
| ( ( ! [SY6796: $i] :
( ~ ( in @ SY6796 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6796 ) @ SV207 )
| ~ ( in @ SY6796 @ SV190 ) )
| ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1894,plain,
! [SV191: $i,SV64: $i,SV208: $i] :
( ( ( relation @ SV208 )
= $false )
| ( ( ~ ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1895,plain,
! [SV157: $i] :
( ( ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1896,plain,
! [SV158: $i] :
( ( ( well_founded_relation @ SV158 )
= $false )
| ( ( ! [SY6761: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SY6761 @ SV158 ) ) @ SY6761 )
| ~ ( in @ ( sK38_C @ SY6761 @ SV158 ) @ SY6761 ) )
| ( SY6761 = empty_set )
| ~ ( subset @ SY6761 @ ( relation_field @ SV158 ) ) ) )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1897,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 )
| ~ ( is_transitive_in @ SV65 @ SV243 )
| ~ ( is_antisymmetric_in @ SV65 @ SV243 )
| ~ ( is_connected_in @ SV65 @ SV243 )
| ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1898,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1899,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1761]) ).
thf(1900,plain,
! [SV192: $i,SV66: $i,SV209: $i] :
( ( ( relation @ SV209 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SV209 )
| ( in @ SV66 @ ( relation_field @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1901,plain,
! [SV193: $i,SV66: $i,SV210: $i] :
( ( ( relation @ SV210 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SV210 )
| ( in @ SV193 @ ( relation_field @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1902,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_C @ SV244 @ SV67 ) @ SV244 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 ) ) )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(1903,plain,
! [SV245: $i,SV67: $i] :
( ( ( ~ ( is_reflexive_in @ SV67 @ SV245 ) )
= $true )
| ( ( ! [SY6838: $i] :
( ~ ( in @ SY6838 @ SV245 )
| ( in @ ( ordered_pair @ SY6838 @ SY6838 ) @ SV67 ) ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1904,plain,
! [SV161: $i] :
( ( ( relation @ SV161 )
= $false )
| ( ( function @ SV161 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
| ( one_to_one @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1905,plain,
! [SV162: $i] :
( ( ( relation @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( ~ ( one_to_one @ SV162 )
| ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1906,plain,
! [SV194: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 )
| ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1907,plain,
! [SV195: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 )
| ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1908,plain,
! [SV165: $i] :
( ( ( ! [SY6766: $i,SY6767: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SY6766 @ SY6767 ) ) )
= $true )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1909,plain,
! [SV165: $i] :
( ( ( in @ ( sK45_B @ SV165 ) @ SV165 )
= $true )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1910,plain,
! [SV166: $i,SV246: $i] :
( ( ( SV246
= ( ordered_pair @ ( sK43_C @ SV246 @ SV166 ) @ ( sK44_SY6449 @ SV246 @ SV166 ) ) )
= $true )
| ( ( ~ ( in @ SV246 @ SV166 ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1911,plain,
! [SV196: $i,SV68: $i,SV211: $i] :
( ( ( relation @ SV211 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SV211 )
| ( in @ SV68 @ ( relation_dom @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1912,plain,
! [SV197: $i,SV68: $i,SV212: $i] :
( ( ( relation @ SV212 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SV212 )
| ( in @ SV197 @ ( relation_rng @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1913,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1914,plain,
( ( ~ ( epsilon_transitive @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1915,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1916,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1917,plain,
! [SV167: $i] :
( ( ( function @ SV167 )
= $false )
| ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( ~ ( one_to_one @ SV167 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1918,plain,
! [SV168: $i] :
( ( ( function @ SV168 )
= $false )
| ( ( ~ ( relation @ SV168 ) )
= $true )
| ( ( ~ ( one_to_one @ SV168 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1919,plain,
! [SV198: $i,SV69: $i,SV213: $i] :
( ( ( relation @ SV213 )
= $false )
| ( ( ! [SY6797: $i] :
( ~ ( in @ SY6797 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SY6797 @ SV69 ) @ SV213 )
| ~ ( in @ SY6797 @ SV198 ) )
| ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1920,plain,
! [SV199: $i,SV69: $i,SV214: $i] :
( ( ( relation @ SV214 )
= $false )
| ( ( ~ ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1921,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ~ ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) ) )
| ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(1922,plain,
! [SV248: $i,SV70: $i,SV269: $i] :
( ( ( ( SV269
!= ( relation_inverse_image @ SV70 @ SV248 ) )
| ~ ( ~ ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) )
| ~ ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1923,plain,
! [SV71: $i,SV200: $i,SV215: $i] :
( ( ( ~ ( function @ SV215 ) )
= $true )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1783]) ).
thf(1924,plain,
! [SV71: $i,SV270: $i] :
( ( ! [SY6876: $i] :
( ~ ( function @ SY6876 )
| ~ ( relation @ SY6876 )
| ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SY6876 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SY6876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1925,plain,
! [SV71: $i,SV271: $i] :
( ( ! [SY6877: $i] :
( ~ ( function @ SY6877 )
| ~ ( relation @ SY6877 )
| ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SY6877 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1926,plain,
! [SV72: $i] :
( ( ( ! [SY6669: $i] :
( ~ ( ~ ( ! [SY6670: $i] :
( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ SY6670 ) )
| ~ ( in @ SY6670 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) )
| ~ ( ~ ( ( ( sK27_C @ SY6669 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SY6669 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY6669 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SY6669 @ SV72 ) @ SY6669 ) ) )
| ( SY6669
= ( relation_rng @ SV72 ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1927,plain,
! [SV72: $i] :
( ( ( ! [SY6671: $i] :
( ( SY6671
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6672: $i] :
( ! [SY6673: $i] :
( ( SY6672
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6672 @ SY6671 ) )
| ~ ! [SY6674: $i] :
( ~ ( in @ SY6674 @ SY6671 )
| ~ ( ( SY6674
!= ( apply @ SV72 @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6674 @ SY6671 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1928,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1929,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1930,plain,
! [SV74: $i] :
( ( ( ! [SY6680: $i,SY6681: $i] :
( ~ ( ~ ( ! [SY6682: $i] :
( ~ ( in @ SY6682 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6682 @ SY6680 )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ SY6682 ) ) )
| ~ ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) @ SY6680 ) )
| ( ( sK56_D @ SY6681 @ SY6680 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6681 @ SY6680 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6681 @ SY6680 @ SV74 ) @ SY6681 ) ) )
| ( SY6681
= ( relation_image @ SV74 @ SY6680 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1931,plain,
! [SV74: $i] :
( ( ( ! [SY6683: $i,SY6684: $i] :
( ( SY6684
!= ( relation_image @ SV74 @ SY6683 ) )
| ~ ( ~ ! [SY6685: $i] :
( ! [SY6686: $i] :
( ~ ( in @ SY6686 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6686 @ SY6683 )
| ( SY6685
!= ( apply @ SV74 @ SY6686 ) ) )
| ( in @ SY6685 @ SY6684 ) )
| ~ ! [SY6687: $i] :
( ~ ( in @ SY6687 @ SY6684 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) @ SY6683 ) )
| ( SY6687
!= ( apply @ SV74 @ ( sK55_E @ SY6687 @ SY6684 @ SY6683 @ SV74 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1932,plain,
! [SV171: $i] :
( ( ( relation @ SV171 )
= $false )
| ( ( function @ SV171 )
= $false )
| ( ( ! [SY6769: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY6769 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1933,plain,
! [SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( function @ SV172 )
= $false )
| ( ( ! [SY6770: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY6770 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1934,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
| ( subset @ SV75 @ SV249 ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1935,plain,
! [SV75: $i,SV250: $i] :
( ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( ~ ( subset @ SV75 @ SV250 )
| ! [SY6845: $i,SY6846: $i] :
( ~ ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV250 ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1936,plain,
! [SV173: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(1937,plain,
! [SV174: $i] :
( ( ( connected @ SV174 )
= $false )
| ( ( ! [SY6771: $i,SY6772: $i] :
( ( SY6771 = SY6772 )
| ~ ( in @ SY6771 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6772 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SY6771 @ SY6772 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6772 @ SY6771 ) @ SV174 ) ) )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1938,plain,
! [SV201: $i,SV175: $i] :
( ( ( empty @ SV175 )
= $false )
| ( ( ~ ( relation @ SV201 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV201 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1939,plain,
! [SV202: $i,SV176: $i] :
( ( ( empty @ SV176 )
= $false )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV202 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1940,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1941,plain,
! [SV252: $i,SV76: $i] :
( ( ( ~ ( is_connected_in @ SV76 @ SV252 ) )
= $true )
| ( ( ! [SY6847: $i,SY6848: $i] :
( ( SY6847 = SY6848 )
| ~ ( in @ SY6847 @ SV252 )
| ~ ( in @ SY6848 @ SV252 )
| ( in @ ( ordered_pair @ SY6847 @ SY6848 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6848 @ SY6847 ) @ SV76 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1942,plain,
! [SV177: $i] :
( ( ( relation @ SV177 )
= $false )
| ( ( function @ SV177 )
= $false )
| ( ( function @ ( function_inverse @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1943,plain,
! [SV178: $i] :
( ( ( relation @ SV178 )
= $false )
| ( ( function @ SV178 )
= $false )
| ( ( relation @ ( function_inverse @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1944,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1945,plain,
! [SV77: $i] :
( ( ( ~ ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1946,plain,
! [SV179: $i] :
( ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 )
| ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1947,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1948,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1806]) ).
thf(1949,plain,
! [SV253: $i] :
( ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( ~ ( well_ordering @ SV253 )
| ( well_founded_relation @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1950,plain,
! [SV91: $i,SV17: $i,SV216: $i] :
( ( ( ~ ( function @ SV216 ) )
= $true )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1951,plain,
! [SV92: $i,SV18: $i,SV217: $i] :
( ( ( ~ ( function @ SV217 ) )
= $true )
| ( ( ~ ( relation @ SV217 ) )
= $true )
| ( ( ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) ) )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1952,plain,
! [SV25: $i,SV110: $i,SV93: $i] :
( ( ( in @ SV93 @ ( relation_dom @ ( relation_dom_restriction @ SV110 @ SV25 ) ) )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV110 @ SV25 ) @ SV93 )
= ( apply @ SV110 @ SV93 ) )
= $true )
| ( ( function @ SV110 )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1953,plain,
! [SV111: $i,SV26: $i,SV94: $i] :
( ( ( in @ SV94 @ SV26 )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV111 @ SV26 ) @ SV94 )
= ( apply @ SV111 @ SV94 ) )
= $true )
| ( ( function @ SV111 )
= $false )
| ( ( relation @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1954,plain,
! [SV45: $i,SV218: $i] :
( ( ( ~ ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) ) )
= $false )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1955,plain,
! [SV45: $i,SV219: $i] :
( ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( ~ ( ~ ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) )
| ~ ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1956,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( ( ( sK29_C @ SV220 @ SV46 )
!= ( sK30_SY6442 @ SV220 @ SV46 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1957,plain,
! [SV221: $i,SV46: $i] :
( ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( ! [SY6802: $i,SY6803: $i] :
( ~ ( in @ SY6802 @ SV221 )
| ~ ( in @ SY6803 @ SV221 )
| ~ ( in @ ( ordered_pair @ SY6802 @ SY6803 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6803 @ SY6802 ) @ SV46 )
| ( SY6802 = SY6803 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1958,plain,
! [SV272: $i,SV118: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV118 @ SV272 ) )
= $true )
| ( ( relation @ SV118 )
= $false )
| ( ( relation_empty_yielding @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1959,plain,
! [SV273: $i,SV119: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV119 @ SV273 ) )
= $true )
| ( ( relation @ SV119 )
= $false )
| ( ( relation_empty_yielding @ SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(1960,plain,
! [SV104: $i,SV203: $i,SV47: $i,SV222: $i] :
( ( ( relation @ SV222 )
= $false )
| ( ( ~ ( in @ SV47 @ SV203 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1961,plain,
! [SV274: $i,SV104: $i,SV47: $i] :
( ( ! [SY6878: $i] :
( ~ ( relation @ SY6878 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SY6878 ) )
| ( in @ SV47 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(1962,plain,
! [SV275: $i,SV104: $i,SV47: $i] :
( ( ! [SY6879: $i] :
( ~ ( relation @ SY6879 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SY6879 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SY6879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(1963,plain,
! [SV204: $i,SV180: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV180 )
| ~ ( in @ SV48 @ ( relation_dom @ SV204 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1964,plain,
! [SV254: $i,SV48: $i,SV276: $i] :
( ( ~ ( relation @ SV276 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV276 @ SV254 ) ) )
| ( in @ SV48 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1965,plain,
! [SV255: $i,SV48: $i,SV277: $i] :
( ( ~ ( relation @ SV277 )
| ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV277 @ SV255 ) ) )
| ( in @ SV48 @ ( relation_dom @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1966,plain,
! [SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1967,plain,
! [SV120: $i] :
( ( ( ~ ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1968,plain,
! [SV121: $i,SV278: $i] :
( ( ( ! [SY6880: $i] :
( ~ ( in @ ( ordered_pair @ SV278 @ SY6880 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SY6880 @ SV278 ) @ SV121 )
| ( SV278 = SY6880 ) ) )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1969,plain,
! [SV49: $i,SV126: $i] :
( ( ( ! [SY6735: $i] :
( ~ ( relation @ SY6735 )
| ~ ( ~ ( ! [SY6736: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ SY6736 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6736 @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY6735 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SY6735 @ SV126 @ SV49 ) ) @ SY6735 ) ) )
| ( SY6735
= ( relation_composition @ SV49 @ SV126 ) ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1970,plain,
! [SV126: $i,SV49: $i] :
( ( ( ! [SY6737: $i] :
( ~ ( relation @ SY6737 )
| ( SY6737
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6738: $i,SY6739: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6738 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6739 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6738 @ SY6739 ) @ SY6737 ) )
| ~ ! [SY6741: $i,SY6742: $i] :
( ~ ( in @ ( ordered_pair @ SY6741 @ SY6742 ) @ SY6737 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6741 @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6742 @ SY6741 @ SY6737 @ SV126 @ SV49 ) @ SY6742 ) @ SV126 ) ) ) ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(1971,plain,
! [SV223: $i,SV50: $i] :
( ( ( ~ ! [SY6804: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6804 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SY6804 @ ( sK35_C @ SV223 @ SV50 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1972,plain,
! [SV224: $i,SV50: $i] :
( ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( ! [SY6805: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) ) @ SY6805 )
| ~ ( in @ ( sK34_D @ SY6805 @ SV224 @ SV50 ) @ SY6805 ) )
| ( SY6805 = empty_set )
| ~ ( subset @ SY6805 @ SV224 ) ) )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1973,plain,
! [SV105: $i,SV51: $i] :
( ( ( ! [SY6716: $i] :
( ~ ( function @ SY6716 )
| ~ ( relation @ SY6716 )
| ~ ( in @ SV51 @ ( relation_dom @ SY6716 ) )
| ~ ( in @ ( apply @ SY6716 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6716 @ SV105 ) ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1974,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1841]) ).
thf(1975,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( relation @ SV256 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
| ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(1976,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ( relation @ SV257 ) )
= $true )
| ( ( ( SV257
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1977,plain,
! [SV225: $i] :
( ( ( ~ ( empty @ SV225 )
| ~ ( relation @ SV225 ) )
= $true )
| ( ( ~ ( function @ SV225 ) )
= $true )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1978,plain,
! [SV226: $i] :
( ( ( ~ ( empty @ SV226 )
| ~ ( relation @ SV226 ) )
= $true )
| ( ( ~ ( function @ SV226 ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1979,plain,
! [SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( empty @ SV133 )
= $false )
| ( ( ~ ( function @ SV133 ) )
= $true )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1848]) ).
thf(1980,plain,
! [SV53: $i,SV279: $i] :
( ( ( ! [SY6881: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) @ SY6881 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) @ SY6881 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SY6881 @ SV279 @ SV53 ) @ SY6881 ) ) ) )
| ( SY6881
= ( relation_inverse_image @ SV53 @ SV279 ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1981,plain,
! [SV280: $i,SV53: $i] :
( ( ( ! [SY6882: $i] :
( ( SY6882
!= ( relation_inverse_image @ SV53 @ SV280 ) )
| ~ ( ~ ! [SY6883: $i] :
( ~ ( in @ SY6883 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6883 ) @ SV280 )
| ( in @ SY6883 @ SY6882 ) )
| ~ ~ ( ~ ! [SY6560: $i] :
( ~ ( in @ SY6560 @ SY6882 )
| ( in @ SY6560 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6885: $i] :
( ~ ( in @ SY6885 @ SY6882 )
| ( in @ ( apply @ SV53 @ SY6885 ) @ SV280 ) ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1982,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1983,plain,
! [SV228: $i,SV54: $i] :
( ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( ! [SY6806: $i,SY6807: $i,SY6808: $i] :
( ~ ( in @ SY6806 @ SV228 )
| ~ ( in @ SY6807 @ SV228 )
| ~ ( in @ SY6808 @ SV228 )
| ~ ( in @ ( ordered_pair @ SY6806 @ SY6807 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6807 @ SY6808 ) @ SV54 )
| ( in @ ( ordered_pair @ SY6806 @ SY6808 ) @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1984,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) ) )
= $false )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(1985,plain,
! [SV138: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
= $false )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(1986,plain,
! [SV139: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ ( relation_field @ SV139 ) )
| ( in @ ( ordered_pair @ SV281 @ SV281 ) @ SV139 ) )
= $true )
| ( ( reflexive @ SV139 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(1987,plain,
! [SV205: $i,SV181: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV181 )
| ~ ( in @ SV55 @ ( relation_rng @ SV205 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1988,plain,
! [SV258: $i,SV55: $i,SV282: $i] :
( ( ~ ( relation @ SV282 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SV282 ) ) )
| ( in @ SV55 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(1989,plain,
! [SV259: $i,SV55: $i,SV283: $i] :
( ( ~ ( relation @ SV283 )
| ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SV283 ) ) )
| ( in @ SV55 @ ( relation_rng @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(1990,plain,
! [SV142: $i,SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 )
| ( SV182
= ( identity_relation @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(1991,plain,
! [SV229: $i,SV260: $i] :
( ( ( ~ ( function @ SV260 )
| ~ ( relation @ SV260 ) )
= $true )
| ( ( ( SV260
!= ( identity_relation @ SV229 ) )
| ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1992,plain,
! [SV230: $i,SV261: $i] :
( ( ( ~ ( function @ SV261 )
| ~ ( relation @ SV261 ) )
= $true )
| ( ( ( SV261
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SV261 )
= SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1993,plain,
! [SV56: $i] :
( ( ( ~ ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1994,plain,
! [SV56: $i] :
( ( ( ~ ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1995,plain,
! [SV57: $i,SV231: $i] :
( ( ( relation @ SV231 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
| ( SV57 = SV231 ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1996,plain,
! [SV57: $i,SV232: $i] :
( ( ( relation @ SV232 )
= $false )
| ( ( ( SV57 != SV232 )
| ~ ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) ) )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1997,plain,
! [SV58: $i,SV233: $i] :
( ( ( relation @ SV233 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
| ( SV233
= ( relation_inverse @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1998,plain,
! [SV58: $i,SV234: $i] :
( ( ( relation @ SV234 )
= $false )
| ( ( ( SV234
!= ( relation_inverse @ SV58 ) )
| ~ ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1871]) ).
thf(1999,plain,
! [SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(2000,plain,
! [SV145: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(2001,plain,
! [SV146: $i,SV284: $i] :
( ( ( ! [SY6886: $i,SY6887: $i] :
( ~ ( in @ ( ordered_pair @ SV284 @ SY6886 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SY6886 @ SY6887 ) @ SV146 )
| ( in @ ( ordered_pair @ SV284 @ SY6887 ) @ SV146 ) ) )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2002,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2003,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 ) )
= $true )
| ( ( ( SV263
!= ( relation_dom_restriction @ SV59 @ SV236 ) )
| ~ ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2004,plain,
! [SV60: $i,SV237: $i] :
( ( ( ~ ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) ) )
= $false )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2005,plain,
! [SV60: $i,SV238: $i] :
( ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( ~ ( ~ ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) )
| ~ ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2006,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2007,plain,
! [SV148: $i,SV184: $i] :
( ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( ~ ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) ) )
= $true )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2008,plain,
! [SV61: $i,SV185: $i,SV206: $i] :
( ( ( function @ SV206 )
= $false )
| ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2009,plain,
! [SV264: $i,SV61: $i,SV285: $i] :
( ( ~ ( function @ SV285 )
| ~ ( relation @ SV285 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
| ( SV264
= ( apply @ SV285 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2010,plain,
! [SV265: $i,SV61: $i,SV286: $i] :
( ( ~ ( function @ SV286 )
| ~ ( relation @ SV286 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
| ( in @ SV61 @ ( relation_dom @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2011,plain,
! [SV151: $i,SV186: $i] :
( ( ( relation @ SV186 )
= $false )
| ( ( function @ SV186 )
= $false )
| ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 )
| ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(2012,plain,
! [SV152: $i,SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( function @ SV187 )
= $false )
| ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 )
| ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(2013,plain,
! [SV153: $i] :
( ( ( ~ ( one_to_one @ SV153 ) )
= $true )
| ( ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2014,plain,
! [SV154: $i] :
( ( ( ~ ( one_to_one @ SV154 ) )
= $true )
| ( ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2015,plain,
! [SV62: $i,SV239: $i] :
( ( ( relation @ SV239 )
= $false )
| ( ( ~ ( subset @ SV62 @ SV239 )
| ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SV239 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2016,plain,
! [SV62: $i,SV240: $i] :
( ( ( relation @ SV240 )
= $false )
| ( ( ~ ( subset @ SV62 @ SV240 )
| ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SV240 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2017,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ~ ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) ) ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2018,plain,
! [SV242: $i,SV63: $i,SV267: $i] :
( ( ( ( SV267
!= ( relation_image @ SV63 @ SV242 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) )
| ~ ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2019,plain,
! [SV155: $i,SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( empty @ SV155 )
= $false )
| ( ( empty @ ( relation_composition @ SV155 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2020,plain,
! [SV156: $i,SV189: $i] :
( ( ( relation @ SV189 )
= $false )
| ( ( empty @ SV156 )
= $false )
| ( ( relation @ ( relation_composition @ SV156 @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(2021,plain,
! [SV190: $i,SV64: $i,SV207: $i] :
( ( ( ! [SY6796: $i] :
( ~ ( in @ SY6796 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SY6796 ) @ SV207 )
| ~ ( in @ SY6796 @ SV190 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2022,plain,
! [SV191: $i,SV208: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) ) )
= $true )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2023,plain,
! [SV157: $i] :
( ( ( ~ ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(2024,plain,
! [SV157: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1895]) ).
thf(2025,plain,
! [SV287: $i,SV158: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
| ~ ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 ) )
| ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2026,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 )
| ~ ( is_transitive_in @ SV65 @ SV243 )
| ~ ( is_antisymmetric_in @ SV65 @ SV243 )
| ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2027,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1898]) ).
thf(2028,plain,
! [SV65: $i] :
( ( ( ! [SY6638: $i] :
( ~ ( well_orders @ SV65 @ SY6638 )
| ( is_well_founded_in @ SV65 @ SY6638 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2029,plain,
! [SV209: $i,SV192: $i,SV66: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SV209 ) )
= $true )
| ( ( in @ SV66 @ ( relation_field @ SV209 ) )
= $true )
| ( ( relation @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2030,plain,
! [SV210: $i,SV193: $i,SV66: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SV210 ) )
= $true )
| ( ( in @ SV193 @ ( relation_field @ SV210 ) )
= $true )
| ( ( relation @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2031,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV244 @ SV67 ) @ SV244 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2032,plain,
! [SV245: $i,SV67: $i] :
( ( ( is_reflexive_in @ SV67 @ SV245 )
= $false )
| ( ( ! [SY6838: $i] :
( ~ ( in @ SY6838 @ SV245 )
| ( in @ ( ordered_pair @ SY6838 @ SY6838 ) @ SV67 ) ) )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2033,plain,
! [SV161: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2034,plain,
! [SV162: $i] :
( ( ( ~ ( one_to_one @ SV162 ) )
= $true )
| ( ( ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2035,plain,
! [SV194: $i,SV163: $i] :
( ( ( ~ ( function @ SV163 ) )
= $true )
| ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2036,plain,
! [SV195: $i,SV164: $i] :
( ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2037,plain,
! [SV288: $i,SV165: $i] :
( ( ( ! [SY6888: $i] :
( ( sK45_B @ SV165 )
!= ( ordered_pair @ SV288 @ SY6888 ) ) )
= $true )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2038,plain,
! [SV166: $i,SV246: $i] :
( ( ( in @ SV246 @ SV166 )
= $false )
| ( ( SV246
= ( ordered_pair @ ( sK43_C @ SV246 @ SV166 ) @ ( sK44_SY6449 @ SV246 @ SV166 ) ) )
= $true )
| ( ( relation @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1910]) ).
thf(2039,plain,
! [SV211: $i,SV196: $i,SV68: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SV211 ) )
= $true )
| ( ( in @ SV68 @ ( relation_dom @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2040,plain,
! [SV212: $i,SV197: $i,SV68: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SV212 ) )
= $true )
| ( ( in @ SV197 @ ( relation_rng @ SV212 ) )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2041,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2042,plain,
( ( epsilon_transitive @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2043,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2044,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(2045,plain,
! [SV167: $i] :
( ( ( relation @ SV167 )
= $false )
| ( ( function @ SV167 )
= $false )
| ( ( ~ ( one_to_one @ SV167 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2046,plain,
! [SV168: $i] :
( ( ( relation @ SV168 )
= $false )
| ( ( function @ SV168 )
= $false )
| ( ( ~ ( one_to_one @ SV168 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2047,plain,
! [SV198: $i,SV69: $i,SV213: $i] :
( ( ( ! [SY6797: $i] :
( ~ ( in @ SY6797 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SY6797 @ SV69 ) @ SV213 )
| ~ ( in @ SY6797 @ SV198 ) ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(2048,plain,
! [SV199: $i,SV214: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2049,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ~ ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) ) ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2050,plain,
! [SV248: $i,SV70: $i,SV269: $i] :
( ( ( ( SV269
!= ( relation_inverse_image @ SV70 @ SV248 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) )
| ~ ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2051,plain,
! [SV71: $i,SV200: $i,SV215: $i] :
( ( ( function @ SV215 )
= $false )
| ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2052,plain,
! [SV71: $i,SV270: $i,SV289: $i] :
( ( ~ ( function @ SV289 )
| ~ ( relation @ SV289 )
| ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2053,plain,
! [SV71: $i,SV271: $i,SV290: $i] :
( ( ~ ( function @ SV290 )
| ~ ( relation @ SV290 )
| ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2054,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ~ ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
| ~ ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) ) )
| ( SV291
= ( relation_rng @ SV72 ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2055,plain,
! [SV72: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_rng @ SV72 ) )
| ~ ( ~ ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) )
| ~ ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2056,plain,
! [SV73: $i,SV107: $i] :
( ( ( ! [SY6727: $i] :
( ~ ( function @ SY6727 )
| ~ ( relation @ SY6727 )
| ~ ( ~ ( in @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) )
!= ( apply @ SY6727 @ ( sK62_D @ SY6727 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SY6727 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SY6727 @ SV73 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(2057,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(2058,plain,
! [SV293: $i,SV74: $i] :
( ( ( ! [SY6893: $i] :
( ~ ( ~ ( ! [SY6894: $i] :
( ~ ( in @ SY6894 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6894 @ SV293 )
| ( ( sK56_D @ SY6893 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6894 ) ) )
| ~ ( in @ ( sK56_D @ SY6893 @ SV293 @ SV74 ) @ SY6893 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY6893 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SY6893 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SY6893 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SY6893 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SY6893 @ SV293 @ SV74 ) @ SY6893 ) ) )
| ( SY6893
= ( relation_image @ SV74 @ SV293 ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2059,plain,
! [SV294: $i,SV74: $i] :
( ( ( ! [SY6895: $i] :
( ( SY6895
!= ( relation_image @ SV74 @ SV294 ) )
| ~ ( ~ ! [SY6896: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6896
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6896 @ SY6895 ) )
| ~ ! [SY6898: $i] :
( ~ ( in @ SY6898 @ SY6895 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6898 @ SY6895 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6898 @ SY6895 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6898
!= ( apply @ SV74 @ ( sK55_E @ SY6898 @ SY6895 @ SV294 @ SV74 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2060,plain,
! [SV295: $i,SV171: $i] :
( ( ( function @ ( relation_dom_restriction @ SV171 @ SV295 ) )
= $true )
| ( ( function @ SV171 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2061,plain,
! [SV296: $i,SV172: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV172 @ SV296 ) )
= $true )
| ( ( function @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2062,plain,
! [SV75: $i,SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
| ( subset @ SV75 @ SV249 ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2063,plain,
! [SV75: $i,SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( ~ ( subset @ SV75 @ SV250 )
| ! [SY6845: $i,SY6846: $i] :
( ~ ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV250 ) ) )
= $true )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2064,plain,
! [SV173: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2065,plain,
! [SV173: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1936]) ).
thf(2066,plain,
! [SV174: $i,SV297: $i] :
( ( ( ! [SY6899: $i] :
( ( SV297 = SY6899 )
| ~ ( in @ SV297 @ ( relation_field @ SV174 ) )
| ~ ( in @ SY6899 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SV297 @ SY6899 ) @ SV174 )
| ( in @ ( ordered_pair @ SY6899 @ SV297 ) @ SV174 ) ) )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2067,plain,
! [SV175: $i,SV201: $i] :
( ( ( relation @ SV201 )
= $false )
| ( ( empty @ SV175 )
= $false )
| ( ( empty @ ( relation_composition @ SV201 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2068,plain,
! [SV176: $i,SV202: $i] :
( ( ( relation @ SV202 )
= $false )
| ( ( empty @ SV176 )
= $false )
| ( ( relation @ ( relation_composition @ SV202 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2069,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2070,plain,
! [SV252: $i,SV76: $i] :
( ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( ! [SY6847: $i,SY6848: $i] :
( ( SY6847 = SY6848 )
| ~ ( in @ SY6847 @ SV252 )
| ~ ( in @ SY6848 @ SV252 )
| ( in @ ( ordered_pair @ SY6847 @ SY6848 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6848 @ SY6847 ) @ SV76 ) ) )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(2071,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) )
| ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2072,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) )
| ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2073,plain,
! [SV179: $i] :
( ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 )
| ~ ( antisymmetric @ SV179 ) )
= $true )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2074,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2075,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2076,plain,
! [SV253: $i] :
( ( ( relation @ SV253 )
= $false )
| ( ( ~ ( well_ordering @ SV253 )
| ( well_founded_relation @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2077,plain,
! [SV91: $i,SV17: $i,SV216: $i] :
( ( ( function @ SV216 )
= $false )
| ( ( ~ ( relation @ SV216 ) )
= $true )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2078,plain,
! [SV92: $i,SV18: $i,SV217: $i] :
( ( ( function @ SV217 )
= $false )
| ( ( ~ ( relation @ SV217 ) )
= $true )
| ( ( ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) ) )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2079,plain,
! [SV45: $i,SV218: $i] :
( ( ( ~ ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) ) )
= $false )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2080,plain,
! [SV45: $i,SV218: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) ) )
= $false )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1954]) ).
thf(2081,plain,
! [SV219: $i,SV45: $i] :
( ( ( ~ ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) )
| ~ ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) )
= $false )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2082,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2083,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ( ( sK29_C @ SV220 @ SV46 )
!= ( sK30_SY6442 @ SV220 @ SV46 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2084,plain,
! [SV46: $i,SV221: $i,SV298: $i] :
( ( ( ! [SY6900: $i] :
( ~ ( in @ SV298 @ SV221 )
| ~ ( in @ SY6900 @ SV221 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY6900 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SY6900 @ SV298 ) @ SV46 )
| ( SV298 = SY6900 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2085,plain,
! [SV222: $i,SV104: $i,SV203: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV203 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) )
= $true )
| ( ( relation @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2086,plain,
! [SV274: $i,SV104: $i,SV47: $i,SV299: $i] :
( ( ~ ( relation @ SV299 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SV299 ) )
| ( in @ SV47 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2087,plain,
! [SV275: $i,SV104: $i,SV47: $i,SV300: $i] :
( ( ~ ( relation @ SV300 )
| ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SV300 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2088,plain,
! [SV204: $i,SV180: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV180 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ SV204 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2089,plain,
! [SV254: $i,SV48: $i,SV276: $i] :
( ( ( ~ ( relation @ SV276 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV276 @ SV254 ) ) )
| ( in @ SV48 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2090,plain,
! [SV255: $i,SV48: $i,SV277: $i] :
( ( ( ~ ( relation @ SV277 ) )
= $true )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV277 @ SV255 ) ) )
| ( in @ SV48 @ ( relation_dom @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2091,plain,
! [SV120: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) ) )
= $true )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2092,plain,
! [SV120: $i] :
( ( ( ( ( sK72_B @ SV120 )
!= ( sK73_SY6464 @ SV120 ) ) )
= $true )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2093,plain,
! [SV121: $i,SV301: $i,SV278: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV278 @ SV301 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SV301 @ SV278 ) @ SV121 )
| ( SV278 = SV301 ) )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2094,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( relation @ SV302 )
| ~ ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
| ( SV302
= ( relation_composition @ SV49 @ SV126 ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2095,plain,
! [SV126: $i,SV49: $i,SV303: $i] :
( ( ( ~ ( relation @ SV303 )
| ( SV303
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2096,plain,
! [SV223: $i,SV50: $i] :
( ( ( ~ ! [SY6804: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6804 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SY6804 @ ( sK35_C @ SV223 @ SV50 ) ) ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2097,plain,
! [SV50: $i,SV223: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1971]) ).
thf(2098,plain,
! [SV224: $i,SV304: $i,SV50: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
| ~ ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 ) )
| ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2099,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( ~ ( function @ SV305 )
| ~ ( relation @ SV305 )
| ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2100,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) )
| ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2101,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( relation @ SV256 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
| ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2102,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( relation @ SV257 )
= $false )
| ( ( ( SV257
!= ( relation_rng_restriction @ SV52 @ SV106 ) )
| ~ ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2103,plain,
! [SV225: $i] :
( ( ( ~ ( empty @ SV225 ) )
= $true )
| ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( ~ ( function @ SV225 ) )
= $true )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(2104,plain,
! [SV226: $i] :
( ( ( ~ ( empty @ SV226 ) )
= $true )
| ( ( ~ ( relation @ SV226 ) )
= $true )
| ( ( ~ ( function @ SV226 ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2105,plain,
! [SV133: $i] :
( ( ( function @ SV133 )
= $false )
| ( ( empty @ SV133 )
= $false )
| ( ( relation @ SV133 )
= $false )
| ( ( one_to_one @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2106,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) ) )
| ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2107,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ( SV307
!= ( relation_inverse_image @ SV53 @ SV280 ) )
| ~ ( ~ ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) )
| ~ ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2108,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2109,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2110,plain,
! [SV54: $i,SV228: $i,SV308: $i] :
( ( ( ! [SY6910: $i,SY6911: $i] :
( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SY6910 @ SV228 )
| ~ ( in @ SY6911 @ SV228 )
| ~ ( in @ ( ordered_pair @ SV308 @ SY6910 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SY6910 @ SY6911 ) @ SV54 )
| ( in @ ( ordered_pair @ SV308 @ SY6911 ) @ SV54 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2111,plain,
! [SV138: $i] :
( ( ( in @ ( sK77_B @ SV138 ) @ ( relation_field @ SV138 ) )
= $true )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2112,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 ) )
= $true )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2113,plain,
! [SV139: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ ( relation_field @ SV139 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV281 @ SV281 ) @ SV139 )
= $true )
| ( ( reflexive @ SV139 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2114,plain,
! [SV205: $i,SV181: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV181 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ SV205 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2115,plain,
! [SV258: $i,SV55: $i,SV282: $i] :
( ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SV282 ) ) )
| ( in @ SV55 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2116,plain,
! [SV259: $i,SV55: $i,SV283: $i] :
( ( ( ~ ( relation @ SV283 ) )
= $true )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SV283 ) ) )
| ( in @ SV55 @ ( relation_rng @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2117,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
| ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2118,plain,
! [SV229: $i,SV260: $i] :
( ( ( ~ ( function @ SV260 ) )
= $true )
| ( ( ~ ( relation @ SV260 ) )
= $true )
| ( ( ( SV260
!= ( identity_relation @ SV229 ) )
| ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2119,plain,
! [SV230: $i,SV261: $i] :
( ( ( ~ ( function @ SV261 ) )
= $true )
| ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ( SV261
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SV261 )
= SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2120,plain,
! [SV56: $i] :
( ( ( ! [SY6573: $i] :
( ~ ( function @ SY6573 )
| ~ ( relation @ SY6573 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY6573 @ SV56 )
= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SY6573 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SY6573 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY6573 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SY6573 @ SV56 )
!= ( apply @ SY6573 @ ( sK65_C @ SY6573 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SY6573 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SY6573 )
!= ( relation_rng @ SV56 ) )
| ( SY6573
= ( function_inverse @ SV56 ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1993]) ).
thf(2121,plain,
! [SV56: $i] :
( ( ( ~ ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2122,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) ) )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2123,plain,
! [SV232: $i,SV57: $i] :
( ( ( ( SV57 != SV232 ) )
= $true )
| ( ( ~ ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) ) )
= $true )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2124,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) ) )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2125,plain,
! [SV58: $i,SV234: $i] :
( ( ( ( SV234
!= ( relation_inverse @ SV58 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) ) )
= $true )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2126,plain,
! [SV145: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) ) )
= $true )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2127,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
= $true )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2128,plain,
! [SV146: $i,SV309: $i,SV284: $i] :
( ( ( ! [SY6912: $i] :
( ~ ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SV309 @ SY6912 ) @ SV146 )
| ( in @ ( ordered_pair @ SV284 @ SY6912 ) @ SV146 ) ) )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2129,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( relation @ SV262 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
| ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2130,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( relation @ SV263 )
= $false )
| ( ( ( SV263
!= ( relation_dom_restriction @ SV59 @ SV236 ) )
| ~ ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2131,plain,
! [SV60: $i,SV237: $i] :
( ( ( ~ ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) ) )
= $false )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2132,plain,
! [SV60: $i,SV237: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) ) )
= $false )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2133,plain,
! [SV238: $i,SV60: $i] :
( ( ( ~ ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) )
| ~ ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) )
= $false )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2134,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2135,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2136,plain,
! [SV184: $i,SV148: $i] :
( ( ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) )
| ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2137,plain,
! [SV61: $i,SV185: $i,SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( function @ SV206 )
= $false )
| ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) )
| ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2138,plain,
! [SV264: $i,SV61: $i,SV285: $i] :
( ( ( ~ ( function @ SV285 )
| ~ ( relation @ SV285 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
| ( SV264
= ( apply @ SV285 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2139,plain,
! [SV265: $i,SV61: $i,SV286: $i] :
( ( ( ~ ( function @ SV286 )
| ~ ( relation @ SV286 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
| ( in @ SV61 @ ( relation_dom @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2140,plain,
! [SV186: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) )
| ~ ( one_to_one @ SV186 ) )
= $true )
| ( ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) )
= $true )
| ( ( function @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2141,plain,
! [SV187: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) )
| ~ ( one_to_one @ SV187 ) )
= $true )
| ( ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) )
= $true )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2142,plain,
! [SV153: $i] :
( ( ( one_to_one @ SV153 )
= $false )
| ( ( ( relation_rng @ SV153 )
= ( relation_dom @ ( function_inverse @ SV153 ) ) )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2143,plain,
! [SV154: $i] :
( ( ( one_to_one @ SV154 )
= $false )
| ( ( ( relation_dom @ SV154 )
= ( relation_rng @ ( function_inverse @ SV154 ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2144,plain,
! [SV239: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV239 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SV239 ) )
= $true )
| ( ( relation @ SV239 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2145,plain,
! [SV240: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV240 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SV240 ) )
= $true )
| ( ( relation @ SV240 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2146,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) ) )
= $false )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2147,plain,
! [SV242: $i,SV63: $i,SV267: $i] :
( ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( ~ ( ~ ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) )
| ~ ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2148,plain,
! [SV190: $i,SV64: $i,SV207: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 )
| ~ ( in @ SV310 @ SV190 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2149,plain,
! [SV191: $i,SV208: $i,SV64: $i] :
( ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) ) )
= $true )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2150,plain,
! [SV157: $i] :
( ( ( ! [SY6760: $i] :
( ~ ( disjoint @ ( fiber @ SV157 @ SY6760 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SY6760 @ ( sK39_B @ SV157 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2151,plain,
! [SV157: $i] :
( ( ( ~ ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2152,plain,
! [SV287: $i,SV158: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
| ~ ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 ) ) )
= $true )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2025]) ).
thf(2153,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 )
| ~ ( is_transitive_in @ SV65 @ SV243 )
| ~ ( is_antisymmetric_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2154,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
| ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2155,plain,
! [SV311: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV311 )
| ( is_well_founded_in @ SV65 @ SV311 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2156,plain,
! [SV209: $i,SV192: $i,SV66: $i] :
( ( ( in @ ( ordered_pair @ SV66 @ SV192 ) @ SV209 )
= $false )
| ( ( in @ SV66 @ ( relation_field @ SV209 ) )
= $true )
| ( ( relation @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2157,plain,
! [SV210: $i,SV193: $i,SV66: $i] :
( ( ( in @ ( ordered_pair @ SV66 @ SV193 ) @ SV210 )
= $false )
| ( ( in @ SV193 @ ( relation_field @ SV210 ) )
= $true )
| ( ( relation @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2158,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV244 @ SV67 ) @ SV244 ) )
= $false )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2159,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2160,plain,
! [SV67: $i,SV245: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ SV245 )
| ( in @ ( ordered_pair @ SV312 @ SV312 ) @ SV67 ) )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV245 )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2161,plain,
! [SV161: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
| ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2162,plain,
! [SV162: $i] :
( ( ( one_to_one @ SV162 )
= $false )
| ( ( ! [SY6762: $i,SY6763: $i] :
( ~ ( in @ SY6762 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6763 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SY6762 )
!= ( apply @ SV162 @ SY6763 ) )
| ( SY6762 = SY6763 ) ) )
= $true )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2163,plain,
! [SV194: $i,SV163: $i] :
( ( ( function @ SV163 )
= $false )
| ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2164,plain,
! [SV195: $i,SV164: $i] :
( ( ( function @ SV164 )
= $false )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2165,plain,
! [SV313: $i,SV288: $i,SV165: $i] :
( ( ( ( ( sK45_B @ SV165 )
!= ( ordered_pair @ SV288 @ SV313 ) ) )
= $true )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2166,plain,
! [SV211: $i,SV196: $i,SV68: $i] :
( ( ( in @ ( ordered_pair @ SV68 @ SV196 ) @ SV211 )
= $false )
| ( ( in @ SV68 @ ( relation_dom @ SV211 ) )
= $true )
| ( ( relation @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2167,plain,
! [SV212: $i,SV197: $i,SV68: $i] :
( ( ( in @ ( ordered_pair @ SV68 @ SV197 ) @ SV212 )
= $false )
| ( ( in @ SV197 @ ( relation_rng @ SV212 ) )
= $true )
| ( ( relation @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2168,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2169,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2170,plain,
! [SV167: $i] :
( ( ( one_to_one @ SV167 )
= $false )
| ( ( function @ SV167 )
= $false )
| ( ( relation @ SV167 )
= $false )
| ( ( function @ ( relation_inverse @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2171,plain,
! [SV168: $i] :
( ( ( one_to_one @ SV168 )
= $false )
| ( ( function @ SV168 )
= $false )
| ( ( relation @ SV168 )
= $false )
| ( ( relation @ ( relation_inverse @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2172,plain,
! [SV198: $i,SV69: $i,SV213: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 )
| ~ ( in @ SV314 @ SV198 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2173,plain,
! [SV199: $i,SV214: $i,SV69: $i] :
( ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2174,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) ) )
= $false )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2175,plain,
! [SV248: $i,SV70: $i,SV269: $i] :
( ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( ~ ( ~ ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) )
| ~ ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2176,plain,
! [SV71: $i,SV200: $i,SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( function @ SV215 )
= $false )
| ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 )
| ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2177,plain,
! [SV71: $i,SV270: $i,SV289: $i] :
( ( ( ~ ( function @ SV289 )
| ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2178,plain,
! [SV71: $i,SV271: $i,SV290: $i] :
( ( ( ~ ( function @ SV290 )
| ~ ( relation @ SV290 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2179,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ~ ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
| ~ ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) ) ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2180,plain,
! [SV72: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_rng @ SV72 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) )
| ~ ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2181,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( function @ SV315 )
| ~ ( relation @ SV315 )
| ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2182,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) )
| ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2183,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ~ ( ~ ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) )
| ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) ) )
| ( SV316
= ( relation_image @ SV74 @ SV293 ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2184,plain,
! [SV294: $i,SV74: $i,SV317: $i] :
( ( ( ( SV317
!= ( relation_image @ SV74 @ SV294 ) )
| ~ ( ~ ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) )
| ~ ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2185,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) ) )
= $true )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2186,plain,
! [SV250: $i,SV75: $i] :
( ( ( ~ ( subset @ SV75 @ SV250 ) )
= $true )
| ( ( ! [SY6845: $i,SY6846: $i] :
( ~ ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV250 ) ) )
= $true )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2187,plain,
! [SV173: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2188,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2189,plain,
! [SV174: $i,SV318: $i,SV297: $i] :
( ( ( ( SV297 = SV318 )
| ~ ( in @ SV297 @ ( relation_field @ SV174 ) )
| ~ ( in @ SV318 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
| ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 ) )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2190,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2191,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2192,plain,
! [SV76: $i,SV252: $i,SV319: $i] :
( ( ( ! [SY6917: $i] :
( ( SV319 = SY6917 )
| ~ ( in @ SV319 @ SV252 )
| ~ ( in @ SY6917 @ SV252 )
| ( in @ ( ordered_pair @ SV319 @ SY6917 ) @ SV76 )
| ( in @ ( ordered_pair @ SY6917 @ SV319 ) @ SV76 ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2193,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2194,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2071]) ).
thf(2195,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2196,plain,
! [SV77: $i] :
( ( ( ~ ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2197,plain,
! [SV179: $i] :
( ( ( ~ ( reflexive @ SV179 )
| ~ ( transitive @ SV179 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV179 ) )
= $true )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2198,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2199,plain,
! [SV320: $i] :
( ( ~ ( relation @ SV320 )
| ~ ( well_ordering @ SV320 )
| ( connected @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2200,plain,
! [SV253: $i] :
( ( ( ~ ( well_ordering @ SV253 ) )
= $true )
| ( ( well_founded_relation @ SV253 )
= $true )
| ( ( relation @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2201,plain,
! [SV91: $i,SV17: $i,SV216: $i] :
( ( ( relation @ SV216 )
= $false )
| ( ( function @ SV216 )
= $false )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
| ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) ) )
= $true )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2202,plain,
! [SV92: $i,SV18: $i,SV217: $i] :
( ( ( relation @ SV217 )
= $false )
| ( ( function @ SV217 )
= $false )
| ( ( ~ ( in @ SV18 @ ( relation_dom @ SV92 ) )
| ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) ) )
= $true )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2203,plain,
! [SV45: $i,SV218: $i] :
( ( ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 )
| ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2204,plain,
! [SV45: $i,SV218: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
| ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2205,plain,
! [SV219: $i,SV45: $i] :
( ( ( ~ ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) ) )
= $false )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2206,plain,
! [SV45: $i,SV219: $i] :
( ( ( ~ ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) )
= $false )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2081]) ).
thf(2207,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2208,plain,
! [SV46: $i,SV220: $i] :
( ( ( ( ( sK29_C @ SV220 @ SV46 )
!= ( sK30_SY6442 @ SV220 @ SV46 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2209,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV221 )
| ~ ( in @ SV321 @ SV221 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 )
| ( SV298 = SV321 ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2210,plain,
! [SV222: $i,SV104: $i,SV203: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV203 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) )
= $true )
| ( ( relation @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2211,plain,
! [SV274: $i,SV104: $i,SV47: $i,SV299: $i] :
( ( ( ~ ( relation @ SV299 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SV299 ) )
| ( in @ SV47 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2212,plain,
! [SV275: $i,SV104: $i,SV47: $i,SV300: $i] :
( ( ( ~ ( relation @ SV300 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SV300 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2213,plain,
! [SV204: $i,SV180: $i,SV48: $i] :
( ( ( in @ SV48 @ SV180 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ SV204 ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2214,plain,
! [SV254: $i,SV48: $i,SV276: $i] :
( ( ( relation @ SV276 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV276 @ SV254 ) ) )
| ( in @ SV48 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2215,plain,
! [SV255: $i,SV48: $i,SV277: $i] :
( ( ( relation @ SV277 )
= $false )
| ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV277 @ SV255 ) ) )
| ( in @ SV48 @ ( relation_dom @ SV277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2216,plain,
! [SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2217,plain,
! [SV120: $i] :
( ( ( ( sK72_B @ SV120 )
= ( sK73_SY6464 @ SV120 ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2218,plain,
! [SV121: $i,SV301: $i,SV278: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV278 @ SV301 ) @ SV121 )
| ~ ( in @ ( ordered_pair @ SV301 @ SV278 ) @ SV121 ) )
= $true )
| ( ( SV278 = SV301 )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2219,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( relation @ SV302 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
| ( SV302
= ( relation_composition @ SV49 @ SV126 ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2220,plain,
! [SV126: $i,SV49: $i,SV303: $i] :
( ( ( ~ ( relation @ SV303 ) )
= $true )
| ( ( ( SV303
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2221,plain,
! [SV223: $i,SV50: $i] :
( ( ( ! [SY6804: $i] :
( ~ ( disjoint @ ( fiber @ SV50 @ SY6804 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SY6804 @ ( sK35_C @ SV223 @ SV50 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2222,plain,
! [SV50: $i,SV223: $i] :
( ( ( ~ ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2223,plain,
! [SV224: $i,SV304: $i,SV50: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
| ~ ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 ) ) )
= $true )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2224,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( ~ ( function @ SV305 )
| ~ ( relation @ SV305 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2225,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2226,plain,
! [SV105: $i,SV51: $i] :
( ( ( ~ ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2100]) ).
thf(2227,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2228,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ( SV257
!= ( relation_rng_restriction @ SV52 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2229,plain,
! [SV225: $i] :
( ( ( empty @ SV225 )
= $false )
| ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( ~ ( function @ SV225 ) )
= $true )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2230,plain,
! [SV226: $i] :
( ( ( empty @ SV226 )
= $false )
| ( ( ~ ( relation @ SV226 ) )
= $true )
| ( ( ~ ( function @ SV226 ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2231,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) ) ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2232,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ( SV307
!= ( relation_inverse_image @ SV53 @ SV280 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) )
| ~ ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2233,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2234,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2109]) ).
thf(2235,plain,
! [SV54: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ! [SY6918: $i] :
( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 )
| ~ ( in @ SY6918 @ SV228 )
| ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SV322 @ SY6918 ) @ SV54 )
| ( in @ ( ordered_pair @ SV308 @ SY6918 ) @ SV54 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2236,plain,
! [SV138: $i] :
( ( ( in @ ( ordered_pair @ ( sK77_B @ SV138 ) @ ( sK77_B @ SV138 ) ) @ SV138 )
= $false )
| ( ( reflexive @ SV138 )
= $true )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2237,plain,
! [SV139: $i,SV281: $i] :
( ( ( in @ SV281 @ ( relation_field @ SV139 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV281 @ SV281 ) @ SV139 )
= $true )
| ( ( reflexive @ SV139 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2238,plain,
! [SV205: $i,SV181: $i,SV55: $i] :
( ( ( in @ SV55 @ SV181 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ SV205 ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2239,plain,
! [SV258: $i,SV55: $i,SV282: $i] :
( ( ( relation @ SV282 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SV282 ) ) )
| ( in @ SV55 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2240,plain,
! [SV259: $i,SV55: $i,SV283: $i] :
( ( ( relation @ SV283 )
= $false )
| ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SV283 ) ) )
| ( in @ SV55 @ ( relation_rng @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2241,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2242,plain,
! [SV229: $i,SV260: $i] :
( ( ( function @ SV260 )
= $false )
| ( ( ~ ( relation @ SV260 ) )
= $true )
| ( ( ( SV260
!= ( identity_relation @ SV229 ) )
| ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2243,plain,
! [SV230: $i,SV261: $i] :
( ( ( function @ SV261 )
= $false )
| ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ( SV261
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SV261 )
= SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2244,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( function @ SV323 )
| ~ ( relation @ SV323 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) )
| ( SV323
= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2245,plain,
! [SV56: $i] :
( ( ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
| ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2246,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
= $false )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2247,plain,
! [SV232: $i,SV57: $i] :
( ( ( SV57 = SV232 )
= $false )
| ( ( ~ ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) ) )
= $true )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2248,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
= $false )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2249,plain,
! [SV58: $i,SV234: $i] :
( ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( ~ ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) ) )
= $true )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2250,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2251,plain,
! [SV145: $i] :
( ( ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2252,plain,
! [SV324: $i,SV146: $i,SV309: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SV309 @ SV324 ) @ SV146 )
| ( in @ ( ordered_pair @ SV284 @ SV324 ) @ SV146 ) )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2253,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2129]) ).
thf(2254,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( ( SV263
!= ( relation_dom_restriction @ SV59 @ SV236 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2255,plain,
! [SV60: $i,SV237: $i] :
( ( ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2256,plain,
! [SV60: $i,SV237: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
| ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2257,plain,
! [SV238: $i,SV60: $i] :
( ( ( ~ ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) ) )
= $false )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2258,plain,
! [SV60: $i,SV238: $i] :
( ( ( ~ ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) )
= $false )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2259,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2260,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2261,plain,
! [SV184: $i,SV148: $i] :
( ( ( ~ ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2262,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2136]) ).
thf(2263,plain,
! [SV61: $i,SV206: $i,SV185: $i] :
( ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) )
| ~ ( in @ SV61 @ ( relation_dom @ SV206 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2264,plain,
! [SV264: $i,SV61: $i,SV285: $i] :
( ( ( ~ ( function @ SV285 ) )
= $true )
| ( ( ~ ( relation @ SV285 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
| ( SV264
= ( apply @ SV285 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2265,plain,
! [SV265: $i,SV61: $i,SV286: $i] :
( ( ( ~ ( function @ SV286 ) )
= $true )
| ( ( ~ ( relation @ SV286 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
| ( in @ SV61 @ ( relation_dom @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2266,plain,
! [SV186: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ ( relation_rng @ SV186 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV186 ) )
= $true )
| ( ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) )
= $true )
| ( ( function @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2267,plain,
! [SV187: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ ( relation_rng @ SV187 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV187 ) )
= $true )
| ( ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) )
= $true )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2268,plain,
! [SV239: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV239 )
= $false )
| ( ( subset @ ( relation_dom @ SV62 ) @ ( relation_dom @ SV239 ) )
= $true )
| ( ( relation @ SV239 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2269,plain,
! [SV240: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV240 )
= $false )
| ( ( subset @ ( relation_rng @ SV62 ) @ ( relation_rng @ SV240 ) )
= $true )
| ( ( relation @ SV240 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2270,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) ) )
= $false )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2271,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) ) )
= $false )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2272,plain,
! [SV267: $i,SV242: $i,SV63: $i] :
( ( ( ~ ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) )
| ~ ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2273,plain,
! [SV190: $i,SV64: $i,SV207: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( relation_rng @ SV207 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ SV310 @ SV190 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2274,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
| ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2275,plain,
! [SV325: $i,SV157: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV157 @ SV325 ) @ ( sK39_B @ SV157 ) )
| ~ ( in @ SV325 @ ( sK39_B @ SV157 ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2276,plain,
! [SV157: $i] :
( ( ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2277,plain,
! [SV287: $i,SV158: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
| ~ ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 ) )
= $false )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2278,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 )
| ~ ( is_transitive_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2279,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2280,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2281,plain,
! [SV311: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV311 ) )
= $true )
| ( ( is_well_founded_in @ SV65 @ SV311 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2282,plain,
! [SV67: $i,SV244: $i] :
( ( ( in @ ( sK42_C @ SV244 @ SV67 ) @ SV244 )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2283,plain,
! [SV67: $i,SV244: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 ) )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2284,plain,
! [SV67: $i,SV245: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ SV245 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV312 @ SV312 ) @ SV67 )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV245 )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2285,plain,
! [SV161: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2286,plain,
! [SV161: $i] :
( ( ( ~ ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2287,plain,
! [SV162: $i,SV326: $i] :
( ( ( ! [SY6919: $i] :
( ~ ( in @ SV326 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SY6919 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SY6919 ) )
| ( SV326 = SY6919 ) ) )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2288,plain,
! [SV194: $i,SV163: $i] :
( ( ( relation @ SV163 )
= $false )
| ( ( function @ SV163 )
= $false )
| ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2289,plain,
! [SV195: $i,SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( function @ SV164 )
= $false )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2290,plain,
! [SV313: $i,SV288: $i,SV165: $i] :
( ( ( ( sK45_B @ SV165 )
= ( ordered_pair @ SV288 @ SV313 ) )
= $false )
| ( ( relation @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2291,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2168]) ).
thf(2292,plain,
( ( ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2168]) ).
thf(2293,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2294,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2295,plain,
! [SV198: $i,SV69: $i,SV213: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( relation_dom @ SV213 ) )
| ~ ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV314 @ SV198 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2296,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
| ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2297,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) ) )
= $false )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2298,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) ) )
= $false )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2299,plain,
! [SV269: $i,SV248: $i,SV70: $i] :
( ( ( ~ ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) )
| ~ ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2300,plain,
! [SV71: $i,SV215: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) )
| ~ ( in @ SV200 @ SV71 ) )
= $true )
| ( ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2301,plain,
! [SV71: $i,SV270: $i,SV289: $i] :
( ( ( ~ ( function @ SV289 ) )
= $true )
| ( ( ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2302,plain,
! [SV71: $i,SV271: $i,SV290: $i] :
( ( ( ~ ( function @ SV290 ) )
= $true )
| ( ( ~ ( relation @ SV290 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2303,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
| ~ ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2304,plain,
! [SV72: $i,SV292: $i] :
( ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( ~ ( ~ ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) )
| ~ ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2305,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( function @ SV315 )
| ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2306,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2307,plain,
! [SV73: $i,SV107: $i] :
( ( ( ~ ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2308,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ~ ( ~ ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) )
| ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) ) ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2309,plain,
! [SV294: $i,SV74: $i,SV317: $i] :
( ( ( ( SV317
!= ( relation_image @ SV74 @ SV294 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) )
| ~ ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2310,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
= $false )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2311,plain,
! [SV250: $i,SV75: $i] :
( ( ( subset @ SV75 @ SV250 )
= $false )
| ( ( ! [SY6845: $i,SY6846: $i] :
( ~ ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV75 )
| ( in @ ( ordered_pair @ SY6845 @ SY6846 ) @ SV250 ) ) )
= $true )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2312,plain,
! [SV173: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2313,plain,
! [SV173: $i] :
( ( ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV173 ) @ ( sK70_B @ SV173 ) ) @ SV173 )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2314,plain,
! [SV174: $i,SV318: $i,SV297: $i] :
( ( ( ( SV297 = SV318 )
| ~ ( in @ SV297 @ ( relation_field @ SV174 ) )
| ~ ( in @ SV318 @ ( relation_field @ SV174 ) )
| ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2189]) ).
thf(2315,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2316,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2317,plain,
! [SV76: $i,SV252: $i,SV327: $i,SV319: $i] :
( ( ( ( SV319 = SV327 )
| ~ ( in @ SV319 @ SV252 )
| ~ ( in @ SV327 @ SV252 )
| ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
| ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2318,plain,
! [SV77: $i] :
( ( ( ! [SY6696: $i] :
( ~ ( in @ SY6696 @ ( relation_dom @ SV77 ) )
| ! [SY6697: $i] :
( ( SY6697
!= ( apply @ SV77 @ SY6696 ) )
| ( in @ ( ordered_pair @ SY6696 @ SY6697 ) @ SV77 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2193]) ).
thf(2319,plain,
! [SV77: $i] :
( ( ( ! [SY6698: $i] :
( ~ ( in @ SY6698 @ ( relation_dom @ SV77 ) )
| ! [SY6699: $i] :
( ~ ( in @ ( ordered_pair @ SY6698 @ SY6699 ) @ SV77 )
| ( SY6699
= ( apply @ SV77 @ SY6698 ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2320,plain,
! [SV77: $i] :
( ( ( ! [SY6700: $i] :
( ( in @ SY6700 @ ( relation_dom @ SV77 ) )
| ! [SY6701: $i] :
( ( SY6701
!= ( apply @ SV77 @ SY6700 ) )
| ( SY6701 = empty_set ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2321,plain,
! [SV77: $i] :
( ( ( ! [SY6702: $i] :
( ( in @ SY6702 @ ( relation_dom @ SV77 ) )
| ! [SY6703: $i] :
( ( SY6703 != empty_set )
| ( SY6703
= ( apply @ SV77 @ SY6702 ) ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2322,plain,
! [SV179: $i] :
( ( ( ~ ( reflexive @ SV179 ) )
= $true )
| ( ( ~ ( transitive @ SV179 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV179 ) )
= $true )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2323,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2324,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2325,plain,
! [SV320: $i] :
( ( ( ~ ( relation @ SV320 ) )
= $true )
| ( ( ~ ( well_ordering @ SV320 )
| ( connected @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2326,plain,
! [SV253: $i] :
( ( ( well_ordering @ SV253 )
= $false )
| ( ( well_founded_relation @ SV253 )
= $true )
| ( ( relation @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2327,plain,
! [SV91: $i,SV216: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) )
= $true )
| ( ( function @ SV216 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2328,plain,
! [SV217: $i,SV92: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( relation_dom @ SV92 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) )
= $true )
| ( ( function @ SV217 )
= $false )
| ( ( relation @ SV217 )
= $false )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2329,plain,
! [SV45: $i,SV218: $i] :
( ( ( ! [SY6798: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SY6798 ) @ SV45 ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2330,plain,
! [SV45: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ ( sK33_SY6444 @ SV218 @ SV45 ) ) @ SV45 )
= $true )
| ( ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2331,plain,
! [SV219: $i,SV45: $i] :
( ( ( ! [SY6799: $i] :
( ! [SY6510: $i] :
~ ( in @ ( ordered_pair @ SY6799 @ SY6510 ) @ SV45 )
| ( in @ SY6799 @ SV219 ) ) )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2332,plain,
! [SV45: $i,SV219: $i] :
( ( ( ! [SY6801: $i] :
( ~ ( in @ SY6801 @ SV219 )
| ( in @ ( ordered_pair @ SY6801 @ ( sK31_D @ SY6801 @ SV219 @ SV45 ) ) @ SV45 ) ) )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2333,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2334,plain,
! [SV46: $i,SV220: $i] :
( ( ( ( sK29_C @ SV220 @ SV46 )
= ( sK30_SY6442 @ SV220 @ SV46 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2335,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV221 )
| ~ ( in @ SV321 @ SV221 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 )
| ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2336,plain,
! [SV222: $i,SV104: $i,SV203: $i,SV47: $i] :
( ( ( in @ SV47 @ SV203 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) )
= $true )
| ( ( relation @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2337,plain,
! [SV274: $i,SV104: $i,SV47: $i,SV299: $i] :
( ( ( relation @ SV299 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SV299 ) )
| ( in @ SV47 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2338,plain,
! [SV275: $i,SV104: $i,SV47: $i,SV300: $i] :
( ( ( relation @ SV300 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SV300 ) )
| ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2339,plain,
! [SV180: $i,SV204: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_dom @ SV204 ) )
= $false )
| ( ( in @ SV48 @ SV180 )
= $false )
| ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV204 @ SV180 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2340,plain,
! [SV254: $i,SV276: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV276 @ SV254 ) ) ) )
= $true )
| ( ( in @ SV48 @ SV254 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2341,plain,
! [SV255: $i,SV277: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV277 @ SV255 ) ) ) )
= $true )
| ( ( in @ SV48 @ ( relation_dom @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2342,plain,
! [SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2343,plain,
! [SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 ) )
= $false )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2344,plain,
! [SV121: $i,SV301: $i,SV278: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV278 @ SV301 ) @ SV121 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV301 @ SV278 ) @ SV121 ) )
= $true )
| ( ( SV278 = SV301 )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2345,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( relation @ SV302 )
= $false )
| ( ( ~ ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
| ( SV302
= ( relation_composition @ SV49 @ SV126 ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2346,plain,
! [SV126: $i,SV49: $i,SV303: $i] :
( ( ( relation @ SV303 )
= $false )
| ( ( ( SV303
!= ( relation_composition @ SV49 @ SV126 ) )
| ~ ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) ) )
= $true )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2347,plain,
! [SV223: $i,SV328: $i,SV50: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV50 @ SV328 ) @ ( sK35_C @ SV223 @ SV50 ) )
| ~ ( in @ SV328 @ ( sK35_C @ SV223 @ SV50 ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2348,plain,
! [SV50: $i,SV223: $i] :
( ( ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2349,plain,
! [SV224: $i,SV304: $i,SV50: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
| ~ ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 ) )
= $false )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2350,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( ~ ( function @ SV305 ) )
= $true )
| ( ( ~ ( relation @ SV305 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2351,plain,
! [SV105: $i,SV51: $i] :
( ( ( ! [SY6717: $i] :
( ~ ( function @ SY6717 )
| ~ ( relation @ SY6717 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6717 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SY6717 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2352,plain,
! [SV105: $i,SV51: $i] :
( ( ( ! [SY6718: $i] :
( ~ ( function @ SY6718 )
| ~ ( relation @ SY6718 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SY6718 @ SV105 ) ) )
| ( in @ ( apply @ SY6718 @ SV51 ) @ ( relation_dom @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2353,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2354,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2355,plain,
! [SV225: $i] :
( ( ( relation @ SV225 )
= $false )
| ( ( empty @ SV225 )
= $false )
| ( ( ~ ( function @ SV225 ) )
= $true )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2356,plain,
! [SV226: $i] :
( ( ( relation @ SV226 )
= $false )
| ( ( empty @ SV226 )
= $false )
| ( ( ~ ( function @ SV226 ) )
= $true )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2357,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2358,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( ~ ( ~ ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) )
| ~ ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2359,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2360,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2361,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 )
| ~ ( in @ SV329 @ SV228 )
| ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 )
| ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2362,plain,
! [SV181: $i,SV205: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_rng @ SV205 ) )
= $false )
| ( ( in @ SV55 @ SV181 )
= $false )
| ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV181 @ SV205 ) ) )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2363,plain,
! [SV282: $i,SV258: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SV282 ) ) ) )
= $true )
| ( ( in @ SV55 @ SV258 )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2364,plain,
! [SV283: $i,SV259: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SV283 ) ) ) )
= $true )
| ( ( in @ SV55 @ ( relation_rng @ SV283 ) )
= $true )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2365,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
| ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2366,plain,
! [SV229: $i,SV260: $i] :
( ( ( relation @ SV260 )
= $false )
| ( ( function @ SV260 )
= $false )
| ( ( ( SV260
!= ( identity_relation @ SV229 ) )
| ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2367,plain,
! [SV230: $i,SV261: $i] :
( ( ( relation @ SV261 )
= $false )
| ( ( function @ SV261 )
= $false )
| ( ( ( SV261
!= ( identity_relation @ SV230 ) )
| ( ( relation_dom @ SV261 )
= SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2368,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( function @ SV323 )
| ~ ( relation @ SV323 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) )
| ( SV323
= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2369,plain,
! [SV56: $i] :
( ( ( ~ ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2370,plain,
! [SV56: $i] :
( ( ( ~ ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2371,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
= $false )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2246]) ).
thf(2372,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) ) )
= $false )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2246]) ).
thf(2373,plain,
! [SV232: $i,SV57: $i] :
( ( ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) )
| ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) )
= $false )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2374,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
= $false )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2375,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) ) )
= $false )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2376,plain,
! [SV58: $i,SV234: $i] :
( ( ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) )
| ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) )
= $false )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2377,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2378,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2379,plain,
! [SV324: $i,SV146: $i,SV309: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 )
| ~ ( in @ ( ordered_pair @ SV309 @ SV324 ) @ SV146 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV324 ) @ SV146 )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2380,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2381,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( ~ ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2382,plain,
! [SV60: $i,SV237: $i] :
( ( ( ! [SY6828: $i] :
~ ( in @ ( ordered_pair @ SY6828 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2383,plain,
! [SV60: $i,SV237: $i] :
( ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV237 @ SV60 ) @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
= $true )
| ( ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2384,plain,
! [SV238: $i,SV60: $i] :
( ( ( ! [SY6829: $i] :
( ! [SY6610: $i] :
~ ( in @ ( ordered_pair @ SY6610 @ SY6829 ) @ SV60 )
| ( in @ SY6829 @ SV238 ) ) )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2385,plain,
! [SV60: $i,SV238: $i] :
( ( ( ! [SY6831: $i] :
( ~ ( in @ SY6831 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY6831 @ SV238 @ SV60 ) @ SY6831 ) @ SV60 ) ) )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2258]) ).
thf(2386,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2387,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
| ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2388,plain,
! [SV184: $i,SV148: $i] :
( ( ( ! [SY6777: $i,SY6778: $i] :
( ( SY6777 != SY6778 )
| ~ ( in @ SY6777 @ SV148 )
| ( in @ ( ordered_pair @ SY6777 @ SY6778 ) @ SV184 ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2389,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2390,plain,
! [SV61: $i,SV206: $i,SV185: $i] :
( ( ( ( SV185
!= ( apply @ SV206 @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV61 @ ( relation_dom @ SV206 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2391,plain,
! [SV264: $i,SV61: $i,SV285: $i] :
( ( ( function @ SV285 )
= $false )
| ( ( ~ ( relation @ SV285 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
| ( SV264
= ( apply @ SV285 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2392,plain,
! [SV265: $i,SV61: $i,SV286: $i] :
( ( ( function @ SV286 )
= $false )
| ( ( ~ ( relation @ SV286 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
| ( in @ SV61 @ ( relation_dom @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2393,plain,
! [SV186: $i,SV151: $i] :
( ( ( in @ SV151 @ ( relation_rng @ SV186 ) )
= $false )
| ( ( ~ ( one_to_one @ SV186 ) )
= $true )
| ( ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) )
= $true )
| ( ( function @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2394,plain,
! [SV187: $i,SV152: $i] :
( ( ( in @ SV152 @ ( relation_rng @ SV187 ) )
= $false )
| ( ( ~ ( one_to_one @ SV187 ) )
= $true )
| ( ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) )
= $true )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2395,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) )
| ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2270]) ).
thf(2396,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
| ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2271]) ).
thf(2397,plain,
! [SV267: $i,SV242: $i,SV63: $i] :
( ( ( ~ ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) ) )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2398,plain,
! [SV63: $i,SV242: $i,SV267: $i] :
( ( ( ~ ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2399,plain,
! [SV190: $i,SV64: $i,SV207: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( relation_rng @ SV207 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ SV310 @ SV190 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2400,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2401,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2402,plain,
! [SV325: $i,SV157: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV157 @ SV325 ) @ ( sK39_B @ SV157 ) ) )
= $true )
| ( ( ~ ( in @ SV325 @ ( sK39_B @ SV157 ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2403,plain,
! [SV157: $i] :
( ( ( ~ ( ( ( sK39_B @ SV157 )
!= empty_set ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2404,plain,
! [SV157: $i] :
( ( ( ~ ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2405,plain,
! [SV287: $i,SV158: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 ) )
= $false )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2406,plain,
! [SV158: $i,SV287: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 ) )
= $false )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2407,plain,
! [SV243: $i,SV65: $i] :
( ( ( ~ ( is_reflexive_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2408,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2409,plain,
! [SV65: $i] :
( ( ( ! [SY6637: $i] :
( ~ ( well_orders @ SV65 @ SY6637 )
| ( is_connected_in @ SV65 @ SY6637 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2410,plain,
! [SV311: $i,SV65: $i] :
( ( ( well_orders @ SV65 @ SV311 )
= $false )
| ( ( is_well_founded_in @ SV65 @ SV311 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2411,plain,
! [SV67: $i,SV244: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_C @ SV244 @ SV67 ) @ ( sK42_C @ SV244 @ SV67 ) ) @ SV67 )
= $false )
| ( ( is_reflexive_in @ SV67 @ SV244 )
= $true )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2412,plain,
! [SV67: $i,SV245: $i,SV312: $i] :
( ( ( in @ SV312 @ SV245 )
= $false )
| ( ( in @ ( ordered_pair @ SV312 @ SV312 ) @ SV67 )
= $true )
| ( ( is_reflexive_in @ SV67 @ SV245 )
= $false )
| ( ( relation @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2413,plain,
! [SV161: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2285]) ).
thf(2414,plain,
! [SV161: $i] :
( ( ( ( ( sK17_B @ SV161 )
!= ( sK18_SY6435 @ SV161 ) ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2286]) ).
thf(2415,plain,
! [SV330: $i,SV162: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SV330 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) )
| ( SV326 = SV330 ) )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2416,plain,
! [SV163: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( function @ SV163 )
= $false )
| ( ( relation @ SV163 )
= $false )
| ( ( ~ ( function @ SV194 ) )
= $true )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2417,plain,
! [SV164: $i,SV195: $i] :
( ( ( relation @ SV195 )
= $false )
| ( ( function @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2418,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2419,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2420,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2421,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2422,plain,
! [SV198: $i,SV69: $i,SV213: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( relation_dom @ SV213 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV314 @ SV198 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2423,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2424,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2425,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) )
| ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2426,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
| ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2298]) ).
thf(2427,plain,
! [SV269: $i,SV248: $i,SV70: $i] :
( ( ( ~ ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) ) )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2428,plain,
! [SV70: $i,SV248: $i,SV269: $i] :
( ( ( ~ ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2429,plain,
! [SV71: $i,SV215: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ ( relation_dom @ SV215 ) ) )
= $true )
| ( ( ~ ( in @ SV200 @ SV71 ) )
= $true )
| ( ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2430,plain,
! [SV71: $i,SV270: $i,SV289: $i] :
( ( ( function @ SV289 )
= $false )
| ( ( ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2431,plain,
! [SV71: $i,SV271: $i,SV290: $i] :
( ( ( function @ SV290 )
= $false )
| ( ( ~ ( relation @ SV290 ) )
= $true )
| ( ( ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2432,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2433,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) ) )
= $false )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2434,plain,
! [SV292: $i,SV72: $i] :
( ( ( ~ ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) )
| ~ ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2435,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( function @ SV315 ) )
= $true )
| ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2436,plain,
! [SV73: $i,SV107: $i] :
( ( ( ! [SY6728: $i] :
( ~ ( function @ SY6728 )
| ~ ( relation @ SY6728 )
| ( SV107
!= ( relation_dom_restriction @ SY6728 @ SV73 ) )
| ! [SY6729: $i] :
( ~ ( in @ SY6729 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6729 )
= ( apply @ SY6728 @ SY6729 ) ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2437,plain,
! [SV73: $i,SV107: $i] :
( ( ( ! [SY6730: $i] :
( ~ ( function @ SY6730 )
| ~ ( relation @ SY6730 )
| ( SV107
!= ( relation_dom_restriction @ SY6730 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SY6730 ) @ SV73 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2438,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ~ ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) )
| ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2439,plain,
! [SV294: $i,SV74: $i,SV317: $i] :
( ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( ~ ( ~ ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) )
| ~ ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2440,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 ) )
= $false )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2441,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
= $false )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2442,plain,
! [SV250: $i,SV75: $i,SV331: $i] :
( ( ( ! [SY6920: $i] :
( ~ ( in @ ( ordered_pair @ SV331 @ SY6920 ) @ SV75 )
| ( in @ ( ordered_pair @ SV331 @ SY6920 ) @ SV250 ) ) )
= $true )
| ( ( subset @ SV75 @ SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2443,plain,
! [SV173: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2444,plain,
! [SV173: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2445,plain,
! [SV174: $i,SV318: $i,SV297: $i] :
( ( ( ( SV297 = SV318 )
| ~ ( in @ SV297 @ ( relation_field @ SV174 ) )
| ~ ( in @ SV318 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2446,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2447,plain,
! [SV76: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV251 @ SV76 ) @ ( sK21_C @ SV251 @ SV76 ) ) @ SV76 )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2448,plain,
! [SV76: $i,SV252: $i,SV327: $i,SV319: $i] :
( ( ( ( SV319 = SV327 )
| ~ ( in @ SV319 @ SV252 )
| ~ ( in @ SV327 @ SV252 )
| ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2449,plain,
! [SV77: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV77 ) )
| ! [SY6921: $i] :
( ( SY6921
!= ( apply @ SV77 @ SV332 ) )
| ( in @ ( ordered_pair @ SV332 @ SY6921 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2450,plain,
! [SV77: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( relation_dom @ SV77 ) )
| ! [SY6922: $i] :
( ~ ( in @ ( ordered_pair @ SV333 @ SY6922 ) @ SV77 )
| ( SY6922
= ( apply @ SV77 @ SV333 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2451,plain,
! [SV77: $i,SV334: $i] :
( ( ( ( in @ SV334 @ ( relation_dom @ SV77 ) )
| ! [SY6923: $i] :
( ( SY6923
!= ( apply @ SV77 @ SV334 ) )
| ( SY6923 = empty_set ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2452,plain,
! [SV77: $i,SV335: $i] :
( ( ( ( in @ SV335 @ ( relation_dom @ SV77 ) )
| ! [SY6924: $i] :
( ( SY6924 != empty_set )
| ( SY6924
= ( apply @ SV77 @ SV335 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2453,plain,
! [SV179: $i] :
( ( ( reflexive @ SV179 )
= $false )
| ( ( ~ ( transitive @ SV179 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV179 ) )
= $true )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2454,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2323]) ).
thf(2455,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2456,plain,
! [SV320: $i] :
( ( ( relation @ SV320 )
= $false )
| ( ( ~ ( well_ordering @ SV320 )
| ( connected @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2457,plain,
! [SV91: $i,SV216: $i,SV17: $i] :
( ( ( in @ SV17 @ ( relation_dom @ ( relation_composition @ SV216 @ SV91 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV216 @ SV91 ) @ SV17 )
= ( apply @ SV91 @ ( apply @ SV216 @ SV17 ) ) )
= $true )
| ( ( function @ SV216 )
= $false )
| ( ( relation @ SV216 )
= $false )
| ( ( function @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2458,plain,
! [SV217: $i,SV92: $i,SV18: $i] :
( ( ( in @ SV18 @ ( relation_dom @ SV92 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV92 @ SV217 ) @ SV18 )
= ( apply @ SV217 @ ( apply @ SV92 @ SV18 ) ) )
= $true )
| ( ( function @ SV217 )
= $false )
| ( ( relation @ SV217 )
= $false )
| ( ( function @ SV92 )
= $false )
| ( ( relation @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2459,plain,
! [SV336: $i,SV45: $i,SV218: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SV336 ) @ SV45 ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2460,plain,
! [SV219: $i,SV45: $i,SV337: $i] :
( ( ( ! [SY6925: $i] :
~ ( in @ ( ordered_pair @ SV337 @ SY6925 ) @ SV45 )
| ( in @ SV337 @ SV219 ) )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2461,plain,
! [SV45: $i,SV219: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ SV219 )
| ( in @ ( ordered_pair @ SV338 @ ( sK31_D @ SV338 @ SV219 @ SV45 ) ) @ SV45 ) )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2462,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2333]) ).
thf(2463,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2333]) ).
thf(2464,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV221 )
| ~ ( in @ SV321 @ SV221 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2465,plain,
! [SV203: $i,SV222: $i,SV104: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV222 )
= $false )
| ( ( in @ SV47 @ SV203 )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV203 ) @ SV222 ) )
= $true )
| ( ( relation @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2466,plain,
! [SV299: $i,SV274: $i,SV104: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SV299 ) ) )
= $true )
| ( ( in @ SV47 @ SV274 )
= $true )
| ( ( relation @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2467,plain,
! [SV300: $i,SV275: $i,SV104: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SV300 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV300 )
= $true )
| ( ( relation @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2468,plain,
! [SV254: $i,SV276: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV276 @ SV254 ) ) )
= $false )
| ( ( in @ SV48 @ SV254 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2469,plain,
! [SV255: $i,SV277: $i,SV48: $i] :
( ( ( in @ SV48 @ ( relation_dom @ ( relation_dom_restriction @ SV277 @ SV255 ) ) )
= $false )
| ( ( in @ SV48 @ ( relation_dom @ SV277 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2470,plain,
! [SV120: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_B @ SV120 ) @ ( sK73_SY6464 @ SV120 ) ) @ SV120 )
= $true )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2471,plain,
! [SV120: $i] :
( ( ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV120 ) @ ( sK72_B @ SV120 ) ) @ SV120 )
= $true )
| ( ( antisymmetric @ SV120 )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2472,plain,
! [SV121: $i,SV301: $i,SV278: $i] :
( ( ( in @ ( ordered_pair @ SV278 @ SV301 ) @ SV121 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV301 @ SV278 ) @ SV121 ) )
= $true )
| ( ( SV278 = SV301 )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2473,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2474,plain,
! [SV126: $i,SV49: $i,SV303: $i] :
( ( ( ( SV303
!= ( relation_composition @ SV49 @ SV126 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2475,plain,
! [SV223: $i,SV328: $i,SV50: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV50 @ SV328 ) @ ( sK35_C @ SV223 @ SV50 ) ) )
= $true )
| ( ( ~ ( in @ SV328 @ ( sK35_C @ SV223 @ SV50 ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2476,plain,
! [SV50: $i,SV223: $i] :
( ( ( ~ ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2348]) ).
thf(2477,plain,
! [SV50: $i,SV223: $i] :
( ( ( ~ ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2348]) ).
thf(2478,plain,
! [SV224: $i,SV304: $i,SV50: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 ) )
= $false )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2349]) ).
thf(2479,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 ) )
= $false )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2349]) ).
thf(2480,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( function @ SV305 )
= $false )
| ( ( ~ ( relation @ SV305 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2481,plain,
! [SV105: $i,SV51: $i,SV339: $i] :
( ( ( ~ ( function @ SV339 )
| ~ ( relation @ SV339 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SV339 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2482,plain,
! [SV105: $i,SV51: $i,SV340: $i] :
( ( ( ~ ( function @ SV340 )
| ~ ( relation @ SV340 )
| ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
| ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2483,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2484,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2485,plain,
! [SV257: $i,SV106: $i,SV52: $i] :
( ( ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) )
| ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2486,plain,
! [SV225: $i] :
( ( ( function @ SV225 )
= $false )
| ( ( empty @ SV225 )
= $false )
| ( ( relation @ SV225 )
= $false )
| ( ( function @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2487,plain,
! [SV226: $i] :
( ( ( function @ SV226 )
= $false )
| ( ( empty @ SV226 )
= $false )
| ( ( relation @ SV226 )
= $false )
| ( ( relation @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2488,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2489,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2490,plain,
! [SV307: $i,SV280: $i,SV53: $i] :
( ( ( ~ ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) )
| ~ ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2491,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2492,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2493,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 )
| ~ ( in @ SV329 @ SV228 )
| ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 )
| ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2494,plain,
! [SV282: $i,SV258: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV258 @ SV282 ) ) )
= $false )
| ( ( in @ SV55 @ SV258 )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2495,plain,
! [SV283: $i,SV259: $i,SV55: $i] :
( ( ( in @ SV55 @ ( relation_rng @ ( relation_rng_restriction @ SV259 @ SV283 ) ) )
= $false )
| ( ( in @ SV55 @ ( relation_rng @ SV283 ) )
= $true )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2496,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 ) )
= $false )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2497,plain,
! [SV142: $i,SV182: $i] :
( ( ( ~ ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2498,plain,
! [SV229: $i,SV260: $i] :
( ( ( ( SV260
!= ( identity_relation @ SV229 ) ) )
= $true )
| ( ( ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true )
| ( ( function @ SV260 )
= $false )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2499,plain,
! [SV230: $i,SV261: $i] :
( ( ( ( SV261
!= ( identity_relation @ SV230 ) ) )
= $true )
| ( ( ( relation_dom @ SV261 )
= SV230 )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2500,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( function @ SV323 ) )
= $true )
| ( ( ~ ( relation @ SV323 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) )
| ( SV323
= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2501,plain,
! [SV56: $i] :
( ( ( ! [SY6574: $i] :
( ~ ( function @ SY6574 )
| ~ ( relation @ SY6574 )
| ( SY6574
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6575: $i,SY6576: $i] :
( ( SY6576
!= ( apply @ SY6574 @ SY6575 ) )
| ~ ( in @ SY6575 @ ( relation_rng @ SV56 ) )
| ( SY6575
= ( apply @ SV56 @ SY6576 ) ) )
| ~ ! [SY6577: $i,SY6578: $i] :
( ( SY6578
!= ( apply @ SY6574 @ SY6577 ) )
| ~ ( in @ SY6577 @ ( relation_rng @ SV56 ) )
| ( in @ SY6578 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6579: $i,SY6580: $i] :
( ( SY6579
!= ( apply @ SV56 @ SY6580 ) )
| ~ ( in @ SY6580 @ ( relation_dom @ SV56 ) )
| ( SY6580
= ( apply @ SY6574 @ SY6579 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2502,plain,
! [SV56: $i] :
( ( ( ! [SY6583: $i] :
( ~ ( function @ SY6583 )
| ~ ( relation @ SY6583 )
| ( SY6583
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SY6583 )
= ( relation_rng @ SV56 ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2503,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2504,plain,
! [SV57: $i,SV231: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2505,plain,
! [SV232: $i,SV57: $i] :
( ( ( ~ ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) ) )
= $false )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2506,plain,
! [SV57: $i,SV232: $i] :
( ( ( ~ ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) )
= $false )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2507,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2508,plain,
! [SV58: $i,SV233: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2509,plain,
! [SV58: $i,SV234: $i] :
( ( ( ~ ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) ) )
= $false )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2510,plain,
! [SV234: $i,SV58: $i] :
( ( ( ~ ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) )
= $false )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2511,plain,
! [SV145: $i] :
( ( ( in @ ( ordered_pair @ ( sK74_B @ SV145 ) @ ( sK75_SY6465 @ SV145 ) ) @ SV145 )
= $true )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2512,plain,
! [SV145: $i] :
( ( ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV145 ) @ ( sK76_SY6467 @ SV145 ) ) @ SV145 )
= $true )
| ( ( transitive @ SV145 )
= $true )
| ( ( relation @ SV145 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2513,plain,
! [SV324: $i,SV146: $i,SV309: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV309 @ SV324 ) @ SV146 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV324 ) @ SV146 )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2514,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2515,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2516,plain,
! [SV263: $i,SV59: $i,SV236: $i] :
( ( ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) )
| ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2517,plain,
! [SV60: $i,SV237: $i,SV341: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV341 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2518,plain,
! [SV238: $i,SV60: $i,SV342: $i] :
( ( ( ! [SY6926: $i] :
~ ( in @ ( ordered_pair @ SY6926 @ SV342 ) @ SV60 )
| ( in @ SV342 @ SV238 ) )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2519,plain,
! [SV60: $i,SV238: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV238 )
| ( in @ ( ordered_pair @ ( sK23_D @ SV343 @ SV238 @ SV60 ) @ SV343 ) @ SV60 ) )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2520,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( ( sK60_C @ SV183 @ SV147 )
!= ( sK61_SY6460 @ SV183 @ SV147 ) ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2521,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2522,plain,
! [SV147: $i,SV183: $i] :
( ( ( ~ ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) ) )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2523,plain,
! [SV184: $i,SV148: $i,SV344: $i] :
( ( ( ! [SY6927: $i] :
( ( SV344 != SY6927 )
| ~ ( in @ SV344 @ SV148 )
| ( in @ ( ordered_pair @ SV344 @ SY6927 ) @ SV184 ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2524,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) )
| ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2525,plain,
! [SV61: $i,SV206: $i,SV185: $i] :
( ( ( SV185
= ( apply @ SV206 @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV61 @ ( relation_dom @ SV206 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2526,plain,
! [SV264: $i,SV61: $i,SV285: $i] :
( ( ( relation @ SV285 )
= $false )
| ( ( function @ SV285 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
| ( SV264
= ( apply @ SV285 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2527,plain,
! [SV265: $i,SV61: $i,SV286: $i] :
( ( ( relation @ SV286 )
= $false )
| ( ( function @ SV286 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
| ( in @ SV61 @ ( relation_dom @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2528,plain,
! [SV151: $i,SV186: $i] :
( ( ( one_to_one @ SV186 )
= $false )
| ( ( in @ SV151 @ ( relation_rng @ SV186 ) )
= $false )
| ( ( SV151
= ( apply @ SV186 @ ( apply @ ( function_inverse @ SV186 ) @ SV151 ) ) )
= $true )
| ( ( function @ SV186 )
= $false )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2529,plain,
! [SV152: $i,SV187: $i] :
( ( ( one_to_one @ SV187 )
= $false )
| ( ( in @ SV152 @ ( relation_rng @ SV187 ) )
= $false )
| ( ( SV152
= ( apply @ ( relation_composition @ ( function_inverse @ SV187 ) @ SV187 ) @ SV152 ) )
= $true )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2530,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ! [SY6868: $i] :
( ~ ( in @ ( ordered_pair @ SY6868 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SY6868 @ SV241 ) ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2531,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) ) )
= $true )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2532,plain,
! [SV267: $i,SV242: $i,SV63: $i] :
( ( ( ! [SY6869: $i] :
( ! [SY6836: $i] :
( ~ ( in @ ( ordered_pair @ SY6836 @ SY6869 ) @ SV63 )
| ~ ( in @ SY6836 @ SV242 ) )
| ( in @ SY6869 @ SV267 ) ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2533,plain,
! [SV63: $i,SV242: $i,SV267: $i] :
( ( ( ! [SY6871: $i] :
( ~ ( in @ SY6871 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SY6871 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SY6871 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2534,plain,
! [SV190: $i,SV64: $i,SV207: $i,SV310: $i] :
( ( ( in @ SV310 @ ( relation_rng @ SV207 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 ) )
= $true )
| ( ( ~ ( in @ SV310 @ SV190 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2535,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2536,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ SV191 )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2537,plain,
! [SV325: $i,SV157: $i] :
( ( ( disjoint @ ( fiber @ SV157 @ SV325 ) @ ( sK39_B @ SV157 ) )
= $false )
| ( ( ~ ( in @ SV325 @ ( sK39_B @ SV157 ) ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2538,plain,
! [SV157: $i] :
( ( ( ( ( sK39_B @ SV157 )
!= empty_set ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2539,plain,
! [SV157: $i] :
( ( ( subset @ ( sK39_B @ SV157 ) @ ( relation_field @ SV157 ) )
= $true )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2404]) ).
thf(2540,plain,
! [SV287: $i,SV158: $i] :
( ( ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
= $true )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2541,plain,
! [SV158: $i,SV287: $i] :
( ( ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 )
= $true )
| ( ( ( SV287 = empty_set )
| ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2542,plain,
! [SV243: $i,SV65: $i] :
( ( ( is_reflexive_in @ SV65 @ SV243 )
= $false )
| ( ( ~ ( is_transitive_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2543,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
| ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2544,plain,
! [SV345: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV345 )
| ( is_connected_in @ SV65 @ SV345 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2545,plain,
! [SV161: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
| ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2546,plain,
! [SV161: $i] :
( ( ( ( sK17_B @ SV161 )
= ( sK18_SY6435 @ SV161 ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2547,plain,
! [SV330: $i,SV162: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SV330 @ ( relation_dom @ SV162 ) )
| ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) ) )
= $true )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2548,plain,
! [SV163: $i,SV194: $i] :
( ( ( function @ SV194 )
= $false )
| ( ( relation @ SV163 )
= $false )
| ( ( function @ SV163 )
= $false )
| ( ( relation @ SV194 )
= $false )
| ( ( function @ ( relation_composition @ SV163 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2549,plain,
! [SV164: $i,SV195: $i] :
( ( ( function @ SV195 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( function @ SV164 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( relation @ ( relation_composition @ SV164 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2550,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2551,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2552,plain,
! [SV198: $i,SV69: $i,SV213: $i,SV314: $i] :
( ( ( in @ SV314 @ ( relation_dom @ SV213 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV314 @ SV198 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2553,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2554,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV199 )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2555,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ! [SY6872: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SY6872 ) @ SV70 )
| ~ ( in @ SY6872 @ SV247 ) ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2556,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) ) )
= $true )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2557,plain,
! [SV269: $i,SV248: $i,SV70: $i] :
( ( ( ! [SY6873: $i] :
( ! [SY6843: $i] :
( ~ ( in @ ( ordered_pair @ SY6873 @ SY6843 ) @ SV70 )
| ~ ( in @ SY6843 @ SV248 ) )
| ( in @ SY6873 @ SV269 ) ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2427]) ).
thf(2558,plain,
! [SV70: $i,SV248: $i,SV269: $i] :
( ( ( ! [SY6875: $i] :
( ~ ( in @ SY6875 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6875 @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SY6875 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2559,plain,
! [SV71: $i,SV215: $i,SV200: $i] :
( ( ( in @ SV200 @ ( relation_dom @ SV215 ) )
= $false )
| ( ( ~ ( in @ SV200 @ SV71 ) )
= $true )
| ( ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2560,plain,
! [SV71: $i,SV270: $i,SV289: $i] :
( ( ( relation @ SV289 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
| ( in @ SV270 @ ( relation_dom @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2561,plain,
! [SV71: $i,SV271: $i,SV290: $i] :
( ( ( relation @ SV290 )
= $false )
| ( ( function @ SV290 )
= $false )
| ( ( ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
| ( in @ SV271 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2562,plain,
! [SV72: $i,SV291: $i] :
( ( ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) )
| ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2432]) ).
thf(2563,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
| ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2564,plain,
! [SV292: $i,SV72: $i] :
( ( ( ~ ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) ) )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2565,plain,
! [SV72: $i,SV292: $i] :
( ( ( ~ ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2434]) ).
thf(2566,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( function @ SV315 )
= $false )
| ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2567,plain,
! [SV73: $i,SV107: $i,SV346: $i] :
( ( ( ~ ( function @ SV346 )
| ~ ( relation @ SV346 )
| ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) )
| ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2568,plain,
! [SV73: $i,SV107: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 )
| ~ ( relation @ SV347 )
| ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2569,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ~ ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) )
| ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2570,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) ) )
= $false )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2438]) ).
thf(2571,plain,
! [SV317: $i,SV294: $i,SV74: $i] :
( ( ( ~ ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) )
| ~ ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2572,plain,
! [SV75: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV75 )
= $true )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2573,plain,
! [SV75: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 ) )
= $true )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2574,plain,
! [SV250: $i,SV75: $i,SV348: $i,SV331: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV75 )
| ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV250 ) )
= $true )
| ( ( subset @ SV75 @ SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2575,plain,
! [SV173: $i] :
( ( ( ~ ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2576,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2577,plain,
! [SV174: $i,SV318: $i,SV297: $i] :
( ( ( SV297 = SV318 )
= $true )
| ( ( ~ ( in @ SV297 @ ( relation_field @ SV174 ) )
| ~ ( in @ SV318 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2578,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2579,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2446]) ).
thf(2580,plain,
! [SV76: $i,SV252: $i,SV327: $i,SV319: $i] :
( ( ( ( SV319 = SV327 )
| ~ ( in @ SV319 @ SV252 )
| ~ ( in @ SV327 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2581,plain,
! [SV77: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_dom @ SV77 ) ) )
= $true )
| ( ( ! [SY6921: $i] :
( ( SY6921
!= ( apply @ SV77 @ SV332 ) )
| ( in @ ( ordered_pair @ SV332 @ SY6921 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2582,plain,
! [SV77: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( relation_dom @ SV77 ) ) )
= $true )
| ( ( ! [SY6922: $i] :
( ~ ( in @ ( ordered_pair @ SV333 @ SY6922 ) @ SV77 )
| ( SY6922
= ( apply @ SV77 @ SV333 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2583,plain,
! [SV77: $i,SV334: $i] :
( ( ( in @ SV334 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( ! [SY6923: $i] :
( ( SY6923
!= ( apply @ SV77 @ SV334 ) )
| ( SY6923 = empty_set ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2584,plain,
! [SV77: $i,SV335: $i] :
( ( ( in @ SV335 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( ! [SY6924: $i] :
( ( SY6924 != empty_set )
| ( SY6924
= ( apply @ SV77 @ SV335 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2585,plain,
! [SV179: $i] :
( ( ( transitive @ SV179 )
= $false )
| ( ( reflexive @ SV179 )
= $false )
| ( ( ~ ( antisymmetric @ SV179 ) )
= $true )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2586,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2587,plain,
! [SV349: $i] :
( ( ~ ( relation @ SV349 )
| ~ ( well_ordering @ SV349 )
| ( antisymmetric @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2588,plain,
! [SV320: $i] :
( ( ( ~ ( well_ordering @ SV320 ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2589,plain,
! [SV336: $i,SV45: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SV336 ) @ SV45 )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 ) )
= $true )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2590,plain,
! [SV219: $i,SV45: $i,SV337: $i] :
( ( ( ! [SY6925: $i] :
~ ( in @ ( ordered_pair @ SV337 @ SY6925 ) @ SV45 ) )
= $true )
| ( ( in @ SV337 @ SV219 )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2591,plain,
! [SV45: $i,SV219: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ SV219 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV338 @ ( sK31_D @ SV338 @ SV219 @ SV45 ) ) @ SV45 )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2592,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2462]) ).
thf(2593,plain,
! [SV46: $i,SV220: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV220 @ SV46 ) @ ( sK29_C @ SV220 @ SV46 ) ) @ SV46 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2463]) ).
thf(2594,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV221 )
| ~ ( in @ SV321 @ SV221 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2595,plain,
! [SV299: $i,SV274: $i,SV104: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV274 ) @ SV299 ) )
= $false )
| ( ( in @ SV47 @ SV274 )
= $true )
| ( ( relation @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2596,plain,
! [SV300: $i,SV275: $i,SV104: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ ( relation_composition @ ( identity_relation @ SV275 ) @ SV300 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV104 ) @ SV300 )
= $true )
| ( ( relation @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2597,plain,
! [SV121: $i,SV278: $i,SV301: $i] :
( ( ( in @ ( ordered_pair @ SV301 @ SV278 ) @ SV121 )
= $false )
| ( ( in @ ( ordered_pair @ SV278 @ SV301 ) @ SV121 )
= $false )
| ( ( SV278 = SV301 )
= $true )
| ( ( antisymmetric @ SV121 )
= $false )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2598,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2599,plain,
! [SV126: $i,SV49: $i,SV303: $i] :
( ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( ~ ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) ) )
= $true )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2600,plain,
! [SV223: $i,SV328: $i,SV50: $i] :
( ( ( disjoint @ ( fiber @ SV50 @ SV328 ) @ ( sK35_C @ SV223 @ SV50 ) )
= $false )
| ( ( ~ ( in @ SV328 @ ( sK35_C @ SV223 @ SV50 ) ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2601,plain,
! [SV50: $i,SV223: $i] :
( ( ( ( ( sK35_C @ SV223 @ SV50 )
!= empty_set ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2602,plain,
! [SV50: $i,SV223: $i] :
( ( ( subset @ ( sK35_C @ SV223 @ SV50 ) @ SV223 )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2603,plain,
! [SV224: $i,SV304: $i,SV50: $i] :
( ( ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
= $true )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2478]) ).
thf(2604,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 )
= $true )
| ( ( ( SV304 = empty_set )
| ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2479]) ).
thf(2605,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( relation @ SV305 )
= $false )
| ( ( function @ SV305 )
= $false )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
| ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2606,plain,
! [SV105: $i,SV51: $i,SV339: $i] :
( ( ( ~ ( function @ SV339 )
| ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SV339 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2607,plain,
! [SV105: $i,SV51: $i,SV340: $i] :
( ( ( ~ ( function @ SV340 )
| ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
| ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2608,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2609,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2610,plain,
! [SV257: $i,SV106: $i,SV52: $i] :
( ( ( ~ ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2611,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2485]) ).
thf(2612,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2613,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2614,plain,
! [SV307: $i,SV280: $i,SV53: $i] :
( ( ( ~ ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2615,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ~ ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2616,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2491]) ).
thf(2617,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV227 @ SV54 ) @ ( sK12_SY6429 @ SV227 @ SV54 ) ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2618,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 )
| ~ ( in @ SV329 @ SV228 )
| ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2619,plain,
! [SV142: $i,SV182: $i] :
( ( ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
= $true )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2620,plain,
! [SV142: $i,SV182: $i] :
( ( ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
!= ( sK67_C @ SV182 @ SV142 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2621,plain,
! [SV229: $i,SV260: $i] :
( ( ( SV260
= ( identity_relation @ SV229 ) )
= $false )
| ( ( ! [SY6859: $i] :
( ~ ( in @ SY6859 @ SV229 )
| ( ( apply @ SV260 @ SY6859 )
= SY6859 ) ) )
= $true )
| ( ( function @ SV260 )
= $false )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2622,plain,
! [SV230: $i,SV261: $i] :
( ( ( SV261
= ( identity_relation @ SV230 ) )
= $false )
| ( ( ( relation_dom @ SV261 )
= SV230 )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2623,plain,
! [SV56: $i,SV323: $i] :
( ( ( function @ SV323 )
= $false )
| ( ( ~ ( relation @ SV323 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) )
| ( SV323
= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2624,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ( function @ SV350 )
| ~ ( relation @ SV350 )
| ( SV350
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(2625,plain,
! [SV56: $i,SV351: $i] :
( ( ( ~ ( function @ SV351 )
| ~ ( relation @ SV351 )
| ( SV351
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2626,plain,
! [SV57: $i,SV231: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2627,plain,
! [SV57: $i,SV231: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2628,plain,
! [SV232: $i,SV57: $i] :
( ( ( ! [SY6812: $i,SY6813: $i] :
( ~ ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV57 )
| ( in @ ( ordered_pair @ SY6812 @ SY6813 ) @ SV232 ) ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2629,plain,
! [SV57: $i,SV232: $i] :
( ( ( ! [SY6814: $i,SY6815: $i] :
( ~ ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV232 )
| ( in @ ( ordered_pair @ SY6814 @ SY6815 ) @ SV57 ) ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2630,plain,
! [SV58: $i,SV233: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2631,plain,
! [SV58: $i,SV233: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2632,plain,
! [SV58: $i,SV234: $i] :
( ( ( ! [SY6816: $i,SY6817: $i] :
( ~ ( in @ ( ordered_pair @ SY6816 @ SY6817 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6817 @ SY6816 ) @ SV58 ) ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2633,plain,
! [SV234: $i,SV58: $i] :
( ( ( ! [SY6818: $i,SY6819: $i] :
( ~ ( in @ ( ordered_pair @ SY6819 @ SY6818 ) @ SV58 )
| ( in @ ( ordered_pair @ SY6818 @ SY6819 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2634,plain,
! [SV324: $i,SV146: $i,SV309: $i,SV284: $i] :
( ( ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV309 @ SV324 ) @ SV146 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV324 ) @ SV146 )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2635,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2514]) ).
thf(2636,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2637,plain,
! [SV263: $i,SV59: $i,SV236: $i] :
( ( ( ~ ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2638,plain,
! [SV59: $i,SV236: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2516]) ).
thf(2639,plain,
! [SV60: $i,SV237: $i,SV341: $i] :
( ( ( in @ ( ordered_pair @ SV341 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
= $false )
| ( ( ~ ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 ) )
= $true )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2640,plain,
! [SV238: $i,SV60: $i,SV342: $i] :
( ( ( ! [SY6926: $i] :
~ ( in @ ( ordered_pair @ SY6926 @ SV342 ) @ SV60 ) )
= $true )
| ( ( in @ SV342 @ SV238 )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2641,plain,
! [SV60: $i,SV238: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ SV238 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_D @ SV343 @ SV238 @ SV60 ) @ SV343 ) @ SV60 )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2642,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
= $false )
| ( ( ~ ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2643,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2644,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2522]) ).
thf(2645,plain,
! [SV184: $i,SV148: $i,SV352: $i,SV344: $i] :
( ( ( ( SV344 != SV352 )
| ~ ( in @ SV344 @ SV148 )
| ( in @ ( ordered_pair @ SV344 @ SV352 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2646,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2647,plain,
! [SV148: $i,SV184: $i] :
( ( ( ~ ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) )
= $false )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2648,plain,
! [SV185: $i,SV206: $i,SV61: $i] :
( ( ( in @ SV61 @ ( relation_dom @ SV206 ) )
= $false )
| ( ( SV185
= ( apply @ SV206 @ SV61 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV61 @ SV185 ) @ SV206 )
= $true )
| ( ( function @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2649,plain,
! [SV285: $i,SV264: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 ) )
= $true )
| ( ( SV264
= ( apply @ SV285 @ SV61 ) )
= $true )
| ( ( function @ SV285 )
= $false )
| ( ( relation @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2650,plain,
! [SV286: $i,SV265: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 ) )
= $true )
| ( ( in @ SV61 @ ( relation_dom @ SV286 ) )
= $true )
| ( ( function @ SV286 )
= $false )
| ( ( relation @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2651,plain,
! [SV63: $i,SV241: $i,SV266: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV353 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ SV353 @ SV241 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2652,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
= $false )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2653,plain,
! [SV267: $i,SV242: $i,SV63: $i,SV354: $i] :
( ( ( ! [SY6937: $i] :
( ~ ( in @ ( ordered_pair @ SY6937 @ SV354 ) @ SV63 )
| ~ ( in @ SY6937 @ SV242 ) )
| ( in @ SV354 @ SV267 ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2654,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ SV267 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2655,plain,
! [SV190: $i,SV207: $i,SV310: $i,SV64: $i] :
( ( ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 )
= $false )
| ( ( in @ SV310 @ ( relation_rng @ SV207 ) )
= $false )
| ( ( ~ ( in @ SV310 @ SV190 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2656,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
| ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2657,plain,
! [SV157: $i,SV325: $i] :
( ( ( in @ SV325 @ ( sK39_B @ SV157 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV157 @ SV325 ) @ ( sK39_B @ SV157 ) )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2658,plain,
! [SV157: $i] :
( ( ( ( sK39_B @ SV157 )
= empty_set )
= $false )
| ( ( well_founded_relation @ SV157 )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2659,plain,
! [SV158: $i,SV287: $i] :
( ( ( SV287 = empty_set )
= $true )
| ( ( ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2660,plain,
! [SV158: $i,SV287: $i] :
( ( ( SV287 = empty_set )
= $true )
| ( ( ~ ( subset @ SV287 @ ( relation_field @ SV158 ) ) )
= $true )
| ( ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2661,plain,
! [SV243: $i,SV65: $i] :
( ( ( is_transitive_in @ SV65 @ SV243 )
= $false )
| ( ( is_reflexive_in @ SV65 @ SV243 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2662,plain,
! [SV65: $i] :
( ( ( ~ ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2663,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2664,plain,
! [SV345: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV345 ) )
= $true )
| ( ( is_connected_in @ SV65 @ SV345 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2665,plain,
! [SV161: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2666,plain,
! [SV161: $i] :
( ( ( ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
!= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2667,plain,
! [SV330: $i,SV162: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( relation_dom @ SV162 ) )
| ~ ( in @ SV330 @ ( relation_dom @ SV162 ) ) )
= $true )
| ( ( ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) ) )
= $true )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2668,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2550]) ).
thf(2669,plain,
( ( ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2550]) ).
thf(2670,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2671,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2672,plain,
! [SV198: $i,SV213: $i,SV69: $i,SV314: $i] :
( ( ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 )
= $false )
| ( ( in @ SV314 @ ( relation_dom @ SV213 ) )
= $false )
| ( ( ~ ( in @ SV314 @ SV198 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2673,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2674,plain,
! [SV356: $i,SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV356 ) @ SV70 )
| ~ ( in @ SV356 @ SV247 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2675,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
= $false )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2676,plain,
! [SV269: $i,SV248: $i,SV70: $i,SV357: $i] :
( ( ( ! [SY6938: $i] :
( ~ ( in @ ( ordered_pair @ SV357 @ SY6938 ) @ SV70 )
| ~ ( in @ SY6938 @ SV248 ) )
| ( in @ SV357 @ SV269 ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(2677,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ SV269 )
| ~ ( ~ ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(2678,plain,
! [SV215: $i,SV71: $i,SV200: $i] :
( ( ( in @ SV200 @ SV71 )
= $false )
| ( ( in @ SV200 @ ( relation_dom @ SV215 ) )
= $false )
| ( ( in @ SV200 @ ( relation_dom @ ( relation_dom_restriction @ SV215 @ SV71 ) ) )
= $true )
| ( ( function @ SV215 )
= $false )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2679,plain,
! [SV71: $i,SV289: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) ) )
= $true )
| ( ( in @ SV270 @ ( relation_dom @ SV289 ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2680,plain,
! [SV71: $i,SV290: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) ) )
= $true )
| ( ( in @ SV271 @ SV71 )
= $true )
| ( ( function @ SV290 )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2681,plain,
! [SV72: $i,SV291: $i] :
( ( ( ! [SY6889: $i] :
( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SY6889 ) )
| ~ ( in @ SY6889 @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2682,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2683,plain,
! [SV292: $i,SV72: $i] :
( ( ( ! [SY6890: $i] :
( ! [SY6673: $i] :
( ( SY6890
!= ( apply @ SV72 @ SY6673 ) )
| ~ ( in @ SY6673 @ ( relation_dom @ SV72 ) ) )
| ( in @ SY6890 @ SV292 ) ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2684,plain,
! [SV72: $i,SV292: $i] :
( ( ( ! [SY6892: $i] :
( ~ ( in @ SY6892 @ SV292 )
| ~ ( ( SY6892
!= ( apply @ SV72 @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SY6892 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2685,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( function @ SV315 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
| ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2686,plain,
! [SV73: $i,SV107: $i,SV346: $i] :
( ( ( ~ ( function @ SV346 )
| ~ ( relation @ SV346 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) )
| ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2687,plain,
! [SV73: $i,SV107: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 )
| ~ ( relation @ SV347 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2688,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) )
| ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2569]) ).
thf(2689,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
| ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2690,plain,
! [SV317: $i,SV294: $i,SV74: $i] :
( ( ( ~ ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) ) )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2691,plain,
! [SV74: $i,SV294: $i,SV317: $i] :
( ( ( ~ ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2692,plain,
! [SV75: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV249 @ SV75 ) @ ( sK37_SY6446 @ SV249 @ SV75 ) ) @ SV249 )
= $false )
| ( ( subset @ SV75 @ SV249 )
= $true )
| ( ( relation @ SV249 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2693,plain,
! [SV250: $i,SV75: $i,SV348: $i,SV331: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV75 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV250 )
= $true )
| ( ( subset @ SV75 @ SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2694,plain,
! [SV173: $i] :
( ( ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2695,plain,
! [SV173: $i] :
( ( ( in @ ( ordered_pair @ ( sK70_B @ SV173 ) @ ( sK71_SY6463 @ SV173 ) ) @ SV173 )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2696,plain,
! [SV318: $i,SV174: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( ~ ( in @ SV318 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( SV297 = SV318 )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2697,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2698,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2699,plain,
! [SV76: $i,SV252: $i,SV327: $i,SV319: $i] :
( ( ( SV319 = SV327 )
= $true )
| ( ( ~ ( in @ SV319 @ SV252 )
| ~ ( in @ SV327 @ SV252 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2700,plain,
! [SV77: $i,SV332: $i] :
( ( ( in @ SV332 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ! [SY6921: $i] :
( ( SY6921
!= ( apply @ SV77 @ SV332 ) )
| ( in @ ( ordered_pair @ SV332 @ SY6921 ) @ SV77 ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2701,plain,
! [SV77: $i,SV333: $i] :
( ( ( in @ SV333 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( ! [SY6922: $i] :
( ~ ( in @ ( ordered_pair @ SV333 @ SY6922 ) @ SV77 )
| ( SY6922
= ( apply @ SV77 @ SV333 ) ) ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2702,plain,
! [SV334: $i,SV77: $i,SV359: $i] :
( ( ( ( SV359
!= ( apply @ SV77 @ SV334 ) )
| ( SV359 = empty_set ) )
= $true )
| ( ( in @ SV334 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(2703,plain,
! [SV335: $i,SV77: $i,SV360: $i] :
( ( ( ( SV360 != empty_set )
| ( SV360
= ( apply @ SV77 @ SV335 ) ) )
= $true )
| ( ( in @ SV335 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2704,plain,
! [SV179: $i] :
( ( ( antisymmetric @ SV179 )
= $false )
| ( ( reflexive @ SV179 )
= $false )
| ( ( transitive @ SV179 )
= $false )
| ( ( ~ ( connected @ SV179 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2706,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2707,plain,
! [SV349: $i] :
( ( ( ~ ( relation @ SV349 ) )
= $true )
| ( ( ~ ( well_ordering @ SV349 )
| ( antisymmetric @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2708,plain,
! [SV320: $i] :
( ( ( well_ordering @ SV320 )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2709,plain,
! [SV336: $i,SV45: $i,SV218: $i] :
( ( ( in @ ( sK32_C @ SV218 @ SV45 ) @ SV218 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_C @ SV218 @ SV45 ) @ SV336 ) @ SV45 )
= $false )
| ( ( SV218
= ( relation_dom @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2710,plain,
! [SV219: $i,SV45: $i,SV361: $i,SV337: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV337 @ SV361 ) @ SV45 ) )
= $true )
| ( ( in @ SV337 @ SV219 )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2711,plain,
! [SV45: $i,SV219: $i,SV338: $i] :
( ( ( in @ SV338 @ SV219 )
= $false )
| ( ( in @ ( ordered_pair @ SV338 @ ( sK31_D @ SV338 @ SV219 @ SV45 ) ) @ SV45 )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2712,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2713,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV221 ) )
= $true )
| ( ( ~ ( in @ SV321 @ SV221 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2714,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2715,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2716,plain,
! [SV303: $i,SV126: $i,SV49: $i] :
( ( ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) )
| ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2717,plain,
! [SV50: $i,SV223: $i,SV328: $i] :
( ( ( in @ SV328 @ ( sK35_C @ SV223 @ SV50 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV50 @ SV328 ) @ ( sK35_C @ SV223 @ SV50 ) )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2718,plain,
! [SV50: $i,SV223: $i] :
( ( ( ( sK35_C @ SV223 @ SV50 )
= empty_set )
= $false )
| ( ( is_well_founded_in @ SV50 @ SV223 )
= $true )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2719,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( SV304 = empty_set )
= $true )
| ( ( ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2720,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( SV304 = empty_set )
= $true )
| ( ( ~ ( subset @ SV304 @ SV224 ) )
= $true )
| ( ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2721,plain,
! [SV105: $i,SV305: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) )
| ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) )
= $true )
| ( ( function @ SV305 )
= $false )
| ( ( relation @ SV305 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2722,plain,
! [SV105: $i,SV51: $i,SV339: $i] :
( ( ( ~ ( function @ SV339 ) )
= $true )
| ( ( ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SV339 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2723,plain,
! [SV105: $i,SV51: $i,SV340: $i] :
( ( ( ~ ( function @ SV340 ) )
= $true )
| ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
| ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2724,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2725,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2726,plain,
! [SV257: $i,SV106: $i,SV52: $i] :
( ( ( ! [SY6851: $i,SY6852: $i] :
( ~ ( in @ SY6852 @ SV52 )
| ~ ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV106 )
| ( in @ ( ordered_pair @ SY6851 @ SY6852 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2727,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2728,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2729,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
| ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2730,plain,
! [SV307: $i,SV280: $i,SV53: $i] :
( ( ( ! [SY6907: $i] :
( ~ ( in @ SY6907 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SY6907 ) @ SV280 )
| ( in @ SY6907 @ SV307 ) ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2731,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ~ ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2615]) ).
thf(2732,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2733,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 )
| ~ ( in @ SV329 @ SV228 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2734,plain,
! [SV142: $i,SV182: $i] :
( ( ( ( relation_dom @ SV182 )
= SV142 )
= $false )
| ( ( in @ ( sK67_C @ SV182 @ SV142 ) @ SV142 )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2735,plain,
! [SV142: $i,SV182: $i] :
( ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
= ( sK67_C @ SV182 @ SV142 ) )
= $false )
| ( ( ( ( relation_dom @ SV182 )
!= SV142 ) )
= $true )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2736,plain,
! [SV260: $i,SV229: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV229 )
| ( ( apply @ SV260 @ SV362 )
= SV362 ) )
= $true )
| ( ( SV260
= ( identity_relation @ SV229 ) )
= $false )
| ( ( function @ SV260 )
= $false )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2737,plain,
! [SV56: $i,SV323: $i] :
( ( ( relation @ SV323 )
= $false )
| ( ( function @ SV323 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) )
| ( SV323
= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2738,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ( function @ SV350 )
| ~ ( relation @ SV350 ) )
= $true )
| ( ( ( SV350
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2739,plain,
! [SV56: $i,SV351: $i] :
( ( ( ~ ( function @ SV351 )
| ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV351
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2740,plain,
! [SV57: $i,SV231: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 ) )
= $true )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2741,plain,
! [SV232: $i,SV57: $i,SV363: $i] :
( ( ( ! [SY6939: $i] :
( ~ ( in @ ( ordered_pair @ SV363 @ SY6939 ) @ SV57 )
| ( in @ ( ordered_pair @ SV363 @ SY6939 ) @ SV232 ) ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(2742,plain,
! [SV57: $i,SV232: $i,SV364: $i] :
( ( ( ! [SY6940: $i] :
( ~ ( in @ ( ordered_pair @ SV364 @ SY6940 ) @ SV232 )
| ( in @ ( ordered_pair @ SV364 @ SY6940 ) @ SV57 ) ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(2743,plain,
! [SV58: $i,SV233: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 ) )
= $true )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2744,plain,
! [SV58: $i,SV234: $i,SV365: $i] :
( ( ( ! [SY6941: $i] :
( ~ ( in @ ( ordered_pair @ SV365 @ SY6941 ) @ SV234 )
| ( in @ ( ordered_pair @ SY6941 @ SV365 ) @ SV58 ) ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(2745,plain,
! [SV234: $i,SV58: $i,SV366: $i] :
( ( ( ! [SY6942: $i] :
( ~ ( in @ ( ordered_pair @ SY6942 @ SV366 ) @ SV58 )
| ( in @ ( ordered_pair @ SV366 @ SY6942 ) @ SV234 ) ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(2746,plain,
! [SV284: $i,SV146: $i,SV324: $i,SV309: $i] :
( ( ( in @ ( ordered_pair @ SV309 @ SV324 ) @ SV146 )
= $false )
| ( ( in @ ( ordered_pair @ SV284 @ SV309 ) @ SV146 )
= $false )
| ( ( in @ ( ordered_pair @ SV284 @ SV324 ) @ SV146 )
= $true )
| ( ( transitive @ SV146 )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2747,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2635]) ).
thf(2748,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2749,plain,
! [SV263: $i,SV59: $i,SV236: $i] :
( ( ( ! [SY6860: $i,SY6861: $i] :
( ~ ( in @ SY6860 @ SV236 )
| ~ ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV59 )
| ( in @ ( ordered_pair @ SY6860 @ SY6861 ) @ SV263 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2750,plain,
! [SV59: $i,SV236: $i,SV263: $i] :
( ( ( ~ ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2751,plain,
! [SV341: $i,SV60: $i,SV237: $i] :
( ( ( in @ ( sK24_C @ SV237 @ SV60 ) @ SV237 )
= $false )
| ( ( in @ ( ordered_pair @ SV341 @ ( sK24_C @ SV237 @ SV60 ) ) @ SV60 )
= $false )
| ( ( SV237
= ( relation_rng @ SV60 ) )
= $true )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2752,plain,
! [SV238: $i,SV60: $i,SV342: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV367 @ SV342 ) @ SV60 ) )
= $true )
| ( ( in @ SV342 @ SV238 )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(2753,plain,
! [SV60: $i,SV238: $i,SV343: $i] :
( ( ( in @ SV343 @ SV238 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_D @ SV343 @ SV238 @ SV60 ) @ SV343 ) @ SV60 )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2754,plain,
! [SV147: $i,SV183: $i] :
( ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
= $false )
| ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 ) )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2755,plain,
! [SV147: $i,SV183: $i] :
( ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2756,plain,
! [SV147: $i,SV183: $i] :
( ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 )
= $true )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2757,plain,
! [SV184: $i,SV148: $i,SV352: $i,SV344: $i] :
( ( ( ( SV344 != SV352 )
| ~ ( in @ SV344 @ SV148 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV344 @ SV352 ) @ SV184 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2758,plain,
! [SV148: $i,SV184: $i] :
( ( ( ! [SY6779: $i,SY6780: $i] :
( ~ ( in @ ( ordered_pair @ SY6779 @ SY6780 ) @ SV184 )
| ( SY6779 = SY6780 ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2759,plain,
! [SV148: $i,SV184: $i] :
( ( ( ! [SY6781: $i] :
( ! [SY6782: $i] :
~ ( in @ ( ordered_pair @ SY6781 @ SY6782 ) @ SV184 )
| ( in @ SY6781 @ SV148 ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2760,plain,
! [SV285: $i,SV264: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV264 ) @ SV285 )
= $false )
| ( ( SV264
= ( apply @ SV285 @ SV61 ) )
= $true )
| ( ( function @ SV285 )
= $false )
| ( ( relation @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2761,plain,
! [SV286: $i,SV265: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV265 ) @ SV286 )
= $false )
| ( ( in @ SV61 @ ( relation_dom @ SV286 ) )
= $true )
| ( ( function @ SV286 )
= $false )
| ( ( relation @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2762,plain,
! [SV63: $i,SV241: $i,SV266: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV353 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV353 @ SV241 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2763,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2764,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( ~ ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 ) )
= $false )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2765,plain,
! [SV267: $i,SV242: $i,SV63: $i,SV354: $i] :
( ( ( ! [SY6937: $i] :
( ~ ( in @ ( ordered_pair @ SY6937 @ SV354 ) @ SV63 )
| ~ ( in @ SY6937 @ SV242 ) ) )
= $true )
| ( ( in @ SV354 @ SV267 )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2766,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ SV267 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2767,plain,
! [SV64: $i,SV207: $i,SV190: $i,SV310: $i] :
( ( ( in @ SV310 @ SV190 )
= $false )
| ( ( in @ SV310 @ ( relation_rng @ SV207 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV64 @ SV310 ) @ SV207 )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV207 @ SV190 ) )
= $true )
| ( ( relation @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2768,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2769,plain,
! [SV191: $i,SV208: $i,SV64: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 ) )
= $false )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2770,plain,
! [SV158: $i,SV287: $i] :
( ( ( subset @ SV287 @ ( relation_field @ SV158 ) )
= $false )
| ( ( SV287 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV158 @ ( sK38_C @ SV287 @ SV158 ) ) @ SV287 )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2771,plain,
! [SV158: $i,SV287: $i] :
( ( ( subset @ SV287 @ ( relation_field @ SV158 ) )
= $false )
| ( ( SV287 = empty_set )
= $true )
| ( ( in @ ( sK38_C @ SV287 @ SV158 ) @ SV287 )
= $true )
| ( ( well_founded_relation @ SV158 )
= $false )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2772,plain,
! [SV243: $i,SV65: $i] :
( ( ( is_antisymmetric_in @ SV65 @ SV243 )
= $false )
| ( ( is_reflexive_in @ SV65 @ SV243 )
= $false )
| ( ( is_transitive_in @ SV65 @ SV243 )
= $false )
| ( ( ~ ( is_connected_in @ SV65 @ SV243 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2773,plain,
! [SV65: $i] :
( ( ( ~ ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2774,plain,
! [SV65: $i] :
( ( ( ! [SY6636: $i] :
( ~ ( well_orders @ SV65 @ SY6636 )
| ( is_antisymmetric_in @ SV65 @ SY6636 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2775,plain,
! [SV345: $i,SV65: $i] :
( ( ( well_orders @ SV65 @ SV345 )
= $false )
| ( ( is_connected_in @ SV65 @ SV345 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2776,plain,
! [SV161: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2777,plain,
! [SV161: $i] :
( ( ( ( apply @ SV161 @ ( sK17_B @ SV161 ) )
= ( apply @ SV161 @ ( sK18_SY6435 @ SV161 ) ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2666]) ).
thf(2778,plain,
! [SV330: $i,SV162: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( relation_dom @ SV162 ) ) )
= $true )
| ( ( ~ ( in @ SV330 @ ( relation_dom @ SV162 ) ) )
= $true )
| ( ( ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) ) )
= $true )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2779,plain,
( ( ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2780,plain,
( ( one_to_one @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2781,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2782,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2783,plain,
! [SV69: $i,SV213: $i,SV198: $i,SV314: $i] :
( ( ( in @ SV314 @ SV198 )
= $false )
| ( ( in @ SV314 @ ( relation_dom @ SV213 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV314 @ SV69 ) @ SV213 )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV213 @ SV198 ) )
= $true )
| ( ( relation @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2784,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2785,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 ) )
= $false )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2786,plain,
! [SV356: $i,SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV356 ) @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV356 @ SV247 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2787,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 ) )
= $false )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2788,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 ) )
= $false )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2789,plain,
! [SV269: $i,SV248: $i,SV70: $i,SV357: $i] :
( ( ( ! [SY6938: $i] :
( ~ ( in @ ( ordered_pair @ SV357 @ SY6938 ) @ SV70 )
| ~ ( in @ SY6938 @ SV248 ) ) )
= $true )
| ( ( in @ SV357 @ SV269 )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2790,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2791,plain,
! [SV71: $i,SV289: $i,SV270: $i] :
( ( ( in @ SV270 @ ( relation_dom @ ( relation_dom_restriction @ SV289 @ SV71 ) ) )
= $false )
| ( ( in @ SV270 @ ( relation_dom @ SV289 ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2792,plain,
! [SV71: $i,SV290: $i,SV271: $i] :
( ( ( in @ SV271 @ ( relation_dom @ ( relation_dom_restriction @ SV290 @ SV71 ) ) )
= $false )
| ( ( in @ SV271 @ SV71 )
= $true )
| ( ( function @ SV290 )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2793,plain,
! [SV368: $i,SV72: $i,SV291: $i] :
( ( ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SV368 ) )
| ~ ( in @ SV368 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(2794,plain,
! [SV72: $i,SV291: $i] :
( ( ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2795,plain,
! [SV292: $i,SV72: $i,SV369: $i] :
( ( ( ! [SY6943: $i] :
( ( SV369
!= ( apply @ SV72 @ SY6943 ) )
| ~ ( in @ SY6943 @ ( relation_dom @ SV72 ) ) )
| ( in @ SV369 @ SV292 ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2796,plain,
! [SV72: $i,SV292: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV292 )
| ~ ( ( SV370
!= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(2797,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
| ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(2798,plain,
! [SV73: $i,SV107: $i,SV346: $i] :
( ( ( ~ ( function @ SV346 ) )
= $true )
| ( ( ~ ( relation @ SV346 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) )
| ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2799,plain,
! [SV73: $i,SV107: $i,SV347: $i] :
( ( ( ~ ( function @ SV347 ) )
= $true )
| ( ( ~ ( relation @ SV347 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2800,plain,
! [SV316: $i,SV293: $i,SV74: $i] :
( ( ( ! [SY6913: $i] :
( ~ ( in @ SY6913 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6913 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SY6913 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(2801,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(2802,plain,
! [SV317: $i,SV294: $i,SV74: $i] :
( ( ( ! [SY6914: $i] :
( ! [SY6897: $i] :
( ~ ( in @ SY6897 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6897 @ SV294 )
| ( SY6914
!= ( apply @ SV74 @ SY6897 ) ) )
| ( in @ SY6914 @ SV317 ) ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2690]) ).
thf(2803,plain,
! [SV74: $i,SV294: $i,SV317: $i] :
( ( ( ! [SY6916: $i] :
( ~ ( in @ SY6916 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SY6916
!= ( apply @ SV74 @ ( sK55_E @ SY6916 @ SV317 @ SV294 @ SV74 ) ) ) ) ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2691]) ).
thf(2804,plain,
! [SV250: $i,SV75: $i,SV348: $i,SV331: $i] :
( ( ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV75 )
= $false )
| ( ( in @ ( ordered_pair @ SV331 @ SV348 ) @ SV250 )
= $true )
| ( ( subset @ SV75 @ SV250 )
= $false )
| ( ( relation @ SV250 )
= $false )
| ( ( relation @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2805,plain,
! [SV173: $i] :
( ( ( ~ ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2806,plain,
! [SV173: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2807,plain,
! [SV318: $i,SV174: $i,SV297: $i] :
( ( ( in @ SV297 @ ( relation_field @ SV174 ) )
= $false )
| ( ( ~ ( in @ SV318 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( SV297 = SV318 )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2808,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2809,plain,
! [SV76: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_C @ SV251 @ SV76 ) @ ( sK22_SY6437 @ SV251 @ SV76 ) ) @ SV76 )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2810,plain,
! [SV76: $i,SV327: $i,SV252: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ SV252 ) )
= $true )
| ( ( ~ ( in @ SV327 @ SV252 ) )
= $true )
| ( ( SV319 = SV327 )
= $true )
| ( ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2699]) ).
thf(2811,plain,
! [SV332: $i,SV77: $i,SV371: $i] :
( ( ( ( SV371
!= ( apply @ SV77 @ SV332 ) )
| ( in @ ( ordered_pair @ SV332 @ SV371 ) @ SV77 ) )
= $true )
| ( ( in @ SV332 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2812,plain,
! [SV77: $i,SV372: $i,SV333: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV333 @ SV372 ) @ SV77 )
| ( SV372
= ( apply @ SV77 @ SV333 ) ) )
= $true )
| ( ( in @ SV333 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(2813,plain,
! [SV334: $i,SV77: $i,SV359: $i] :
( ( ( ( SV359
!= ( apply @ SV77 @ SV334 ) ) )
= $true )
| ( ( SV359 = empty_set )
= $true )
| ( ( in @ SV334 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2814,plain,
! [SV335: $i,SV77: $i,SV360: $i] :
( ( ( ( SV360 != empty_set ) )
= $true )
| ( ( SV360
= ( apply @ SV77 @ SV335 ) )
= $true )
| ( ( in @ SV335 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2815,plain,
! [SV179: $i] :
( ( ( connected @ SV179 )
= $false )
| ( ( transitive @ SV179 )
= $false )
| ( ( reflexive @ SV179 )
= $false )
| ( ( antisymmetric @ SV179 )
= $false )
| ( ( ~ ( well_founded_relation @ SV179 ) )
= $true )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2816,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2817,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2818,plain,
! [SV349: $i] :
( ( ( relation @ SV349 )
= $false )
| ( ( ~ ( well_ordering @ SV349 )
| ( antisymmetric @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2819,plain,
! [SV219: $i,SV45: $i,SV361: $i,SV337: $i] :
( ( ( in @ ( ordered_pair @ SV337 @ SV361 ) @ SV45 )
= $false )
| ( ( in @ SV337 @ SV219 )
= $true )
| ( ( SV219
= ( relation_dom @ SV45 ) )
= $false )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2820,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2821,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2822,plain,
! [SV46: $i,SV321: $i,SV221: $i,SV298: $i] :
( ( ( in @ SV298 @ SV221 )
= $false )
| ( ( ~ ( in @ SV321 @ SV221 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2823,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2824,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2825,plain,
! [SV303: $i,SV126: $i,SV49: $i] :
( ( ( ~ ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) ) )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2826,plain,
! [SV49: $i,SV126: $i,SV303: $i] :
( ( ( ~ ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2827,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( subset @ SV304 @ SV224 )
= $false )
| ( ( SV304 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV50 @ ( sK34_D @ SV304 @ SV224 @ SV50 ) ) @ SV304 )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2828,plain,
! [SV50: $i,SV224: $i,SV304: $i] :
( ( ( subset @ SV304 @ SV224 )
= $false )
| ( ( SV304 = empty_set )
= $true )
| ( ( in @ ( sK34_D @ SV304 @ SV224 @ SV50 ) @ SV304 )
= $true )
| ( ( is_well_founded_in @ SV50 @ SV224 )
= $false )
| ( ( relation @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2829,plain,
! [SV105: $i,SV305: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( relation_dom @ SV305 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) )
= $true )
| ( ( function @ SV305 )
= $false )
| ( ( relation @ SV305 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(2830,plain,
! [SV105: $i,SV51: $i,SV339: $i] :
( ( ( function @ SV339 )
= $false )
| ( ( ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SV339 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2831,plain,
! [SV105: $i,SV51: $i,SV340: $i] :
( ( ( function @ SV340 )
= $false )
| ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
| ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2832,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2833,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2834,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) ) )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2725]) ).
thf(2835,plain,
! [SV257: $i,SV106: $i,SV373: $i,SV52: $i] :
( ( ( ! [SY6944: $i] :
( ~ ( in @ SY6944 @ SV52 )
| ~ ( in @ ( ordered_pair @ SV373 @ SY6944 ) @ SV106 )
| ( in @ ( ordered_pair @ SV373 @ SY6944 ) @ SV257 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2836,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) )
| ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2837,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2838,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ~ ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2729]) ).
thf(2839,plain,
! [SV279: $i,SV306: $i,SV53: $i] :
( ( ( ~ ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) ) )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2729]) ).
thf(2840,plain,
! [SV307: $i,SV280: $i,SV53: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SV374 ) @ SV280 )
| ( in @ SV374 @ SV307 ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(2841,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) )
| ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2842,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2843,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2844,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 )
| ~ ( in @ SV322 @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV329 @ SV228 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2845,plain,
! [SV142: $i,SV182: $i] :
( ( ( ( relation_dom @ SV182 )
= SV142 )
= $false )
| ( ( ( apply @ SV182 @ ( sK67_C @ SV182 @ SV142 ) )
= ( sK67_C @ SV182 @ SV142 ) )
= $false )
| ( ( SV182
= ( identity_relation @ SV142 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2846,plain,
! [SV260: $i,SV229: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV229 ) )
= $true )
| ( ( ( apply @ SV260 @ SV362 )
= SV362 )
= $true )
| ( ( SV260
= ( identity_relation @ SV229 ) )
= $false )
| ( ( function @ SV260 )
= $false )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(2847,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2848,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ( function @ SV350 ) )
= $true )
| ( ( ~ ( relation @ SV350 ) )
= $true )
| ( ( ( SV350
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2849,plain,
! [SV56: $i,SV351: $i] :
( ( ( ~ ( function @ SV351 ) )
= $true )
| ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV351
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2850,plain,
! [SV57: $i,SV231: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV231 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV231 @ SV57 ) @ ( sK41_SY6448 @ SV231 @ SV57 ) ) @ SV57 )
= $false )
| ( ( SV57 = SV231 )
= $true )
| ( ( relation @ SV231 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2851,plain,
! [SV232: $i,SV57: $i,SV375: $i,SV363: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV57 )
| ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV232 ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2852,plain,
! [SV57: $i,SV232: $i,SV376: $i,SV364: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV232 )
| ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV57 ) )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2853,plain,
! [SV58: $i,SV233: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV233 @ SV58 ) @ ( sK19_C @ SV233 @ SV58 ) ) @ SV58 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK19_C @ SV233 @ SV58 ) @ ( sK20_SY6436 @ SV233 @ SV58 ) ) @ SV233 )
= $false )
| ( ( SV233
= ( relation_inverse @ SV58 ) )
= $true )
| ( ( relation @ SV233 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2854,plain,
! [SV58: $i,SV234: $i,SV377: $i,SV365: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV365 @ SV377 ) @ SV234 )
| ( in @ ( ordered_pair @ SV377 @ SV365 ) @ SV58 ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(2855,plain,
! [SV234: $i,SV58: $i,SV366: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV378 @ SV366 ) @ SV58 )
| ( in @ ( ordered_pair @ SV366 @ SV378 ) @ SV234 ) )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2856,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2857,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2858,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) ) )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2859,plain,
! [SV263: $i,SV59: $i,SV236: $i,SV379: $i] :
( ( ( ! [SY6945: $i] :
( ~ ( in @ SV379 @ SV236 )
| ~ ( in @ ( ordered_pair @ SV379 @ SY6945 ) @ SV59 )
| ( in @ ( ordered_pair @ SV379 @ SY6945 ) @ SV263 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(2860,plain,
! [SV59: $i,SV236: $i,SV263: $i] :
( ( ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) )
| ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2861,plain,
! [SV238: $i,SV60: $i,SV342: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ SV367 @ SV342 ) @ SV60 )
= $false )
| ( ( in @ SV342 @ SV238 )
= $true )
| ( ( SV238
= ( relation_rng @ SV60 ) )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2862,plain,
! [SV147: $i,SV183: $i] :
( ( ( in @ ( ordered_pair @ ( sK60_C @ SV183 @ SV147 ) @ ( sK61_SY6460 @ SV183 @ SV147 ) ) @ SV183 )
= $false )
| ( ( ( sK60_C @ SV183 @ SV147 )
= ( sK61_SY6460 @ SV183 @ SV147 ) )
= $false )
| ( ( in @ ( sK60_C @ SV183 @ SV147 ) @ SV147 )
= $false )
| ( ( SV183
= ( identity_relation @ SV147 ) )
= $true )
| ( ( relation @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2863,plain,
! [SV184: $i,SV148: $i,SV352: $i,SV344: $i] :
( ( ( ( SV344 != SV352 ) )
= $true )
| ( ( ~ ( in @ SV344 @ SV148 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV344 @ SV352 ) @ SV184 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(2864,plain,
! [SV148: $i,SV184: $i,SV380: $i] :
( ( ( ! [SY6946: $i] :
( ~ ( in @ ( ordered_pair @ SV380 @ SY6946 ) @ SV184 )
| ( SV380 = SY6946 ) ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(2865,plain,
! [SV148: $i,SV184: $i,SV381: $i] :
( ( ( ! [SY6947: $i] :
~ ( in @ ( ordered_pair @ SV381 @ SY6947 ) @ SV184 )
| ( in @ SV381 @ SV148 ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(2866,plain,
! [SV63: $i,SV241: $i,SV266: $i,SV353: $i] :
( ( ( in @ ( ordered_pair @ SV353 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
= $false )
| ( ( ~ ( in @ SV353 @ SV241 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2867,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
= $true )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2763]) ).
thf(2868,plain,
! [SV63: $i,SV241: $i,SV266: $i] :
( ( ( in @ ( sK51_SY6455 @ SV266 @ SV241 @ SV63 ) @ SV241 )
= $true )
| ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2764]) ).
thf(2869,plain,
! [SV267: $i,SV242: $i,SV63: $i,SV354: $i,SV382: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV382 @ SV354 ) @ SV63 )
| ~ ( in @ SV382 @ SV242 ) )
= $true )
| ( ( in @ SV354 @ SV267 )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(2870,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( in @ SV355 @ SV267 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 ) ) )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2871,plain,
! [SV64: $i,SV191: $i,SV208: $i] :
( ( ( in @ ( sK68_D @ SV208 @ SV191 @ SV64 ) @ ( relation_rng @ SV208 ) )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2872,plain,
! [SV191: $i,SV208: $i,SV64: $i] :
( ( ( in @ ( ordered_pair @ SV64 @ ( sK68_D @ SV208 @ SV191 @ SV64 ) ) @ SV208 )
= $true )
| ( ( in @ SV64 @ ( relation_inverse_image @ SV208 @ SV191 ) )
= $false )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2769]) ).
thf(2873,plain,
! [SV243: $i,SV65: $i] :
( ( ( is_connected_in @ SV65 @ SV243 )
= $false )
| ( ( is_transitive_in @ SV65 @ SV243 )
= $false )
| ( ( is_reflexive_in @ SV65 @ SV243 )
= $false )
| ( ( is_antisymmetric_in @ SV65 @ SV243 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV65 @ SV243 ) )
= $true )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2874,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) )
| ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2875,plain,
! [SV383: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV383 )
| ( is_antisymmetric_in @ SV65 @ SV383 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(2876,plain,
! [SV161: $i] :
( ( ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
| ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2877,plain,
! [SV330: $i,SV162: $i,SV326: $i] :
( ( ( in @ SV326 @ ( relation_dom @ SV162 ) )
= $false )
| ( ( ~ ( in @ SV330 @ ( relation_dom @ SV162 ) ) )
= $true )
| ( ( ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) ) )
= $true )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2878,plain,
( ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(2879,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2880,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( in @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ ( relation_dom @ SV214 ) )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2881,plain,
! [SV69: $i,SV199: $i,SV214: $i] :
( ( ( in @ ( ordered_pair @ ( sK69_D @ SV214 @ SV199 @ SV69 ) @ SV69 ) @ SV214 )
= $true )
| ( ( in @ SV69 @ ( relation_image @ SV214 @ SV199 ) )
= $false )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2882,plain,
! [SV356: $i,SV70: $i,SV247: $i,SV268: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV356 ) @ SV70 )
= $false )
| ( ( ~ ( in @ SV356 @ SV247 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2883,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) ) @ SV70 )
= $true )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2787]) ).
thf(2884,plain,
! [SV70: $i,SV247: $i,SV268: $i] :
( ( ( in @ ( sK48_SY6453 @ SV268 @ SV247 @ SV70 ) @ SV247 )
= $true )
| ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2885,plain,
! [SV269: $i,SV248: $i,SV70: $i,SV384: $i,SV357: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV357 @ SV384 ) @ SV70 )
| ~ ( in @ SV384 @ SV248 ) )
= $true )
| ( ( in @ SV357 @ SV269 )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(2886,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( in @ SV358 @ SV269 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 ) ) )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2887,plain,
! [SV368: $i,SV72: $i,SV291: $i] :
( ( ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ SV368 ) ) )
= $true )
| ( ( ~ ( in @ SV368 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2888,plain,
! [SV72: $i,SV291: $i] :
( ( ( ( ( sK27_C @ SV291 @ SV72 )
!= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2889,plain,
! [SV72: $i,SV291: $i] :
( ( ( ~ ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2794]) ).
thf(2890,plain,
! [SV292: $i,SV72: $i,SV369: $i] :
( ( ( ! [SY6943: $i] :
( ( SV369
!= ( apply @ SV72 @ SY6943 ) )
| ~ ( in @ SY6943 @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( in @ SV369 @ SV292 )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2891,plain,
! [SV72: $i,SV292: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV292 ) )
= $true )
| ( ( ~ ( ( SV370
!= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2892,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2893,plain,
! [SV73: $i,SV107: $i,SV346: $i] :
( ( ( function @ SV346 )
= $false )
| ( ( ~ ( relation @ SV346 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) )
| ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2894,plain,
! [SV73: $i,SV107: $i,SV347: $i] :
( ( ( function @ SV347 )
= $false )
| ( ( ~ ( relation @ SV347 ) )
= $true )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(2895,plain,
! [SV316: $i,SV293: $i,SV74: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SV385 @ SV293 )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SV385 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(2896,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
| ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2897,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i] :
( ( ( ! [SY6948: $i] :
( ~ ( in @ SY6948 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6948 @ SV294 )
| ( SV386
!= ( apply @ SV74 @ SY6948 ) ) )
| ( in @ SV386 @ SV317 ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(2898,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV317 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SV387
!= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) ) ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(2899,plain,
! [SV173: $i] :
( ( ( ( ( sK70_B @ SV173 )
!= ( sK71_SY6463 @ SV173 ) ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2900,plain,
! [SV173: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2806]) ).
thf(2901,plain,
! [SV297: $i,SV174: $i,SV318: $i] :
( ( ( in @ SV318 @ ( relation_field @ SV174 ) )
= $false )
| ( ( in @ SV297 @ ( relation_field @ SV174 ) )
= $false )
| ( ( SV297 = SV318 )
= $true )
| ( ( in @ ( ordered_pair @ SV297 @ SV318 ) @ SV174 )
= $true )
| ( ( in @ ( ordered_pair @ SV318 @ SV297 ) @ SV174 )
= $true )
| ( ( connected @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2902,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2903,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(2904,plain,
! [SV76: $i,SV327: $i,SV252: $i,SV319: $i] :
( ( ( in @ SV319 @ SV252 )
= $false )
| ( ( ~ ( in @ SV327 @ SV252 ) )
= $true )
| ( ( SV319 = SV327 )
= $true )
| ( ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2905,plain,
! [SV332: $i,SV77: $i,SV371: $i] :
( ( ( ( SV371
!= ( apply @ SV77 @ SV332 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV332 @ SV371 ) @ SV77 )
= $true )
| ( ( in @ SV332 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2906,plain,
! [SV77: $i,SV372: $i,SV333: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV333 @ SV372 ) @ SV77 ) )
= $true )
| ( ( SV372
= ( apply @ SV77 @ SV333 ) )
= $true )
| ( ( in @ SV333 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2907,plain,
! [SV334: $i,SV77: $i,SV359: $i] :
( ( ( SV359
= ( apply @ SV77 @ SV334 ) )
= $false )
| ( ( SV359 = empty_set )
= $true )
| ( ( in @ SV334 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2908,plain,
! [SV335: $i,SV77: $i,SV360: $i] :
( ( ( SV360 = empty_set )
= $false )
| ( ( SV360
= ( apply @ SV77 @ SV335 ) )
= $true )
| ( ( in @ SV335 @ ( relation_dom @ SV77 ) )
= $true )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2909,plain,
! [SV179: $i] :
( ( ( well_founded_relation @ SV179 )
= $false )
| ( ( antisymmetric @ SV179 )
= $false )
| ( ( reflexive @ SV179 )
= $false )
| ( ( transitive @ SV179 )
= $false )
| ( ( connected @ SV179 )
= $false )
| ( ( well_ordering @ SV179 )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2910,plain,
! [SV388: $i] :
( ( ~ ( relation @ SV388 )
| ~ ( well_ordering @ SV388 )
| ( reflexive @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(2911,plain,
! [SV389: $i] :
( ( ~ ( relation @ SV389 )
| ~ ( well_ordering @ SV389 )
| ( transitive @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(2912,plain,
! [SV349: $i] :
( ( ( ~ ( well_ordering @ SV349 ) )
= $true )
| ( ( antisymmetric @ SV349 )
= $true )
| ( ( relation @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2913,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2820]) ).
thf(2914,plain,
! [SV46: $i,SV220: $i] :
( ( ( in @ ( ordered_pair @ ( sK29_C @ SV220 @ SV46 ) @ ( sK30_SY6442 @ SV220 @ SV46 ) ) @ SV46 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2821]) ).
thf(2915,plain,
! [SV46: $i,SV298: $i,SV221: $i,SV321: $i] :
( ( ( in @ SV321 @ SV221 )
= $false )
| ( ( in @ SV298 @ SV221 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2916,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ! [SY6901: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SY6901 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6901 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2917,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(2918,plain,
! [SV303: $i,SV126: $i,SV49: $i] :
( ( ( ! [SY6902: $i,SY6903: $i] :
( ! [SY6740: $i] :
( ~ ( in @ ( ordered_pair @ SY6902 @ SY6740 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6740 @ SY6903 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SY6902 @ SY6903 ) @ SV303 ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2919,plain,
! [SV49: $i,SV126: $i,SV303: $i] :
( ( ( ! [SY6905: $i,SY6906: $i] :
( ~ ( in @ ( ordered_pair @ SY6905 @ SY6906 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SY6905 @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6906 @ SY6905 @ SV303 @ SV126 @ SV49 ) @ SY6906 ) @ SV126 ) ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2920,plain,
! [SV105: $i,SV305: $i,SV51: $i] :
( ( ( in @ SV51 @ ( relation_dom @ SV305 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) )
= $true )
| ( ( function @ SV305 )
= $false )
| ( ( relation @ SV305 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2921,plain,
! [SV105: $i,SV51: $i,SV339: $i] :
( ( ( relation @ SV339 )
= $false )
| ( ( function @ SV339 )
= $false )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
| ( in @ SV51 @ ( relation_dom @ SV339 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2922,plain,
! [SV105: $i,SV51: $i,SV340: $i] :
( ( ( relation @ SV340 )
= $false )
| ( ( function @ SV340 )
= $false )
| ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
| ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) ) )
= $true )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2923,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2924,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(2925,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2926,plain,
! [SV257: $i,SV106: $i,SV373: $i,SV52: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV52 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV106 )
| ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV257 ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(2927,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ~ ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(2928,plain,
! [SV52: $i,SV106: $i,SV257: $i] :
( ( ( ~ ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) )
= $false )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2836]) ).
thf(2929,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2930,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2838]) ).
thf(2931,plain,
! [SV279: $i,SV306: $i,SV53: $i] :
( ( ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
| ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2839]) ).
thf(2932,plain,
! [SV307: $i,SV280: $i,SV53: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( relation_dom @ SV53 ) )
| ~ ( in @ ( apply @ SV53 @ SV374 ) @ SV280 ) )
= $true )
| ( ( in @ SV374 @ SV307 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2933,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ~ ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2934,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ~ ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) )
= $false )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(2935,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(2936,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV227 @ SV54 ) @ ( sK11_SY6427 @ SV227 @ SV54 ) ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2843]) ).
thf(2937,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV322 @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV329 @ SV228 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2938,plain,
! [SV260: $i,SV229: $i,SV362: $i] :
( ( ( in @ SV362 @ SV229 )
= $false )
| ( ( ( apply @ SV260 @ SV362 )
= SV362 )
= $true )
| ( ( SV260
= ( identity_relation @ SV229 ) )
= $false )
| ( ( function @ SV260 )
= $false )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2939,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(2940,plain,
! [SV56: $i,SV350: $i] :
( ( ( function @ SV350 )
= $false )
| ( ( ~ ( relation @ SV350 ) )
= $true )
| ( ( ( SV350
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2941,plain,
! [SV56: $i,SV351: $i] :
( ( ( function @ SV351 )
= $false )
| ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV351
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2942,plain,
! [SV232: $i,SV57: $i,SV375: $i,SV363: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV57 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV232 )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2943,plain,
! [SV57: $i,SV232: $i,SV376: $i,SV364: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV232 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV57 )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(2944,plain,
! [SV58: $i,SV234: $i,SV377: $i,SV365: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV365 @ SV377 ) @ SV234 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV377 @ SV365 ) @ SV58 )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2945,plain,
! [SV234: $i,SV58: $i,SV366: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV378 @ SV366 ) @ SV58 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV366 @ SV378 ) @ SV234 )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2946,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2947,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(2948,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2858]) ).
thf(2949,plain,
! [SV263: $i,SV59: $i,SV391: $i,SV236: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV236 )
| ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV59 )
| ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV263 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(2950,plain,
! [SV59: $i,SV236: $i,SV263: $i] :
( ( ( ~ ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(2951,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( ~ ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) )
= $false )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(2952,plain,
! [SV184: $i,SV148: $i,SV352: $i,SV344: $i] :
( ( ( SV344 = SV352 )
= $false )
| ( ( ~ ( in @ SV344 @ SV148 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV344 @ SV352 ) @ SV184 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2953,plain,
! [SV148: $i,SV184: $i,SV392: $i,SV380: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV380 @ SV392 ) @ SV184 )
| ( SV380 = SV392 ) )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(2954,plain,
! [SV148: $i,SV184: $i,SV381: $i] :
( ( ( ! [SY6947: $i] :
~ ( in @ ( ordered_pair @ SV381 @ SY6947 ) @ SV184 ) )
= $true )
| ( ( in @ SV381 @ SV148 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(2955,plain,
! [SV63: $i,SV266: $i,SV241: $i,SV353: $i] :
( ( ( in @ SV353 @ SV241 )
= $false )
| ( ( in @ ( ordered_pair @ SV353 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
= $false )
| ( ( ~ ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 ) )
= $true )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2956,plain,
! [SV267: $i,SV242: $i,SV63: $i,SV354: $i,SV382: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV382 @ SV354 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV382 @ SV242 ) )
= $true )
| ( ( in @ SV354 @ SV267 )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(2957,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 )
| ~ ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 ) )
= $false )
| ( ( in @ SV355 @ SV267 )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2958,plain,
! [SV243: $i,SV65: $i] :
( ( ( is_well_founded_in @ SV65 @ SV243 )
= $false )
| ( ( is_antisymmetric_in @ SV65 @ SV243 )
= $false )
| ( ( is_reflexive_in @ SV65 @ SV243 )
= $false )
| ( ( is_transitive_in @ SV65 @ SV243 )
= $false )
| ( ( is_connected_in @ SV65 @ SV243 )
= $false )
| ( ( well_orders @ SV65 @ SV243 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(2959,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2874]) ).
thf(2960,plain,
! [SV65: $i] :
( ( ( ~ ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2874]) ).
thf(2961,plain,
! [SV383: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV383 ) )
= $true )
| ( ( is_antisymmetric_in @ SV65 @ SV383 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(2962,plain,
! [SV161: $i] :
( ( ( ~ ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2963,plain,
! [SV161: $i] :
( ( ( ~ ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) ) )
= $false )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2876]) ).
thf(2964,plain,
! [SV326: $i,SV162: $i,SV330: $i] :
( ( ( in @ SV330 @ ( relation_dom @ SV162 ) )
= $false )
| ( ( in @ SV326 @ ( relation_dom @ SV162 ) )
= $false )
| ( ( ( ( apply @ SV162 @ SV326 )
!= ( apply @ SV162 @ SV330 ) ) )
= $true )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2965,plain,
( ( ~ ( function @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(2966,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(2967,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(2968,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(2969,plain,
! [SV70: $i,SV268: $i,SV247: $i,SV356: $i] :
( ( ( in @ SV356 @ SV247 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV356 ) @ SV70 )
= $false )
| ( ( ~ ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 ) )
= $true )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2970,plain,
! [SV269: $i,SV248: $i,SV70: $i,SV384: $i,SV357: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV357 @ SV384 ) @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV384 @ SV248 ) )
= $true )
| ( ( in @ SV357 @ SV269 )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(2971,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
| ~ ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 ) )
= $false )
| ( ( in @ SV358 @ SV269 )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(2972,plain,
! [SV368: $i,SV72: $i,SV291: $i] :
( ( ( ( sK27_C @ SV291 @ SV72 )
= ( apply @ SV72 @ SV368 ) )
= $false )
| ( ( ~ ( in @ SV368 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2973,plain,
! [SV72: $i,SV291: $i] :
( ( ( ( sK27_C @ SV291 @ SV72 )
= ( apply @ SV72 @ ( sK28_SY6441 @ SV291 @ SV72 ) ) )
= $true )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(2974,plain,
! [SV72: $i,SV291: $i] :
( ( ( in @ ( sK28_SY6441 @ SV291 @ SV72 ) @ ( relation_dom @ SV72 ) )
= $true )
| ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2975,plain,
! [SV292: $i,SV393: $i,SV72: $i,SV369: $i] :
( ( ( ( SV369
!= ( apply @ SV72 @ SV393 ) )
| ~ ( in @ SV393 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( in @ SV369 @ SV292 )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(2976,plain,
! [SV72: $i,SV292: $i,SV370: $i] :
( ( ( in @ SV370 @ SV292 )
= $false )
| ( ( ~ ( ( SV370
!= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) ) )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2977,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
| ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(2978,plain,
! [SV73: $i,SV107: $i,SV346: $i] :
( ( ( relation @ SV346 )
= $false )
| ( ( function @ SV346 )
= $false )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) )
| ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(2979,plain,
! [SV73: $i,SV107: $i,SV347: $i] :
( ( ( relation @ SV347 )
= $false )
| ( ( function @ SV347 )
= $false )
| ( ( ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) )
| ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) ) )
= $true )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(2980,plain,
! [SV316: $i,SV293: $i,SV74: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SV385 @ SV293 ) )
= $true )
| ( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SV385 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2981,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2982,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2896]) ).
thf(2983,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i] :
( ( ( ! [SY6948: $i] :
( ~ ( in @ SY6948 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SY6948 @ SV294 )
| ( SV386
!= ( apply @ SV74 @ SY6948 ) ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(2984,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV317 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SV387
!= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) ) ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2898]) ).
thf(2985,plain,
! [SV173: $i] :
( ( ( ( sK70_B @ SV173 )
= ( sK71_SY6463 @ SV173 ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(2986,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
| ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2987,plain,
! [SV76: $i,SV251: $i] :
( ( ( ( ( sK21_C @ SV251 @ SV76 )
!= ( sK22_SY6437 @ SV251 @ SV76 ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(2988,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) ) )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(2989,plain,
! [SV76: $i,SV319: $i,SV252: $i,SV327: $i] :
( ( ( in @ SV327 @ SV252 )
= $false )
| ( ( in @ SV319 @ SV252 )
= $false )
| ( ( SV319 = SV327 )
= $true )
| ( ( in @ ( ordered_pair @ SV319 @ SV327 ) @ SV76 )
= $true )
| ( ( in @ ( ordered_pair @ SV327 @ SV319 ) @ SV76 )
= $true )
| ( ( is_connected_in @ SV76 @ SV252 )
= $false )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2990,plain,
! [SV332: $i,SV77: $i,SV371: $i] :
( ( ( SV371
= ( apply @ SV77 @ SV332 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV332 @ SV371 ) @ SV77 )
= $true )
| ( ( in @ SV332 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2991,plain,
! [SV77: $i,SV372: $i,SV333: $i] :
( ( ( in @ ( ordered_pair @ SV333 @ SV372 ) @ SV77 )
= $false )
| ( ( SV372
= ( apply @ SV77 @ SV333 ) )
= $true )
| ( ( in @ SV333 @ ( relation_dom @ SV77 ) )
= $false )
| ( ( function @ SV77 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(2992,plain,
! [SV388: $i] :
( ( ( ~ ( relation @ SV388 ) )
= $true )
| ( ( ~ ( well_ordering @ SV388 )
| ( reflexive @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(2993,plain,
! [SV389: $i] :
( ( ( ~ ( relation @ SV389 ) )
= $true )
| ( ( ~ ( well_ordering @ SV389 )
| ( transitive @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(2994,plain,
! [SV349: $i] :
( ( ( well_ordering @ SV349 )
= $false )
| ( ( antisymmetric @ SV349 )
= $true )
| ( ( relation @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(2995,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
| ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2996,plain,
! [SV221: $i,SV46: $i,SV321: $i,SV298: $i] :
( ( ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 )
= $false )
| ( ( in @ SV298 @ SV221 )
= $false )
| ( ( in @ SV321 @ SV221 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 ) )
= $true )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(2997,plain,
! [SV394: $i,SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SV394 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SV394 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(2998,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(2999,plain,
! [SV303: $i,SV126: $i,SV49: $i,SV395: $i] :
( ( ( ! [SY6949: $i] :
( ! [SY6950: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY6950 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6950 @ SY6949 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SV395 @ SY6949 ) @ SV303 ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3000,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV396: $i] :
( ( ( ! [SY6951: $i] :
( ~ ( in @ ( ordered_pair @ SV396 @ SY6951 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SY6951 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY6951 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SY6951 ) @ SV126 ) ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3001,plain,
! [SV105: $i,SV51: $i,SV305: $i] :
( ( ( in @ ( apply @ SV305 @ SV51 ) @ ( relation_dom @ SV105 ) )
= $false )
| ( ( in @ SV51 @ ( relation_dom @ SV305 ) )
= $false )
| ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV305 @ SV105 ) ) )
= $true )
| ( ( function @ SV305 )
= $false )
| ( ( relation @ SV305 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3002,plain,
! [SV105: $i,SV339: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) ) )
= $true )
| ( ( in @ SV51 @ ( relation_dom @ SV339 ) )
= $true )
| ( ( function @ SV339 )
= $false )
| ( ( relation @ SV339 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3003,plain,
! [SV105: $i,SV340: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) )
= $true )
| ( ( function @ SV340 )
= $false )
| ( ( relation @ SV340 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3004,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
= $false )
| ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 ) )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3005,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3006,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 )
= $true )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3007,plain,
! [SV257: $i,SV106: $i,SV373: $i,SV52: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV52 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3008,plain,
! [SV106: $i,SV52: $i,SV257: $i] :
( ( ( ! [SY6853: $i,SY6854: $i] :
( ~ ( in @ ( ordered_pair @ SY6853 @ SY6854 ) @ SV257 )
| ( in @ SY6854 @ SV52 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(3009,plain,
! [SV52: $i,SV106: $i,SV257: $i] :
( ( ( ! [SY6855: $i,SY6856: $i] :
( ~ ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV257 )
| ( in @ ( ordered_pair @ SY6855 @ SY6856 ) @ SV106 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(3010,plain,
! [SV279: $i,SV306: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
= $false )
| ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 ) )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3011,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $true )
| ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3012,plain,
! [SV279: $i,SV306: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
= $true )
| ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 )
= $true )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3013,plain,
! [SV307: $i,SV280: $i,SV53: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV53 @ SV374 ) @ SV280 ) )
= $true )
| ( ( in @ SV374 @ SV307 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3014,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ! [SY6908: $i] :
( ~ ( in @ SY6908 @ SV307 )
| ( in @ SY6908 @ ( relation_dom @ SV53 ) ) ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2933]) ).
thf(3015,plain,
! [SV280: $i,SV53: $i,SV307: $i] :
( ( ( ! [SY6909: $i] :
( ~ ( in @ SY6909 @ SV307 )
| ( in @ ( apply @ SV53 @ SY6909 ) @ SV280 ) ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2934]) ).
thf(3016,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
| ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3017,plain,
! [SV54: $i,SV329: $i,SV322: $i,SV228: $i,SV308: $i] :
( ( ( in @ SV308 @ SV228 )
= $false )
| ( ( ~ ( in @ SV322 @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV329 @ SV228 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3018,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3019,plain,
! [SV56: $i,SV350: $i] :
( ( ( relation @ SV350 )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( ( SV350
!= ( function_inverse @ SV56 ) )
| ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3020,plain,
! [SV56: $i,SV351: $i] :
( ( ( relation @ SV351 )
= $false )
| ( ( function @ SV351 )
= $false )
| ( ( ( SV351
!= ( function_inverse @ SV56 ) )
| ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3021,plain,
! [SV232: $i,SV57: $i,SV375: $i,SV363: $i] :
( ( ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV57 )
= $false )
| ( ( in @ ( ordered_pair @ SV363 @ SV375 ) @ SV232 )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3022,plain,
! [SV57: $i,SV232: $i,SV376: $i,SV364: $i] :
( ( ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV232 )
= $false )
| ( ( in @ ( ordered_pair @ SV364 @ SV376 ) @ SV57 )
= $true )
| ( ( SV57 = SV232 )
= $false )
| ( ( relation @ SV232 )
= $false )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3023,plain,
! [SV58: $i,SV234: $i,SV377: $i,SV365: $i] :
( ( ( in @ ( ordered_pair @ SV365 @ SV377 ) @ SV234 )
= $false )
| ( ( in @ ( ordered_pair @ SV377 @ SV365 ) @ SV58 )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3024,plain,
! [SV234: $i,SV58: $i,SV366: $i,SV378: $i] :
( ( ( in @ ( ordered_pair @ SV378 @ SV366 ) @ SV58 )
= $false )
| ( ( in @ ( ordered_pair @ SV366 @ SV378 ) @ SV234 )
= $true )
| ( ( SV234
= ( relation_inverse @ SV58 ) )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3025,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
= $false )
| ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 ) )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3026,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3027,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 )
= $true )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3028,plain,
! [SV263: $i,SV59: $i,SV391: $i,SV236: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV236 )
| ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3029,plain,
! [SV59: $i,SV236: $i,SV263: $i] :
( ( ( ! [SY6862: $i] :
( ! [SY6863: $i] :
~ ( in @ ( ordered_pair @ SY6862 @ SY6863 ) @ SV263 )
| ( in @ SY6862 @ SV236 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2950]) ).
thf(3030,plain,
! [SV236: $i,SV59: $i,SV263: $i] :
( ( ( ! [SY6864: $i,SY6865: $i] :
( ~ ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV263 )
| ( in @ ( ordered_pair @ SY6864 @ SY6865 ) @ SV59 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2951]) ).
thf(3031,plain,
! [SV184: $i,SV352: $i,SV148: $i,SV344: $i] :
( ( ( in @ SV344 @ SV148 )
= $false )
| ( ( SV344 = SV352 )
= $false )
| ( ( in @ ( ordered_pair @ SV344 @ SV352 ) @ SV184 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3032,plain,
! [SV148: $i,SV184: $i,SV392: $i,SV380: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV380 @ SV392 ) @ SV184 ) )
= $true )
| ( ( SV380 = SV392 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3033,plain,
! [SV148: $i,SV184: $i,SV397: $i,SV381: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV381 @ SV397 ) @ SV184 ) )
= $true )
| ( ( in @ SV381 @ SV148 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3034,plain,
! [SV353: $i,SV63: $i,SV241: $i,SV266: $i] :
( ( ( in @ ( sK50_D @ SV266 @ SV241 @ SV63 ) @ SV266 )
= $false )
| ( ( in @ ( ordered_pair @ SV353 @ ( sK50_D @ SV266 @ SV241 @ SV63 ) ) @ SV63 )
= $false )
| ( ( in @ SV353 @ SV241 )
= $false )
| ( ( SV266
= ( relation_image @ SV63 @ SV241 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3035,plain,
! [SV267: $i,SV242: $i,SV63: $i,SV354: $i,SV382: $i] :
( ( ( in @ ( ordered_pair @ SV382 @ SV354 ) @ SV63 )
= $false )
| ( ( ~ ( in @ SV382 @ SV242 ) )
= $true )
| ( ( in @ SV354 @ SV267 )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3036,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 ) )
= $false )
| ( ( in @ SV355 @ SV267 )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3037,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( ~ ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 ) )
= $false )
| ( ( in @ SV355 @ SV267 )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3038,plain,
! [SV65: $i] :
( ( ( ! [SY6634: $i] :
( ~ ( well_orders @ SV65 @ SY6634 )
| ( is_reflexive_in @ SV65 @ SY6634 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2959]) ).
thf(3039,plain,
! [SV65: $i] :
( ( ( ! [SY6635: $i] :
( ~ ( well_orders @ SV65 @ SY6635 )
| ( is_transitive_in @ SV65 @ SY6635 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3040,plain,
! [SV383: $i,SV65: $i] :
( ( ( well_orders @ SV65 @ SV383 )
= $false )
| ( ( is_antisymmetric_in @ SV65 @ SV383 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3041,plain,
! [SV161: $i] :
( ( ( in @ ( sK17_B @ SV161 ) @ ( relation_dom @ SV161 ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3042,plain,
! [SV161: $i] :
( ( ( in @ ( sK18_SY6435 @ SV161 ) @ ( relation_dom @ SV161 ) )
= $true )
| ( ( one_to_one @ SV161 )
= $true )
| ( ( function @ SV161 )
= $false )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3043,plain,
! [SV330: $i,SV326: $i,SV162: $i] :
( ( ( ( apply @ SV162 @ SV326 )
= ( apply @ SV162 @ SV330 ) )
= $false )
| ( ( in @ SV326 @ ( relation_dom @ SV162 ) )
= $false )
| ( ( in @ SV330 @ ( relation_dom @ SV162 ) )
= $false )
| ( ( SV326 = SV330 )
= $true )
| ( ( one_to_one @ SV162 )
= $false )
| ( ( function @ SV162 )
= $false )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3044,plain,
( ( function @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(3045,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(3046,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2967]) ).
thf(3047,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2968]) ).
thf(3048,plain,
! [SV356: $i,SV70: $i,SV247: $i,SV268: $i] :
( ( ( in @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV268 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK47_D @ SV268 @ SV247 @ SV70 ) @ SV356 ) @ SV70 )
= $false )
| ( ( in @ SV356 @ SV247 )
= $false )
| ( ( SV268
= ( relation_inverse_image @ SV70 @ SV247 ) )
= $true )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3049,plain,
! [SV269: $i,SV248: $i,SV70: $i,SV384: $i,SV357: $i] :
( ( ( in @ ( ordered_pair @ SV357 @ SV384 ) @ SV70 )
= $false )
| ( ( ~ ( in @ SV384 @ SV248 ) )
= $true )
| ( ( in @ SV357 @ SV269 )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3050,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 ) )
= $false )
| ( ( in @ SV358 @ SV269 )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2971]) ).
thf(3051,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( ~ ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 ) )
= $false )
| ( ( in @ SV358 @ SV269 )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2971]) ).
thf(3052,plain,
! [SV291: $i,SV72: $i,SV368: $i] :
( ( ( in @ SV368 @ ( relation_dom @ SV72 ) )
= $false )
| ( ( ( sK27_C @ SV291 @ SV72 )
= ( apply @ SV72 @ SV368 ) )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 ) )
= $true )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3053,plain,
! [SV292: $i,SV393: $i,SV72: $i,SV369: $i] :
( ( ( ( SV369
!= ( apply @ SV72 @ SV393 ) ) )
= $true )
| ( ( ~ ( in @ SV393 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( in @ SV369 @ SV292 )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3054,plain,
! [SV292: $i,SV72: $i,SV370: $i] :
( ( ( ( SV370
!= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) )
| ~ ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
= $false )
| ( ( in @ SV370 @ SV292 )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3055,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( ~ ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2977]) ).
thf(3056,plain,
! [SV73: $i,SV315: $i,SV107: $i] :
( ( ( ~ ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2977]) ).
thf(3057,plain,
! [SV73: $i,SV346: $i,SV107: $i] :
( ( ( ( SV107
!= ( relation_dom_restriction @ SV346 @ SV73 ) ) )
= $true )
| ( ( ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV346 )
= $false )
| ( ( relation @ SV346 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3058,plain,
! [SV73: $i,SV347: $i,SV107: $i] :
( ( ( ( SV107
!= ( relation_dom_restriction @ SV347 @ SV73 ) ) )
= $true )
| ( ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) )
= $true )
| ( ( function @ SV347 )
= $false )
| ( ( relation @ SV347 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3059,plain,
! [SV316: $i,SV293: $i,SV74: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV74 ) ) )
= $true )
| ( ( ~ ( in @ SV385 @ SV293 ) )
= $true )
| ( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SV385 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3060,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3061,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
= ( apply @ SV74 @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3062,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SV398 @ SV294 )
| ( SV386
!= ( apply @ SV74 @ SV398 ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3063,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( in @ SV387 @ SV317 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SV387
!= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) ) ) )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3064,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2986]) ).
thf(3065,plain,
! [SV173: $i] :
( ( ( ~ ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) ) )
= $false )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2986]) ).
thf(3066,plain,
! [SV76: $i,SV251: $i] :
( ( ( ( sK21_C @ SV251 @ SV76 )
= ( sK22_SY6437 @ SV251 @ SV76 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3067,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
| ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3068,plain,
! [SV388: $i] :
( ( ( relation @ SV388 )
= $false )
| ( ( ~ ( well_ordering @ SV388 )
| ( reflexive @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3069,plain,
! [SV389: $i] :
( ( ( relation @ SV389 )
= $false )
| ( ( ~ ( well_ordering @ SV389 )
| ( transitive @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3070,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2995]) ).
thf(3071,plain,
! [SV46: $i,SV220: $i] :
( ( ( ~ ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 ) )
= $false )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2995]) ).
thf(3072,plain,
! [SV221: $i,SV46: $i,SV298: $i,SV321: $i] :
( ( ( in @ ( ordered_pair @ SV321 @ SV298 ) @ SV46 )
= $false )
| ( ( in @ SV321 @ SV221 )
= $false )
| ( ( in @ SV298 @ SV221 )
= $false )
| ( ( in @ ( ordered_pair @ SV298 @ SV321 ) @ SV46 )
= $false )
| ( ( SV298 = SV321 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV221 )
= $false )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3073,plain,
! [SV394: $i,SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SV394 ) @ SV49 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV394 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3074,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3075,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3076,plain,
! [SV303: $i,SV126: $i,SV399: $i,SV49: $i,SV395: $i] :
( ( ( ! [SY6952: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY6952 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6952 @ SV399 ) @ SV126 ) )
| ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3077,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
| ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3078,plain,
! [SV105: $i,SV339: $i,SV51: $i] :
( ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV339 @ SV105 ) ) )
= $false )
| ( ( in @ SV51 @ ( relation_dom @ SV339 ) )
= $true )
| ( ( function @ SV339 )
= $false )
| ( ( relation @ SV339 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3079,plain,
! [SV105: $i,SV340: $i,SV51: $i] :
( ( ( in @ SV51 @ ( relation_dom @ ( relation_composition @ SV340 @ SV105 ) ) )
= $false )
| ( ( in @ ( apply @ SV340 @ SV51 ) @ ( relation_dom @ SV105 ) )
= $true )
| ( ( function @ SV340 )
= $false )
| ( ( relation @ SV340 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( relation @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3080,plain,
! [SV52: $i,SV106: $i,SV256: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV256 )
= $false )
| ( ( in @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV256 @ SV106 @ SV52 ) @ ( sK54_SY6456 @ SV256 @ SV106 @ SV52 ) ) @ SV106 )
= $false )
| ( ( SV256
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $true )
| ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3081,plain,
! [SV257: $i,SV106: $i,SV373: $i,SV52: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ SV52 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3082,plain,
! [SV106: $i,SV52: $i,SV257: $i,SV401: $i] :
( ( ( ! [SY6953: $i] :
( ~ ( in @ ( ordered_pair @ SV401 @ SY6953 ) @ SV257 )
| ( in @ SY6953 @ SV52 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3083,plain,
! [SV52: $i,SV106: $i,SV257: $i,SV402: $i] :
( ( ( ! [SY6954: $i] :
( ~ ( in @ ( ordered_pair @ SV402 @ SY6954 ) @ SV257 )
| ( in @ ( ordered_pair @ SV402 @ SY6954 ) @ SV106 ) ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3084,plain,
! [SV53: $i,SV279: $i,SV306: $i] :
( ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ SV306 )
= $false )
| ( ( in @ ( sK52_D @ SV306 @ SV279 @ SV53 ) @ ( relation_dom @ SV53 ) )
= $false )
| ( ( in @ ( apply @ SV53 @ ( sK52_D @ SV306 @ SV279 @ SV53 ) ) @ SV279 )
= $false )
| ( ( SV306
= ( relation_inverse_image @ SV53 @ SV279 ) )
= $true )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3085,plain,
! [SV307: $i,SV280: $i,SV53: $i,SV374: $i] :
( ( ( in @ SV374 @ ( relation_dom @ SV53 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV53 @ SV374 ) @ SV280 ) )
= $true )
| ( ( in @ SV374 @ SV307 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3086,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV307 )
| ( in @ SV403 @ ( relation_dom @ SV53 ) ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3087,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV307 )
| ( in @ ( apply @ SV53 @ SV404 ) @ SV280 ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3088,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3089,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3016]) ).
thf(3090,plain,
! [SV54: $i,SV329: $i,SV308: $i,SV228: $i,SV322: $i] :
( ( ( in @ SV322 @ SV228 )
= $false )
| ( ( in @ SV308 @ SV228 )
= $false )
| ( ( ~ ( in @ SV329 @ SV228 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3091,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3092,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3093,plain,
! [SV56: $i,SV350: $i] :
( ( ( ( SV350
!= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3094,plain,
! [SV56: $i,SV351: $i] :
( ( ( ( SV351
!= ( function_inverse @ SV56 ) ) )
= $true )
| ( ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3095,plain,
! [SV59: $i,SV235: $i,SV262: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV262 )
= $false )
| ( ( in @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ SV235 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV262 @ SV235 @ SV59 ) @ ( sK59_SY6459 @ SV262 @ SV235 @ SV59 ) ) @ SV59 )
= $false )
| ( ( SV262
= ( relation_dom_restriction @ SV59 @ SV235 ) )
= $true )
| ( ( relation @ SV262 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3096,plain,
! [SV263: $i,SV59: $i,SV391: $i,SV236: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV236 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3097,plain,
! [SV59: $i,SV236: $i,SV263: $i,SV405: $i] :
( ( ( ! [SY6955: $i] :
~ ( in @ ( ordered_pair @ SV405 @ SY6955 ) @ SV263 )
| ( in @ SV405 @ SV236 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3098,plain,
! [SV236: $i,SV59: $i,SV263: $i,SV406: $i] :
( ( ( ! [SY6956: $i] :
( ~ ( in @ ( ordered_pair @ SV406 @ SY6956 ) @ SV263 )
| ( in @ ( ordered_pair @ SV406 @ SY6956 ) @ SV59 ) ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3099,plain,
! [SV148: $i,SV184: $i,SV392: $i,SV380: $i] :
( ( ( in @ ( ordered_pair @ SV380 @ SV392 ) @ SV184 )
= $false )
| ( ( SV380 = SV392 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3100,plain,
! [SV148: $i,SV184: $i,SV397: $i,SV381: $i] :
( ( ( in @ ( ordered_pair @ SV381 @ SV397 ) @ SV184 )
= $false )
| ( ( in @ SV381 @ SV148 )
= $true )
| ( ( SV184
= ( identity_relation @ SV148 ) )
= $false )
| ( ( relation @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3101,plain,
! [SV267: $i,SV63: $i,SV354: $i,SV242: $i,SV382: $i] :
( ( ( in @ SV382 @ SV242 )
= $false )
| ( ( in @ ( ordered_pair @ SV382 @ SV354 ) @ SV63 )
= $false )
| ( ( in @ SV354 @ SV267 )
= $true )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3102,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV355 ) @ SV63 )
= $true )
| ( ( in @ SV355 @ SV267 )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3103,plain,
! [SV63: $i,SV242: $i,SV267: $i,SV355: $i] :
( ( ( in @ ( sK49_E @ SV355 @ SV267 @ SV242 @ SV63 ) @ SV242 )
= $true )
| ( ( in @ SV355 @ SV267 )
= $false )
| ( ( SV267
= ( relation_image @ SV63 @ SV242 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3037]) ).
thf(3104,plain,
! [SV407: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV407 )
| ( is_reflexive_in @ SV65 @ SV407 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3105,plain,
! [SV408: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV408 )
| ( is_transitive_in @ SV65 @ SV408 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3106,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3107,plain,
! [SV269: $i,SV70: $i,SV357: $i,SV248: $i,SV384: $i] :
( ( ( in @ SV384 @ SV248 )
= $false )
| ( ( in @ ( ordered_pair @ SV357 @ SV384 ) @ SV70 )
= $false )
| ( ( in @ SV357 @ SV269 )
= $true )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3108,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( in @ ( ordered_pair @ SV358 @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) ) @ SV70 )
= $true )
| ( ( in @ SV358 @ SV269 )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3109,plain,
! [SV70: $i,SV248: $i,SV269: $i,SV358: $i] :
( ( ( in @ ( sK46_E @ SV358 @ SV269 @ SV248 @ SV70 ) @ SV248 )
= $true )
| ( ( in @ SV358 @ SV269 )
= $false )
| ( ( SV269
= ( relation_inverse_image @ SV70 @ SV248 ) )
= $false )
| ( ( relation @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3110,plain,
! [SV368: $i,SV72: $i,SV291: $i] :
( ( ( in @ ( sK27_C @ SV291 @ SV72 ) @ SV291 )
= $false )
| ( ( ( sK27_C @ SV291 @ SV72 )
= ( apply @ SV72 @ SV368 ) )
= $false )
| ( ( in @ SV368 @ ( relation_dom @ SV72 ) )
= $false )
| ( ( SV291
= ( relation_rng @ SV72 ) )
= $true )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3111,plain,
! [SV292: $i,SV393: $i,SV72: $i,SV369: $i] :
( ( ( SV369
= ( apply @ SV72 @ SV393 ) )
= $false )
| ( ( ~ ( in @ SV393 @ ( relation_dom @ SV72 ) ) )
= $true )
| ( ( in @ SV369 @ SV292 )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3112,plain,
! [SV292: $i,SV72: $i,SV370: $i] :
( ( ( ( SV370
!= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) ) )
= $false )
| ( ( in @ SV370 @ SV292 )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3113,plain,
! [SV72: $i,SV292: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) ) )
= $false )
| ( ( in @ SV370 @ SV292 )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3114,plain,
! [SV73: $i,SV107: $i,SV315: $i] :
( ( ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
= $true )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3115,plain,
! [SV73: $i,SV315: $i,SV107: $i] :
( ( ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
!= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3116,plain,
! [SV73: $i,SV346: $i,SV107: $i] :
( ( ( SV107
= ( relation_dom_restriction @ SV346 @ SV73 ) )
= $false )
| ( ( ! [SY6928: $i] :
( ~ ( in @ SY6928 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SY6928 )
= ( apply @ SV346 @ SY6928 ) ) ) )
= $true )
| ( ( function @ SV346 )
= $false )
| ( ( relation @ SV346 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3117,plain,
! [SV73: $i,SV347: $i,SV107: $i] :
( ( ( SV107
= ( relation_dom_restriction @ SV347 @ SV73 ) )
= $false )
| ( ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV347 ) @ SV73 ) )
= $true )
| ( ( function @ SV347 )
= $false )
| ( ( relation @ SV347 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3118,plain,
! [SV316: $i,SV293: $i,SV74: $i,SV385: $i] :
( ( ( in @ SV385 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ~ ( in @ SV385 @ SV293 ) )
= $true )
| ( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SV385 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3119,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3120,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( relation_dom @ SV74 ) )
| ~ ( in @ SV398 @ SV294 ) )
= $true )
| ( ( ( SV386
!= ( apply @ SV74 @ SV398 ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3121,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
| ( SV387
!= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3122,plain,
! [SV173: $i] :
( ( ( in @ ( sK70_B @ SV173 ) @ ( relation_field @ SV173 ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3064]) ).
thf(3123,plain,
! [SV173: $i] :
( ( ( in @ ( sK71_SY6463 @ SV173 ) @ ( relation_field @ SV173 ) )
= $true )
| ( ( connected @ SV173 )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3124,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3125,plain,
! [SV76: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 ) )
= $false )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3126,plain,
! [SV388: $i] :
( ( ( ~ ( well_ordering @ SV388 ) )
= $true )
| ( ( reflexive @ SV388 )
= $true )
| ( ( relation @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3127,plain,
! [SV389: $i] :
( ( ( ~ ( well_ordering @ SV389 ) )
= $true )
| ( ( transitive @ SV389 )
= $true )
| ( ( relation @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3128,plain,
! [SV46: $i,SV220: $i] :
( ( ( in @ ( sK29_C @ SV220 @ SV46 ) @ SV220 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3070]) ).
thf(3129,plain,
! [SV46: $i,SV220: $i] :
( ( ( in @ ( sK30_SY6442 @ SV220 @ SV46 ) @ SV220 )
= $true )
| ( ( is_antisymmetric_in @ SV46 @ SV220 )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3071]) ).
thf(3130,plain,
! [SV394: $i,SV49: $i,SV126: $i,SV302: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SV394 ) @ SV49 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV394 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3131,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) ) @ SV49 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3132,plain,
! [SV49: $i,SV126: $i,SV302: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3075]) ).
thf(3133,plain,
! [SV303: $i,SV126: $i,SV399: $i,SV49: $i,SV395: $i] :
( ( ( ! [SY6952: $i] :
( ~ ( in @ ( ordered_pair @ SV395 @ SY6952 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SY6952 @ SV399 ) @ SV126 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3134,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3135,plain,
! [SV257: $i,SV106: $i,SV373: $i,SV52: $i,SV390: $i] :
( ( ( in @ SV390 @ SV52 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV106 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3136,plain,
! [SV106: $i,SV52: $i,SV257: $i,SV409: $i,SV401: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV401 @ SV409 ) @ SV257 )
| ( in @ SV409 @ SV52 ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3137,plain,
! [SV52: $i,SV106: $i,SV257: $i,SV410: $i,SV402: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV257 )
| ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV106 ) )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3138,plain,
! [SV307: $i,SV280: $i,SV374: $i,SV53: $i] :
( ( ( in @ ( apply @ SV53 @ SV374 ) @ SV280 )
= $false )
| ( ( in @ SV374 @ ( relation_dom @ SV53 ) )
= $false )
| ( ( in @ SV374 @ SV307 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3139,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV307 ) )
= $true )
| ( ( in @ SV403 @ ( relation_dom @ SV53 ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3140,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV307 ) )
= $true )
| ( ( in @ ( apply @ SV53 @ SV404 ) @ SV280 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3141,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) ) )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3088]) ).
thf(3142,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( sK12_SY6429 @ SV227 @ SV54 ) @ SV227 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3089]) ).
thf(3143,plain,
! [SV54: $i,SV322: $i,SV308: $i,SV228: $i,SV329: $i] :
( ( ( in @ SV329 @ SV228 )
= $false )
| ( ( in @ SV308 @ SV228 )
= $false )
| ( ( in @ SV322 @ SV228 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3144,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3091]) ).
thf(3145,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3146,plain,
! [SV56: $i,SV350: $i] :
( ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) ) )
= $true )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3147,plain,
! [SV56: $i,SV351: $i] :
( ( ( SV351
= ( function_inverse @ SV56 ) )
= $false )
| ( ( ( relation_dom @ SV351 )
= ( relation_rng @ SV56 ) )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3148,plain,
! [SV263: $i,SV59: $i,SV391: $i,SV236: $i,SV379: $i] :
( ( ( in @ SV379 @ SV236 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3149,plain,
! [SV59: $i,SV236: $i,SV263: $i,SV405: $i] :
( ( ( ! [SY6955: $i] :
~ ( in @ ( ordered_pair @ SV405 @ SY6955 ) @ SV263 ) )
= $true )
| ( ( in @ SV405 @ SV236 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3150,plain,
! [SV236: $i,SV59: $i,SV263: $i,SV411: $i,SV406: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV263 )
| ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV59 ) )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3151,plain,
! [SV407: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV407 ) )
= $true )
| ( ( is_reflexive_in @ SV65 @ SV407 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3152,plain,
! [SV408: $i,SV65: $i] :
( ( ( ~ ( well_orders @ SV65 @ SV408 ) )
= $true )
| ( ( is_transitive_in @ SV65 @ SV408 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3153,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3154,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3155,plain,
! [SV292: $i,SV369: $i,SV72: $i,SV393: $i] :
( ( ( in @ SV393 @ ( relation_dom @ SV72 ) )
= $false )
| ( ( SV369
= ( apply @ SV72 @ SV393 ) )
= $false )
| ( ( in @ SV369 @ SV292 )
= $true )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3156,plain,
! [SV292: $i,SV72: $i,SV370: $i] :
( ( ( SV370
= ( apply @ SV72 @ ( sK26_D @ SV370 @ SV292 @ SV72 ) ) )
= $true )
| ( ( in @ SV370 @ SV292 )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3157,plain,
! [SV72: $i,SV292: $i,SV370: $i] :
( ( ( in @ ( sK26_D @ SV370 @ SV292 @ SV72 ) @ ( relation_dom @ SV72 ) )
= $true )
| ( ( in @ SV370 @ SV292 )
= $false )
| ( ( SV292
= ( relation_rng @ SV72 ) )
= $false )
| ( ( function @ SV72 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3158,plain,
! [SV73: $i,SV315: $i,SV107: $i] :
( ( ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
= $false )
| ( ( in @ ( sK62_D @ SV315 @ SV107 @ SV73 ) @ ( relation_dom @ SV107 ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3159,plain,
! [SV73: $i,SV315: $i,SV107: $i] :
( ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV107 )
!= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3160,plain,
! [SV73: $i,SV346: $i,SV107: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ ( relation_dom @ SV107 ) )
| ( ( apply @ SV107 @ SV412 )
= ( apply @ SV346 @ SV412 ) ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV346 @ SV73 ) )
= $false )
| ( ( function @ SV346 )
= $false )
| ( ( relation @ SV346 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3161,plain,
! [SV316: $i,SV74: $i,SV293: $i,SV385: $i] :
( ( ( in @ SV385 @ SV293 )
= $false )
| ( ( in @ SV385 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
!= ( apply @ SV74 @ SV385 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3162,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3163,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 ) )
= $false )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3119]) ).
thf(3164,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( relation_dom @ SV74 ) ) )
= $true )
| ( ( ~ ( in @ SV398 @ SV294 ) )
= $true )
| ( ( ( SV386
!= ( apply @ SV74 @ SV398 ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3120]) ).
thf(3165,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3121]) ).
thf(3166,plain,
! [SV294: $i,SV317: $i,SV74: $i,SV387: $i] :
( ( ( ( SV387
!= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3121]) ).
thf(3167,plain,
! [SV76: $i,SV251: $i] :
( ( ( in @ ( sK21_C @ SV251 @ SV76 ) @ SV251 )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3168,plain,
! [SV76: $i,SV251: $i] :
( ( ( in @ ( sK22_SY6437 @ SV251 @ SV76 ) @ SV251 )
= $true )
| ( ( is_connected_in @ SV76 @ SV251 )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3169,plain,
! [SV388: $i] :
( ( ( well_ordering @ SV388 )
= $false )
| ( ( reflexive @ SV388 )
= $true )
| ( ( relation @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3170,plain,
! [SV389: $i] :
( ( ( well_ordering @ SV389 )
= $false )
| ( ( transitive @ SV389 )
= $true )
| ( ( relation @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3171,plain,
! [SV49: $i,SV126: $i,SV302: $i,SV394: $i] :
( ( ( in @ ( ordered_pair @ SV394 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SV394 ) @ SV49 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3172,plain,
! [SV303: $i,SV126: $i,SV399: $i,SV49: $i,SV413: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV413 ) @ SV49 )
| ~ ( in @ ( ordered_pair @ SV413 @ SV399 ) @ SV126 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3173,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 ) ) )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3174,plain,
! [SV257: $i,SV52: $i,SV106: $i,SV390: $i,SV373: $i] :
( ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV106 )
= $false )
| ( ( in @ SV390 @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV257 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3175,plain,
! [SV106: $i,SV52: $i,SV257: $i,SV409: $i,SV401: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV401 @ SV409 ) @ SV257 ) )
= $true )
| ( ( in @ SV409 @ SV52 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3176,plain,
! [SV52: $i,SV106: $i,SV257: $i,SV410: $i,SV402: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV257 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV106 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3177,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV403: $i] :
( ( ( in @ SV403 @ SV307 )
= $false )
| ( ( in @ SV403 @ ( relation_dom @ SV53 ) )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3139]) ).
thf(3178,plain,
! [SV280: $i,SV53: $i,SV307: $i,SV404: $i] :
( ( ( in @ SV404 @ SV307 )
= $false )
| ( ( in @ ( apply @ SV53 @ SV404 ) @ SV280 )
= $true )
| ( ( SV307
= ( relation_inverse_image @ SV53 @ SV280 ) )
= $false )
| ( ( function @ SV53 )
= $false )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3179,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
| ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3180,plain,
! [SV329: $i,SV228: $i,SV54: $i,SV322: $i,SV308: $i] :
( ( ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 )
= $false )
| ( ( in @ SV322 @ SV228 )
= $false )
| ( ( in @ SV308 @ SV228 )
= $false )
| ( ( in @ SV329 @ SV228 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3181,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3182,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3183,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
| ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3146]) ).
thf(3184,plain,
! [SV263: $i,SV236: $i,SV59: $i,SV391: $i,SV379: $i] :
( ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV59 )
= $false )
| ( ( in @ SV379 @ SV236 )
= $false )
| ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV263 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3185,plain,
! [SV59: $i,SV236: $i,SV263: $i,SV414: $i,SV405: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV405 @ SV414 ) @ SV263 ) )
= $true )
| ( ( in @ SV405 @ SV236 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3186,plain,
! [SV236: $i,SV59: $i,SV263: $i,SV411: $i,SV406: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV263 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV59 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3187,plain,
! [SV407: $i,SV65: $i] :
( ( ( well_orders @ SV65 @ SV407 )
= $false )
| ( ( is_reflexive_in @ SV65 @ SV407 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3188,plain,
! [SV408: $i,SV65: $i] :
( ( ( well_orders @ SV65 @ SV408 )
= $false )
| ( ( is_transitive_in @ SV65 @ SV408 )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3189,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3153]) ).
thf(3190,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3191,plain,
! [SV73: $i,SV315: $i,SV107: $i] :
( ( ( ( relation_dom @ SV107 )
= ( set_intersection2 @ ( relation_dom @ SV315 ) @ SV73 ) )
= $false )
| ( ( ( apply @ SV107 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) )
= ( apply @ SV315 @ ( sK62_D @ SV315 @ SV107 @ SV73 ) ) )
= $false )
| ( ( SV107
= ( relation_dom_restriction @ SV315 @ SV73 ) )
= $true )
| ( ( function @ SV315 )
= $false )
| ( ( relation @ SV315 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3192,plain,
! [SV73: $i,SV346: $i,SV107: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ ( relation_dom @ SV107 ) ) )
= $true )
| ( ( ( apply @ SV107 @ SV412 )
= ( apply @ SV346 @ SV412 ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV346 @ SV73 ) )
= $false )
| ( ( function @ SV346 )
= $false )
| ( ( relation @ SV346 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3193,plain,
! [SV385: $i,SV74: $i,SV293: $i,SV316: $i] :
( ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
= ( apply @ SV74 @ SV385 ) )
= $false )
| ( ( in @ SV385 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( in @ SV385 @ SV293 )
= $false )
| ( ( ~ ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 ) )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3194,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ ( relation_dom @ SV74 ) )
= $true )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3195,plain,
! [SV74: $i,SV293: $i,SV316: $i] :
( ( ( in @ ( sK57_SY6458 @ SV316 @ SV293 @ SV74 ) @ SV293 )
= $true )
| ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $true )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3196,plain,
! [SV317: $i,SV386: $i,SV294: $i,SV74: $i,SV398: $i] :
( ( ( in @ SV398 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ~ ( in @ SV398 @ SV294 ) )
= $true )
| ( ( ( SV386
!= ( apply @ SV74 @ SV398 ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3197,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) ) )
= $true )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3165]) ).
thf(3198,plain,
! [SV294: $i,SV317: $i,SV74: $i,SV387: $i] :
( ( ( SV387
= ( apply @ SV74 @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) ) )
= $true )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3199,plain,
! [SV394: $i,SV49: $i,SV126: $i,SV302: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV302 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV302 @ SV126 @ SV49 ) @ SV394 ) @ SV49 )
= $false )
| ( ( in @ ( ordered_pair @ SV394 @ ( sK15_SY6430 @ SV302 @ SV126 @ SV49 ) ) @ SV126 )
= $false )
| ( ( SV302
= ( relation_composition @ SV49 @ SV126 ) )
= $true )
| ( ( relation @ SV302 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3200,plain,
! [SV303: $i,SV126: $i,SV399: $i,SV49: $i,SV413: $i,SV395: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV395 @ SV413 ) @ SV49 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV413 @ SV399 ) @ SV126 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3201,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3202,plain,
! [SV106: $i,SV52: $i,SV257: $i,SV409: $i,SV401: $i] :
( ( ( in @ ( ordered_pair @ SV401 @ SV409 ) @ SV257 )
= $false )
| ( ( in @ SV409 @ SV52 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3203,plain,
! [SV52: $i,SV106: $i,SV257: $i,SV410: $i,SV402: $i] :
( ( ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV257 )
= $false )
| ( ( in @ ( ordered_pair @ SV402 @ SV410 ) @ SV106 )
= $true )
| ( ( SV257
= ( relation_rng_restriction @ SV52 @ SV106 ) )
= $false )
| ( ( relation @ SV257 )
= $false )
| ( ( relation @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3204,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3205,plain,
! [SV54: $i,SV227: $i] :
( ( ( ~ ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 ) )
= $false )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3206,plain,
! [SV308: $i,SV228: $i,SV54: $i,SV329: $i,SV322: $i] :
( ( ( in @ ( ordered_pair @ SV322 @ SV329 ) @ SV54 )
= $false )
| ( ( in @ SV329 @ SV228 )
= $false )
| ( ( in @ SV308 @ SV228 )
= $false )
| ( ( in @ SV322 @ SV228 )
= $false )
| ( ( in @ ( ordered_pair @ SV308 @ SV322 ) @ SV54 )
= $false )
| ( ( in @ ( ordered_pair @ SV308 @ SV329 ) @ SV54 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV228 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3207,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3208,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3181]) ).
thf(3209,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3182]) ).
thf(3210,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3182]) ).
thf(3211,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3212,plain,
! [SV350: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3183]) ).
thf(3213,plain,
! [SV59: $i,SV236: $i,SV263: $i,SV414: $i,SV405: $i] :
( ( ( in @ ( ordered_pair @ SV405 @ SV414 ) @ SV263 )
= $false )
| ( ( in @ SV405 @ SV236 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3214,plain,
! [SV236: $i,SV59: $i,SV263: $i,SV411: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV263 )
= $false )
| ( ( in @ ( ordered_pair @ SV406 @ SV411 ) @ SV59 )
= $true )
| ( ( SV263
= ( relation_dom_restriction @ SV59 @ SV236 ) )
= $false )
| ( ( relation @ SV263 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3215,plain,
! [SV73: $i,SV346: $i,SV107: $i,SV412: $i] :
( ( ( in @ SV412 @ ( relation_dom @ SV107 ) )
= $false )
| ( ( ( apply @ SV107 @ SV412 )
= ( apply @ SV346 @ SV412 ) )
= $true )
| ( ( SV107
= ( relation_dom_restriction @ SV346 @ SV73 ) )
= $false )
| ( ( function @ SV346 )
= $false )
| ( ( relation @ SV346 )
= $false )
| ( ( function @ SV107 )
= $false )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3216,plain,
! [SV385: $i,SV74: $i,SV293: $i,SV316: $i] :
( ( ( in @ ( sK56_D @ SV316 @ SV293 @ SV74 ) @ SV316 )
= $false )
| ( ( in @ SV385 @ SV293 )
= $false )
| ( ( in @ SV385 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ( sK56_D @ SV316 @ SV293 @ SV74 )
= ( apply @ SV74 @ SV385 ) )
= $false )
| ( ( SV316
= ( relation_image @ SV74 @ SV293 ) )
= $true )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3217,plain,
! [SV317: $i,SV386: $i,SV74: $i,SV294: $i,SV398: $i] :
( ( ( in @ SV398 @ SV294 )
= $false )
| ( ( in @ SV398 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( ( SV386
!= ( apply @ SV74 @ SV398 ) ) )
= $true )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3218,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
| ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3219,plain,
! [SV303: $i,SV126: $i,SV399: $i,SV49: $i,SV413: $i,SV395: $i] :
( ( ( in @ ( ordered_pair @ SV395 @ SV413 ) @ SV49 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV413 @ SV399 ) @ SV126 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3220,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3201]) ).
thf(3221,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV396: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3201]) ).
thf(3222,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( sK10_C @ SV227 @ SV54 ) @ SV227 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3204]) ).
thf(3223,plain,
! [SV54: $i,SV227: $i] :
( ( ( in @ ( sK11_SY6427 @ SV227 @ SV54 ) @ SV227 )
= $true )
| ( ( is_transitive_in @ SV54 @ SV227 )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3224,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3225,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3226,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3227,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3228,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3229,plain,
! [SV350: $i,SV56: $i] :
( ( ( ~ ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3212]) ).
thf(3230,plain,
! [SV317: $i,SV294: $i,SV398: $i,SV74: $i,SV386: $i] :
( ( ( SV386
= ( apply @ SV74 @ SV398 ) )
= $false )
| ( ( in @ SV398 @ ( relation_dom @ SV74 ) )
= $false )
| ( ( in @ SV398 @ SV294 )
= $false )
| ( ( in @ SV386 @ SV317 )
= $true )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3231,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3218]) ).
thf(3232,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 ) )
= $false )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3218]) ).
thf(3233,plain,
! [SV303: $i,SV49: $i,SV395: $i,SV126: $i,SV399: $i,SV413: $i] :
( ( ( in @ ( ordered_pair @ SV413 @ SV399 ) @ SV126 )
= $false )
| ( ( in @ ( ordered_pair @ SV395 @ SV413 ) @ SV49 )
= $false )
| ( ( in @ ( ordered_pair @ SV395 @ SV399 ) @ SV303 )
= $true )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3234,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV400: $i,SV396: $i] :
( ( ( in @ ( ordered_pair @ SV396 @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) ) @ SV49 )
= $true )
| ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3220]) ).
thf(3235,plain,
! [SV49: $i,SV126: $i,SV303: $i,SV396: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_F @ SV400 @ SV396 @ SV303 @ SV126 @ SV49 ) @ SV400 ) @ SV126 )
= $true )
| ( ( in @ ( ordered_pair @ SV396 @ SV400 ) @ SV303 )
= $false )
| ( ( SV303
= ( relation_composition @ SV49 @ SV126 ) )
= $false )
| ( ( relation @ SV303 )
= $false )
| ( ( relation @ SV126 )
= $false )
| ( ( relation @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3221]) ).
thf(3236,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3237,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3238,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3239,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3240,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) )
| ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3228]) ).
thf(3241,plain,
! [SV350: $i,SV56: $i] :
( ( ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) )
| ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3242,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ ( relation_dom @ SV74 ) )
= $true )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3231]) ).
thf(3243,plain,
! [SV74: $i,SV294: $i,SV317: $i,SV387: $i] :
( ( ( in @ ( sK55_E @ SV387 @ SV317 @ SV294 @ SV74 ) @ SV294 )
= $true )
| ( ( in @ SV387 @ SV317 )
= $false )
| ( ( SV317
= ( relation_image @ SV74 @ SV294 ) )
= $false )
| ( ( function @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3232]) ).
thf(3244,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3245,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3246,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3237]) ).
thf(3247,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3237]) ).
thf(3248,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3238]) ).
thf(3249,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3238]) ).
thf(3250,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3251,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3252,plain,
! [SV56: $i,SV350: $i] :
( ( ( ~ ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3240]) ).
thf(3253,plain,
! [SV350: $i,SV56: $i] :
( ( ( ~ ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3254,plain,
! [SV350: $i,SV56: $i] :
( ( ( ~ ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) )
= $false )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3255,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3244]) ).
thf(3256,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3257,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3246]) ).
thf(3258,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3247]) ).
thf(3259,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3260,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3261,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3262,plain,
! [SV56: $i,SV350: $i] :
( ( ( ! [SY6929: $i,SY6930: $i] :
( ( SY6930
!= ( apply @ SV350 @ SY6929 ) )
| ~ ( in @ SY6929 @ ( relation_rng @ SV56 ) )
| ( SY6929
= ( apply @ SV56 @ SY6930 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3251]) ).
thf(3263,plain,
! [SV56: $i,SV350: $i] :
( ( ( ! [SY6931: $i,SY6932: $i] :
( ( SY6932
!= ( apply @ SV350 @ SY6931 ) )
| ~ ( in @ SY6931 @ ( relation_rng @ SV56 ) )
| ( in @ SY6932 @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3252]) ).
thf(3264,plain,
! [SV350: $i,SV56: $i] :
( ( ( ! [SY6933: $i,SY6934: $i] :
( ( SY6933
!= ( apply @ SV56 @ SY6934 ) )
| ~ ( in @ SY6934 @ ( relation_dom @ SV56 ) )
| ( SY6934
= ( apply @ SV350 @ SY6933 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3253]) ).
thf(3265,plain,
! [SV350: $i,SV56: $i] :
( ( ( ! [SY6581: $i] :
( ! [SY6582: $i] :
( ( SY6581
!= ( apply @ SV56 @ SY6582 ) )
| ~ ( in @ SY6582 @ ( relation_dom @ SV56 ) ) )
| ( in @ SY6581 @ ( relation_rng @ SV56 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3254]) ).
thf(3266,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3267,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3268,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3269,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3270,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3271,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3272,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3273,plain,
! [SV56: $i,SV415: $i,SV350: $i] :
( ( ( ! [SY6957: $i] :
( ( SY6957
!= ( apply @ SV350 @ SV415 ) )
| ~ ( in @ SV415 @ ( relation_rng @ SV56 ) )
| ( SV415
= ( apply @ SV56 @ SY6957 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3274,plain,
! [SV56: $i,SV416: $i,SV350: $i] :
( ( ( ! [SY6958: $i] :
( ( SY6958
!= ( apply @ SV350 @ SV416 ) )
| ~ ( in @ SV416 @ ( relation_rng @ SV56 ) )
| ( in @ SY6958 @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3275,plain,
! [SV350: $i,SV56: $i,SV417: $i] :
( ( ( ! [SY6959: $i] :
( ( SV417
!= ( apply @ SV56 @ SY6959 ) )
| ~ ( in @ SY6959 @ ( relation_dom @ SV56 ) )
| ( SY6959
= ( apply @ SV350 @ SV417 ) ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3276,plain,
! [SV350: $i,SV56: $i,SV418: $i] :
( ( ( ! [SY6960: $i] :
( ( SV418
!= ( apply @ SV56 @ SY6960 ) )
| ~ ( in @ SY6960 @ ( relation_dom @ SV56 ) ) )
| ( in @ SV418 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3277,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3266]) ).
thf(3278,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3266]) ).
thf(3279,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3280,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3281,plain,
! [SV56: $i,SV323: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3282,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3283,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3284,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK65_C @ SV323 @ SV56 )
!= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3285,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
!= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3286,plain,
! [SV56: $i,SV415: $i,SV350: $i,SV419: $i] :
( ( ( ( SV419
!= ( apply @ SV350 @ SV415 ) )
| ~ ( in @ SV415 @ ( relation_rng @ SV56 ) )
| ( SV415
= ( apply @ SV56 @ SV419 ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3287,plain,
! [SV56: $i,SV416: $i,SV350: $i,SV420: $i] :
( ( ( ( SV420
!= ( apply @ SV350 @ SV416 ) )
| ~ ( in @ SV416 @ ( relation_rng @ SV56 ) )
| ( in @ SV420 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3288,plain,
! [SV350: $i,SV421: $i,SV56: $i,SV417: $i] :
( ( ( ( SV417
!= ( apply @ SV56 @ SV421 ) )
| ~ ( in @ SV421 @ ( relation_dom @ SV56 ) )
| ( SV421
= ( apply @ SV350 @ SV417 ) ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3289,plain,
! [SV350: $i,SV56: $i,SV418: $i] :
( ( ( ! [SY6960: $i] :
( ( SV418
!= ( apply @ SV56 @ SY6960 ) )
| ~ ( in @ SY6960 @ ( relation_dom @ SV56 ) ) ) )
= $true )
| ( ( in @ SV418 @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3290,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3277]) ).
thf(3291,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3278]) ).
thf(3292,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3293,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3280]) ).
thf(3294,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
| ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3281]) ).
thf(3295,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3296,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3297,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3298,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3299,plain,
! [SV56: $i,SV415: $i,SV350: $i,SV419: $i] :
( ( ( ( SV419
!= ( apply @ SV350 @ SV415 ) )
| ~ ( in @ SV415 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV415
= ( apply @ SV56 @ SV419 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3300,plain,
! [SV56: $i,SV416: $i,SV350: $i,SV420: $i] :
( ( ( ( SV420
!= ( apply @ SV350 @ SV416 ) )
| ~ ( in @ SV416 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( in @ SV420 @ ( relation_dom @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3301,plain,
! [SV350: $i,SV421: $i,SV56: $i,SV417: $i] :
( ( ( ( SV417
!= ( apply @ SV56 @ SV421 ) )
| ~ ( in @ SV421 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( SV421
= ( apply @ SV350 @ SV417 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3302,plain,
! [SV350: $i,SV422: $i,SV56: $i,SV418: $i] :
( ( ( ( SV418
!= ( apply @ SV56 @ SV422 ) )
| ~ ( in @ SV422 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV418 @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3303,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3304,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3305,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3306,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3307,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3308,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3309,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3310,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3311,plain,
! [SV56: $i,SV323: $i] :
( ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( ( relation_dom @ SV323 )
!= ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3312,plain,
! [SV56: $i,SV415: $i,SV350: $i,SV419: $i] :
( ( ( ( SV419
!= ( apply @ SV350 @ SV415 ) ) )
= $true )
| ( ( ~ ( in @ SV415 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV415
= ( apply @ SV56 @ SV419 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3299]) ).
thf(3313,plain,
! [SV56: $i,SV416: $i,SV350: $i,SV420: $i] :
( ( ( ( SV420
!= ( apply @ SV350 @ SV416 ) ) )
= $true )
| ( ( ~ ( in @ SV416 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( in @ SV420 @ ( relation_dom @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3314,plain,
! [SV350: $i,SV421: $i,SV56: $i,SV417: $i] :
( ( ( ( SV417
!= ( apply @ SV56 @ SV421 ) ) )
= $true )
| ( ( ~ ( in @ SV421 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( SV421
= ( apply @ SV350 @ SV417 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3315,plain,
! [SV350: $i,SV422: $i,SV56: $i,SV418: $i] :
( ( ( ( SV418
!= ( apply @ SV56 @ SV422 ) ) )
= $true )
| ( ( ~ ( in @ SV422 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV418 @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3316,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3317,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3318,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3319,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3320,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3321,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $true )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3322,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3323,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $true )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3324,plain,
! [SV56: $i,SV323: $i] :
( ( ( ( relation_dom @ SV323 )
= ( relation_rng @ SV56 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV323 @ SV56 ) @ ( relation_dom @ SV56 ) )
= $false )
| ( ( ( sK65_C @ SV323 @ SV56 )
= ( apply @ SV56 @ ( sK66_SY6462 @ SV323 @ SV56 ) ) )
= $false )
| ( ( ( sK66_SY6462 @ SV323 @ SV56 )
= ( apply @ SV323 @ ( sK65_C @ SV323 @ SV56 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV323 @ SV56 ) @ ( relation_rng @ SV56 ) )
= $false )
| ( ( SV323
= ( function_inverse @ SV56 ) )
= $true )
| ( ( function @ SV323 )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3325,plain,
! [SV56: $i,SV415: $i,SV350: $i,SV419: $i] :
( ( ( SV419
= ( apply @ SV350 @ SV415 ) )
= $false )
| ( ( ~ ( in @ SV415 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( SV415
= ( apply @ SV56 @ SV419 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3326,plain,
! [SV56: $i,SV416: $i,SV350: $i,SV420: $i] :
( ( ( SV420
= ( apply @ SV350 @ SV416 ) )
= $false )
| ( ( ~ ( in @ SV416 @ ( relation_rng @ SV56 ) ) )
= $true )
| ( ( in @ SV420 @ ( relation_dom @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3327,plain,
! [SV350: $i,SV421: $i,SV56: $i,SV417: $i] :
( ( ( SV417
= ( apply @ SV56 @ SV421 ) )
= $false )
| ( ( ~ ( in @ SV421 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( SV421
= ( apply @ SV350 @ SV417 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3328,plain,
! [SV350: $i,SV422: $i,SV56: $i,SV418: $i] :
( ( ( SV418
= ( apply @ SV56 @ SV422 ) )
= $false )
| ( ( ~ ( in @ SV422 @ ( relation_dom @ SV56 ) ) )
= $true )
| ( ( in @ SV418 @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3329,plain,
! [SV350: $i,SV419: $i,SV56: $i,SV415: $i] :
( ( ( in @ SV415 @ ( relation_rng @ SV56 ) )
= $false )
| ( ( SV419
= ( apply @ SV350 @ SV415 ) )
= $false )
| ( ( SV415
= ( apply @ SV56 @ SV419 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3330,plain,
! [SV350: $i,SV420: $i,SV56: $i,SV416: $i] :
( ( ( in @ SV416 @ ( relation_rng @ SV56 ) )
= $false )
| ( ( SV420
= ( apply @ SV350 @ SV416 ) )
= $false )
| ( ( in @ SV420 @ ( relation_dom @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3331,plain,
! [SV350: $i,SV417: $i,SV56: $i,SV421: $i] :
( ( ( in @ SV421 @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV417
= ( apply @ SV56 @ SV421 ) )
= $false )
| ( ( SV421
= ( apply @ SV350 @ SV417 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3332,plain,
! [SV350: $i,SV418: $i,SV56: $i,SV422: $i] :
( ( ( in @ SV422 @ ( relation_dom @ SV56 ) )
= $false )
| ( ( SV418
= ( apply @ SV56 @ SV422 ) )
= $false )
| ( ( in @ SV418 @ ( relation_rng @ SV56 ) )
= $true )
| ( ( SV350
= ( function_inverse @ SV56 ) )
= $false )
| ( ( function @ SV350 )
= $false )
| ( ( relation @ SV350 )
= $false )
| ( ( one_to_one @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3333,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[667,3332,3331,3330,3329,3324,3323,3322,3321,3320,3319,3318,3317,3316,3243,3242,3235,3234,3233,3230,3223,3222,3216,3215,3214,3213,3206,3203,3202,3199,3198,3195,3194,3191,3190,3189,3188,3187,3184,3178,3177,3174,3170,3169,3168,3167,3158,3157,3156,3155,3147,3142,3138,3132,3131,3129,3128,3123,3122,3117,3110,3109,3108,3107,3103,3102,3101,3100,3099,3095,3084,3080,3079,3078,3072,3066,3061,3048,3047,3045,3044,3043,3042,3041,3040,3034,3031,3027,3026,3024,3023,3022,3021,3012,3011,3006,3005,3001,2994,2991,2990,2989,2985,2974,2973,2958,2938,2936,2914,2909,2908,2907,2901,2884,2883,2881,2880,2872,2871,2868,2867,2862,2861,2853,2850,2845,2828,2827,2819,2809,2804,2792,2791,2783,2782,2780,2777,2775,2771,2770,2767,2761,2760,2756,2755,2753,2751,2746,2734,2718,2717,2711,2709,2708,2695,2692,2678,2658,2657,2648,2631,2627,2622,2617,2602,2597,2596,2595,2593,2572,2554,2549,2548,2546,2539,2536,2529,2528,2512,2511,2495,2494,2487,2486,2471,2470,2469,2468,2465,2458,2457,2447,2421,2419,2412,2411,2410,2383,2362,2360,2339,2334,2330,2326,2313,2290,2282,2269,2268,2251,2237,2236,2217,2171,2170,2167,2166,2157,2156,2143,2142,2111,2105,2068,2067,2061,2060,2044,2042,2038,2020,2019,1959,1958,1953,1952,1943,1942,1909,1867,1866,1861,1860,1852,1851,1843,1842,1839,1838,1833,1832,1831,1830,1813,1812,1809,1808,1680,1677,1672,1647,1646,1645,1644,1637,1635,1621,1620,1603,1602,1596,1595,1578,1577,1565,1564,1552,1551,1530,1529,1528,1527,1520,1519,1514,1512,1511,1376,1375,1354,1350,1257,1256,1255,1234,1233,1230,1229,1228,1227,1223,1214,1210,1208,1206,1205,1204,1203,1198,1180,1173,1171,1137,1124,1120,1119,1114,1113,1098,1093,1086,1085,1079,1078,1073,1064,1062,1061,1046,1040,781]) ).
thf(3334,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK77_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK77_B @ A ) @ ( sK77_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)],[546]) ).
thf(3335,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK75_SY6465 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK75_SY6465 @ A ) @ ( sK76_SY6467 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK74_B @ A ) @ ( sK76_SY6467 @ 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)],[545]) ).
thf(3336,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK72_B @ A ) @ ( sK73_SY6464 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK73_SY6464 @ A ) @ ( sK72_B @ A ) ) @ A )
& ( ( sK72_B @ A )
!= ( sK73_SY6464 @ 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)],[544]) ).
thf(3337,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK70_B @ A )
!= ( sK71_SY6463 @ A ) )
& ( in @ ( sK70_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK71_SY6463 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK70_B @ A ) @ ( sK71_SY6463 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ A ) @ ( sK70_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)],[543]) ).
thf(3338,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ C ) )
| ~ ( in @ B @ A )
| ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(3339,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_rng @ C ) )
| ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
| ( in @ A @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(3340,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(3341,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(3342,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(3343,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(3344,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(3345,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 @ ( sK69_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK69_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK69_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(3346,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(3347,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(3348,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(3349,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_dom @ B ) )
| ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(3350,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(3351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(3352,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(3353,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 @ ( sK68_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK68_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK68_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(3354,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(3355,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( A = empty_set )
| ~ ( subset @ A @ ( relation_rng @ B ) )
| ( ( relation_inverse_image @ B @ A )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(3356,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(3357,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)],[523]) ).
thf(3358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ~ ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) )
| ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(3359,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(3360,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
| ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(3361,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(3362,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(3363,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)],[517]) ).
thf(3364,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK67_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK67_C @ B @ A ) )
!= ( sK67_C @ B @ A ) ) )
| ( ( relation_dom @ B )
!= A )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( ( apply @ B @ C )
= C ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ( relation_dom @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(3365,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(3366,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(3367,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(3368,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
| ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(3369,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
| ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(3370,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK66_SY6462 @ B @ A )
= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK65_C @ B @ A )
= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK65_C @ B @ A )
!= ( apply @ A @ ( sK66_SY6462 @ B @ A ) ) )
| ~ ( in @ ( sK66_SY6462 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK66_SY6462 @ B @ A )
!= ( apply @ B @ ( sK65_C @ B @ A ) ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ ( relation_rng @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( relation_rng @ A ) )
| ( B
= ( function_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( C
= ( apply @ A @ D ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( apply @ B @ C ) )
| ~ ( in @ C @ ( relation_rng @ A ) )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [C: $i,D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( D
= ( apply @ B @ C ) ) )
& ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ ( relation_rng @ A ) ) ) ) )
& ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( B
!= ( function_inverse @ A ) )
| ( ( relation_dom @ B )
= ( relation_rng @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(3371,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(3372,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK63_B @ A ) @ ( sK64_SY6461 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(3373,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ~ ( in @ A @ ( relation_rng @ B ) )
| ~ ( one_to_one @ B )
| ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(3374,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_well_founded_in @ A @ ( relation_field @ A ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(3375,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(3376,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( A = empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(3377,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_dom @ A )
!= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_rng @ A )
!= empty_set )
| ( ( relation_dom @ A )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(3378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK62_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK62_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK62_D @ C @ B @ A ) ) ) )
| ( ( relation_dom @ B )
!= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
| ( B
= ( relation_dom_restriction @ C @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ B ) )
| ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( relation_dom_restriction @ C @ A ) )
| ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(3379,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(3380,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ B @ A )
| ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(3381,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)],[499]) ).
thf(3382,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ B )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(3383,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(3384,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)],[496]) ).
thf(3385,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(3386,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(3387,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(3388,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(3389,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( function @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(3390,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK60_C @ B @ A )
!= ( sK61_SY6460 @ B @ A ) )
| ~ ( in @ ( sK60_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( ( sK60_C @ B @ A )
= ( sK61_SY6460 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK60_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK60_C @ B @ A ) @ ( sK61_SY6460 @ 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)],[490]) ).
thf(3391,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK58_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY6459 @ 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)],[489]) ).
thf(3392,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6457: $i] :
( ~ ( in @ SY6457 @ ( relation_dom @ A ) )
| ~ ( in @ SY6457 @ B )
| ( ( sK56_D @ C @ B @ A )
!= ( apply @ A @ SY6457 ) ) )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK57_SY6458 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK57_SY6458 @ C @ B @ A ) @ B )
& ( ( sK56_D @ C @ B @ A )
= ( apply @ A @ ( sK57_SY6458 @ C @ B @ A ) ) ) )
| ( in @ ( sK56_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ E @ ( relation_dom @ A ) )
| ~ ( in @ E @ B )
| ( D
!= ( apply @ A @ E ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK55_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK55_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK55_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(3393,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK54_SY6456 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK53_D @ C @ B @ A ) @ ( sK54_SY6456 @ 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)],[487]) ).
thf(3394,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_antisymmetric_in @ A @ ( relation_field @ A ) )
| ( antisymmetric @ A ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(3395,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK52_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK52_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK52_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ D ) @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(3396,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6454: $i] :
( ~ ( in @ ( ordered_pair @ SY6454 @ ( sK50_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY6454 @ B ) )
| ~ ( in @ ( sK50_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK51_SY6455 @ C @ B @ A ) @ ( sK50_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_SY6455 @ C @ B @ A ) @ B ) )
| ( in @ ( sK50_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 @ ( sK49_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK49_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(3397,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY6452: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ SY6452 ) @ A )
| ~ ( in @ SY6452 @ B ) )
| ~ ( in @ ( sK47_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_D @ C @ B @ A ) @ ( sK48_SY6453 @ C @ B @ A ) ) @ A )
& ( in @ ( sK48_SY6453 @ C @ B @ A ) @ B ) )
| ( in @ ( sK47_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 @ ( sK46_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK46_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(3398,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ( is_connected_in @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_connected_in @ A @ ( relation_field @ A ) )
| ( connected @ A ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(3399,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_transitive_in @ A @ ( relation_field @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ( is_transitive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(3400,plain,
( ( ! [A: $i] :
( ( ! [SY6450: $i,SY6451: $i] :
( ( sK45_B @ A )
!= ( ordered_pair @ SY6450 @ SY6451 ) )
& ( in @ ( sK45_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK43_C @ B @ A ) @ ( sK44_SY6449 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(3401,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK42_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK42_C @ B @ A ) @ ( sK42_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)],[479]) ).
thf(3402,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY6448 @ 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)],[478]) ).
thf(3403,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY6447: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6447 ) @ ( sK39_B @ A ) )
| ~ ( in @ SY6447 @ ( sK39_B @ A ) ) )
& ( ( sK39_B @ A )
!= empty_set )
& ( subset @ ( sK39_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK38_C @ B @ A ) ) @ B )
& ( in @ ( sK38_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(3404,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY6446 @ 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)],[476]) ).
thf(3405,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY6445: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY6445 ) @ ( sK35_C @ B @ A ) )
| ~ ( in @ SY6445 @ ( sK35_C @ B @ A ) ) )
& ( ( sK35_C @ B @ A )
!= empty_set )
& ( subset @ ( sK35_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK34_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK34_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(3406,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)],[474]) ).
thf(3407,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6443: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ SY6443 ) @ A )
| ~ ( in @ ( sK32_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK32_C @ B @ A ) @ ( sK33_SY6444 @ B @ A ) ) @ A )
| ( in @ ( sK32_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 @ ( sK31_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(3408,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK29_C @ B @ A ) @ B )
& ( in @ ( sK30_SY6442 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK29_C @ B @ A ) @ ( sK30_SY6442 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK30_SY6442 @ B @ A ) @ ( sK29_C @ B @ A ) ) @ A )
& ( ( sK29_C @ B @ A )
!= ( sK30_SY6442 @ 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)],[472]) ).
thf(3409,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ~ ( transitive @ A )
| ~ ( antisymmetric @ A )
| ~ ( connected @ A )
| ~ ( well_founded_relation @ A )
| ( well_ordering @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_founded_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(3410,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6440: $i] :
( ( ( sK27_C @ B @ A )
!= ( apply @ A @ SY6440 ) )
| ~ ( in @ SY6440 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( ( ( sK27_C @ B @ A )
= ( apply @ A @ ( sK28_SY6441 @ B @ A ) ) )
& ( in @ ( sK28_SY6441 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK27_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ( C
!= ( apply @ A @ D ) )
| ~ ( in @ D @ ( relation_dom @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( C
= ( apply @ A @ ( sK26_D @ C @ B @ A ) ) )
& ( in @ ( sK26_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(3411,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY6438: $i] :
~ ( in @ ( ordered_pair @ SY6438 @ ( sK24_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK24_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ B @ A ) @ ( sK24_C @ B @ A ) ) @ A )
| ( in @ ( sK24_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 @ ( sK23_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(3412,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ~ ( is_transitive_in @ A @ B )
| ~ ( is_antisymmetric_in @ A @ B )
| ~ ( is_connected_in @ A @ B )
| ~ ( is_well_founded_in @ A @ B )
| ( well_orders @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( well_orders @ A @ B )
| ( is_well_founded_in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(3413,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(3414,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK21_C @ B @ A )
!= ( sK22_SY6437 @ B @ A ) )
& ( in @ ( sK21_C @ B @ A ) @ B )
& ( in @ ( sK22_SY6437 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK21_C @ B @ A ) @ ( sK22_SY6437 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ B @ A ) @ ( sK21_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)],[466]) ).
thf(3415,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY6436 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ B @ A ) @ ( sK19_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)],[465]) ).
thf(3416,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK17_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK18_SY6435 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK17_B @ A ) )
= ( apply @ A @ ( sK18_SY6435 @ A ) ) )
& ( ( sK17_B @ A )
!= ( sK18_SY6435 @ A ) ) )
| ( one_to_one @ A ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( apply @ A @ B )
!= ( apply @ A @ C ) )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(3417,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY6433: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ SY6433 ) @ A )
| ~ ( in @ ( ordered_pair @ SY6433 @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK16_SY6434 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_SY6434 @ C @ B @ A ) @ ( sK15_SY6430 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK14_D @ C @ B @ A ) @ ( sK15_SY6430 @ 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 @ ( sK13_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(3418,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK10_C @ B @ A ) @ B )
& ( in @ ( sK11_SY6427 @ B @ A ) @ B )
& ( in @ ( sK12_SY6429 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK11_SY6427 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK11_SY6427 @ B @ A ) @ ( sK12_SY6429 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK10_C @ B @ A ) @ ( sK12_SY6429 @ 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)],[462]) ).
thf(3419,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(3420,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( is_reflexive_in @ A @ ( relation_field @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(3421,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( function @ ( function_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( relation @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(3422,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(3423,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(3424,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[331]) ).
thf(3425,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(3426,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(3427,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(3428,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(3429,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(3430,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( relation_empty_yielding @ A )
| ! [B: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(3431,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(3432,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(3433,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(3434,plain,
( ( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(3435,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(3436,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( function @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(3437,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(3438,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( function @ ( relation_dom_restriction @ A @ B ) ) )
& ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(3439,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(3440,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(3441,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(3442,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(3443,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(3444,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(3445,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(3446,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(3447,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(3448,plain,
( ( ( empty @ sK7_A )
& ( relation @ sK7_A )
& ( function @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(3449,plain,
( ( ( function @ sK6_A )
& ( relation @ sK6_A )
& ( one_to_one @ sK6_A )
& ( empty @ sK6_A )
& ( epsilon_transitive @ sK6_A )
& ( epsilon_connected @ sK6_A )
& ( ordinal @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(3450,plain,
( ( ~ ( empty @ sK5_A )
& ( relation @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(3451,plain,
( ( ( function @ sK4_A )
& ( relation @ sK4_A )
& ( one_to_one @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(3452,plain,
( ( ( relation @ sK3_A )
& ( relation_empty_yielding @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(3453,plain,
( ( ( relation @ sK2_A )
& ( relation_empty_yielding @ sK2_A )
& ( function @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(3454,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(3455,plain,
( ( ( well_ordering @ sK1_A )
& ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(3456,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3399]) ).
thf(3457,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SX2 @ SX1 @ SX0 ) @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK51_SY6455 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK50_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 @ ( sK49_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK49_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3396]) ).
thf(3458,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3438]) ).
thf(3459,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK11_SY6427 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK12_SY6429 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY6427 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SX1 @ SX0 ) @ ( sK12_SY6429 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SX1 @ SX0 ) @ ( sK12_SY6429 @ 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)],[3418]) ).
thf(3460,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( ( sK56_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX3 ) ) )
| ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK56_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK57_SY6458 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ SX4 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX4 @ SX1 )
| ( SX3
!= ( apply @ SX0 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( apply @ SX0 @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3392]) ).
thf(3461,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( apply @ SX0 @ ( sK52_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( apply @ SX0 @ SX3 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3395]) ).
thf(3462,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3400]) ).
thf(3463,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3430]) ).
thf(3464,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3443]) ).
thf(3465,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ~ ( is_transitive_in @ SX0 @ SX1 )
| ~ ( is_antisymmetric_in @ SX0 @ SX1 )
| ~ ( is_connected_in @ SX0 @ SX1 )
| ~ ( is_well_founded_in @ SX0 @ SX1 )
| ( well_orders @ SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_reflexive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_transitive_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_antisymmetric_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_connected_in @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( well_orders @ SX0 @ SX1 )
| ( is_well_founded_in @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3412]) ).
thf(3466,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3429]) ).
thf(3467,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( in @ ( sK62_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( ( ( apply @ SX1 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) )
!= ( apply @ SX2 @ ( sK62_D @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) )
| ( SX1
= ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX1 ) )
| ( ( apply @ SX1 @ SX3 )
= ( apply @ SX2 @ SX3 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( relation_dom_restriction @ SX2 @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( set_intersection2 @ ( relation_dom @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3378]) ).
thf(3468,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3420]) ).
thf(3469,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK32_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SX1 @ SX0 ) @ ( sK33_SY6444 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK32_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 @ ( sK31_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3407]) ).
thf(3470,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK30_SY6442 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SX1 @ SX0 ) @ ( sK30_SY6442 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SX1 @ SX0 ) @ ( sK29_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK29_C @ SX1 @ SX0 )
!= ( sK30_SY6442 @ 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)],[3408]) ).
thf(3471,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_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)],[3337]) ).
thf(3472,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
| ~ ( ordinal @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3449]) ).
thf(3473,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3439]) ).
thf(3474,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 @ ( sK68_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK68_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK68_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3353]) ).
thf(3475,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)],[3363]) ).
thf(3476,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3389]) ).
thf(3477,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3431]) ).
thf(3478,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) )
| ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ( in @ SX0 @ ( relation_rng @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3339]) ).
thf(3479,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY6459 @ 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)],[3391]) ).
thf(3480,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3373]) ).
thf(3481,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK24_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SX1 @ SX0 ) @ ( sK24_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK24_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 @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3411]) ).
thf(3482,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3428]) ).
thf(3483,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK53_D @ SX2 @ SX1 @ SX0 ) @ ( sK54_SY6456 @ 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)],[3393]) ).
thf(3484,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3376]) ).
thf(3485,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY6448 @ 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)],[3402]) ).
thf(3486,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK65_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK66_SY6462 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK66_SY6462 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK65_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ( ( relation_dom @ SX1 )
!= ( relation_rng @ SX0 ) )
| ( SX1
= ( function_inverse @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( SX2
= ( apply @ SX0 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( apply @ SX1 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_rng @ SX0 ) )
| ( in @ SX3 @ ( relation_dom @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX3
= ( apply @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ ( relation_rng @ SX0 ) ) ) ) ) )
| ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( function_inverse @ SX0 ) )
| ( ( relation_dom @ SX1 )
= ( relation_rng @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3370]) ).
thf(3487,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3371]) ).
thf(3488,plain,
( ( ~ ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3452]) ).
thf(3489,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)],[3381]) ).
thf(3490,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3421]) ).
thf(3491,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)],[3384]) ).
thf(3492,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3382]) ).
thf(3493,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SX1 @ SX0 ) @ ( sK42_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)],[3401]) ).
thf(3494,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ 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)],[3335]) ).
thf(3495,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 @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3345]) ).
thf(3496,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX2 ) @ ( sK35_C @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK35_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SX1 @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( is_well_founded_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_well_founded_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK34_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK34_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ( SX2 = empty_set )
| ~ ( subset @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3405]) ).
thf(3497,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3362]) ).
thf(3498,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3434]) ).
thf(3499,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_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)],[3334]) ).
thf(3500,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_dom @ ( relation_composition @ SX2 @ SX1 ) ) )
| ( in @ ( apply @ SX2 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3358]) ).
thf(3501,plain,
( ( ~ ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3447]) ).
thf(3502,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3446]) ).
thf(3503,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
| ~ ( function @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3453]) ).
thf(3504,plain,
( ( ~ ( ~ ( well_ordering @ sK1_A )
| ~ ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3455]) ).
thf(3505,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3450]) ).
thf(3506,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3374]) ).
thf(3507,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= ( sK22_SY6437 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK22_SY6437 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SX1 @ SX0 ) @ ( sK22_SY6437 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SX1 @ SX0 ) @ ( sK21_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)],[3414]) ).
thf(3508,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ 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)],[3336]) ).
thf(3509,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ SX2 ) )
| ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ SX1 @ ( relation_dom @ ( relation_dom_restriction @ SX2 @ SX0 ) ) )
| ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3338]) ).
thf(3510,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3448]) ).
thf(3511,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3377]) ).
thf(3512,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK27_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK27_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK28_SY6441 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( apply @ SX0 @ SX3 ) )
| ~ ( in @ SX3 @ ( relation_dom @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ( SX2
!= ( apply @ SX0 @ ( sK26_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3410]) ).
thf(3513,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY6434 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY6430 @ 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 @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3417]) ).
thf(3514,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)],[3357]) ).
thf(3515,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3427]) ).
thf(3516,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
| ~ ( one_to_one @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3451]) ).
thf(3517,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY6436 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SX1 @ SX0 ) @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY6436 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SX1 @ SX0 ) @ ( sK19_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)],[3415]) ).
thf(3518,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ 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)],[3390]) ).
thf(3519,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY6446 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY6446 @ 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)],[3404]) ).
thf(3520,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3403]) ).
thf(3521,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)],[3406]) ).
thf(3522,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3409]) ).
thf(3523,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3416]) ).
thf(3524,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ ( sK48_SY6453 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK48_SY6453 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK47_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 @ ( sK46_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK46_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3397]) ).
thf(3525,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3365]) ).
thf(3526,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3394]) ).
thf(3527,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3364]) ).
thf(3528,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3444]) ).
thf(3529,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3398]) ).
thf(3530,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3436]) ).
thf(3531,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3433]) ).
thf(3532,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3442]) ).
thf(3533,plain,
! [SV423: $i] :
( ( ! [SY6961: $i] :
( ~ ( relation @ SY6961 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV423 @ SY6961 ) ) @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(3534,plain,
! [SV424: $i] :
( ( ! [SY6962: $i] :
( ~ ( relation @ SY6962 )
| ( subset @ ( relation_rng_restriction @ SV424 @ SY6962 ) @ SY6962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(3535,plain,
! [SV425: $i] :
( ( ! [SY6963: $i] :
( ~ ( relation @ SY6963 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV425 @ SY6963 ) ) @ ( relation_rng @ SY6963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3536,plain,
! [SV426: $i] :
( ( ! [SY6964: $i] :
( ~ ( relation @ SY6964 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV426 @ SY6964 ) )
= ( set_intersection2 @ ( relation_rng @ SY6964 ) @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3537,plain,
! [SV427: $i] :
( ( ! [SY6965: $i,SY6966: $i] :
( ~ ( relation @ SY6966 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV427 @ SY6966 ) @ SY6965 )
= ( relation_rng_restriction @ SV427 @ ( relation_dom_restriction @ SY6966 @ SY6965 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3538,plain,
! [SV428: $i] :
( ( ! [SY6967: $i] :
( ~ ( relation @ SY6967 )
| ( subset @ ( relation_image @ SY6967 @ SV428 ) @ ( relation_rng @ SY6967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3539,plain,
! [SV429: $i] :
( ( ! [SY6968: $i] :
( ~ ( function @ SY6968 )
| ~ ( relation @ SY6968 )
| ( subset @ ( relation_image @ SY6968 @ ( relation_inverse_image @ SY6968 @ SV429 ) ) @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3540,plain,
! [SV430: $i] :
( ( ! [SY6969: $i] :
( ~ ( relation @ SY6969 )
| ( ( relation_image @ SY6969 @ SV430 )
= ( relation_image @ SY6969 @ ( set_intersection2 @ ( relation_dom @ SY6969 ) @ SV430 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3541,plain,
! [SV431: $i] :
( ( ! [SY6970: $i] :
( ~ ( relation @ SY6970 )
| ~ ( subset @ SV431 @ ( relation_dom @ SY6970 ) )
| ( subset @ SV431 @ ( relation_inverse_image @ SY6970 @ ( relation_image @ SY6970 @ SV431 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3542,plain,
! [SV432: $i] :
( ( ~ ( relation @ SV432 )
| ( ( relation_image @ SV432 @ ( relation_dom @ SV432 ) )
= ( relation_rng @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3543,plain,
! [SV433: $i] :
( ( ! [SY6971: $i] :
( ~ ( function @ SY6971 )
| ~ ( relation @ SY6971 )
| ~ ( subset @ SV433 @ ( relation_rng @ SY6971 ) )
| ( ( relation_image @ SY6971 @ ( relation_inverse_image @ SY6971 @ SV433 ) )
= SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3544,plain,
! [SV434: $i] :
( ( ~ ( relation @ SV434 )
| ! [SY6972: $i] :
( ~ ( relation @ SY6972 )
| ( ( relation_rng @ ( relation_composition @ SV434 @ SY6972 ) )
= ( relation_image @ SY6972 @ ( relation_rng @ SV434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3545,plain,
! [SV435: $i] :
( ( ! [SY6973: $i] :
( ~ ( relation @ SY6973 )
| ( subset @ ( relation_inverse_image @ SY6973 @ SV435 ) @ ( relation_dom @ SY6973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(3546,plain,
! [SV436: $i] :
( ( ! [SY6974: $i] :
( ~ ( relation @ SY6974 )
| ( SV436 = empty_set )
| ~ ( subset @ SV436 @ ( relation_rng @ SY6974 ) )
| ( ( relation_inverse_image @ SY6974 @ SV436 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3547,plain,
! [SV437: $i] :
( ( ! [SY6975: $i,SY6976: $i] :
( ~ ( relation @ SY6976 )
| ~ ( subset @ SV437 @ SY6975 )
| ( subset @ ( relation_inverse_image @ SY6976 @ SV437 ) @ ( relation_inverse_image @ SY6976 @ SY6975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3548,plain,
! [SV438: $i] :
( ( ~ ( relation @ SV438 )
| ( subset @ SV438 @ ( cartesian_product2 @ ( relation_dom @ SV438 ) @ ( relation_rng @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3549,plain,
! [SV439: $i] :
( ( ! [SY6977: $i] :
( ~ ( function @ SY6977 )
| ~ ( relation @ SY6977 )
| ! [SY6978: $i] :
( ~ ( function @ SY6978 )
| ~ ( relation @ SY6978 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY6978 @ SY6977 ) ) )
| ( ( apply @ ( relation_composition @ SY6978 @ SY6977 ) @ SV439 )
= ( apply @ SY6977 @ ( apply @ SY6978 @ SV439 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3550,plain,
! [SV440: $i] :
( ( ! [SY6979: $i] :
( ~ ( function @ SY6979 )
| ~ ( relation @ SY6979 )
| ! [SY6980: $i] :
( ~ ( function @ SY6980 )
| ~ ( relation @ SY6980 )
| ~ ( in @ SV440 @ ( relation_dom @ SY6979 ) )
| ( ( apply @ ( relation_composition @ SY6979 @ SY6980 ) @ SV440 )
= ( apply @ SY6980 @ ( apply @ SY6979 @ SV440 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3551,plain,
! [SV441: $i] :
( ( ~ ( relation @ SV441 )
| ! [SY6981: $i] :
( ~ ( relation @ SY6981 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SY6981 ) ) @ ( relation_dom @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3552,plain,
! [SV442: $i] :
( ( ~ ( relation @ SV442 )
| ! [SY6982: $i] :
( ~ ( relation @ SY6982 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SY6982 ) ) @ ( relation_rng @ SY6982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3553,plain,
! [SV443: $i] :
( ( ~ ( relation @ SV443 )
| ! [SY6983: $i] :
( ~ ( relation @ SY6983 )
| ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SY6983 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SY6983 ) )
= ( relation_dom @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3554,plain,
! [SV444: $i] :
( ( ~ ( relation @ SV444 )
| ! [SY6984: $i] :
( ~ ( relation @ SY6984 )
| ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SY6984 ) )
| ( ( relation_rng @ ( relation_composition @ SY6984 @ SV444 ) )
= ( relation_rng @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3555,plain,
! [SV445: $i] :
( ( ~ ( relation @ SV445 )
| ( in @ ( ordered_pair @ ( sK63_B @ SV445 ) @ ( sK64_SY6461 @ SV445 ) ) @ SV445 )
| ( SV445 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3556,plain,
! [SV446: $i] :
( ( ~ ( function @ SV446 )
| ~ ( relation @ SV446 )
| ~ ( one_to_one @ SV446 )
| ( one_to_one @ ( function_inverse @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3557,plain,
! [SV447: $i] :
( ( ! [SY6985: $i,SY6986: $i] :
( ~ ( function @ SY6986 )
| ~ ( relation @ SY6986 )
| ~ ( in @ SY6985 @ ( relation_dom @ ( relation_dom_restriction @ SY6986 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY6986 @ SV447 ) @ SY6985 )
= ( apply @ SY6986 @ SY6985 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3558,plain,
! [SV448: $i] :
( ( ! [SY6987: $i,SY6988: $i] :
( ~ ( function @ SY6988 )
| ~ ( relation @ SY6988 )
| ~ ( in @ SY6987 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SY6988 @ SV448 ) @ SY6987 )
= ( apply @ SY6988 @ SY6987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3559,plain,
! [SV449: $i] :
( ( ! [SY6989: $i] :
( ~ ( relation @ SY6989 )
| ( subset @ ( relation_dom_restriction @ SY6989 @ SV449 ) @ SY6989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3560,plain,
! [SV450: $i] :
( ( ! [SY6990: $i] :
( ~ ( relation @ SY6990 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY6990 @ SV450 ) )
= ( set_intersection2 @ ( relation_dom @ SY6990 ) @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3561,plain,
! [SV451: $i] :
( ( ! [SY6991: $i] :
( ~ ( relation @ SY6991 )
| ( ( relation_dom_restriction @ SY6991 @ SV451 )
= ( relation_composition @ ( identity_relation @ SV451 ) @ SY6991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3562,plain,
! [SV452: $i] :
( ( ! [SY6992: $i] :
( ~ ( relation @ SY6992 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY6992 @ SV452 ) ) @ ( relation_rng @ SY6992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3563,plain,
! [SV453: $i] :
( ( ~ ( empty @ SV453 )
| ( relation @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3564,plain,
! [SV454: $i] :
( ( ~ ( relation @ SV454 )
| ( ( relation_field @ SV454 )
= ( set_union2 @ ( relation_dom @ SV454 ) @ ( relation_rng @ SV454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3565,plain,
! [SV455: $i] :
( ( ~ ( function @ SV455 )
| ~ ( relation @ SV455 )
| ~ ( one_to_one @ SV455 )
| ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3566,plain,
! [SV456: $i] :
( ( ~ ( relation @ SV456 )
| ( relation @ ( relation_inverse @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3567,plain,
! [SV457: $i] :
( ( ! [SY6993: $i] :
( ~ ( relation @ SV457 )
| ~ ( relation @ SY6993 )
| ( relation @ ( relation_composition @ SV457 @ SY6993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3568,plain,
! [SV458: $i] :
( ( relation @ ( identity_relation @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3569,plain,
! [SV459: $i] :
( ( ~ ( relation @ SV459 )
| ! [SY6994: $i] : ( relation @ ( relation_dom_restriction @ SV459 @ SY6994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3570,plain,
! [SV460: $i] :
( ( ! [SY6995: $i] :
( ~ ( relation @ SY6995 )
| ( relation @ ( relation_rng_restriction @ SV460 @ SY6995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(3571,plain,
! [SV461: $i] :
( ( ! [SY6996: $i] :
( ~ ( relation @ SV461 )
| ~ ( relation @ SY6996 )
| ( relation @ ( set_intersection2 @ SV461 @ SY6996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(3572,plain,
! [SV462: $i] :
( ( ! [SY6997: $i] :
( ~ ( relation @ SV462 )
| ~ ( relation @ SY6997 )
| ( relation @ ( set_union2 @ SV462 @ SY6997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3573,plain,
! [SV463: $i] :
( ( ! [SY6998: $i] :
( ~ ( relation @ SV463 )
| ~ ( relation @ SY6998 )
| ( relation @ ( set_difference @ SV463 @ SY6998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(3574,plain,
! [SV464: $i] :
( ( ( empty @ SV464 )
| ~ ( relation @ SV464 )
| ~ ( empty @ ( relation_dom @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3575,plain,
! [SV465: $i] :
( ( ( empty @ SV465 )
| ~ ( relation @ SV465 )
| ~ ( empty @ ( relation_rng @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3576,plain,
! [SV466: $i] :
( ( ~ ( relation @ SV466 )
| ( ( relation_inverse @ ( relation_inverse @ SV466 ) )
= SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3577,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3578,plain,
! [SV467: $i] :
( ( ~ ( relation @ SV467 )
| ~ ( ~ ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) )
| ~ ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3579,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3580,plain,
! [SV468: $i] :
( ( ~ ( relation @ SV468 )
| ~ ( ~ ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) )
| ~ ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3581,plain,
! [SV469: $i] :
( ( ~ ( function @ SV469 )
| ~ ( relation @ SV469 )
| ~ ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3582,plain,
! [SV470: $i] :
( ( ~ ( function @ SV470 )
| ~ ( relation @ SV470 )
| ~ ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(3583,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3584,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3585,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3586,plain,
! [SV471: $i] :
( ( ~ ( relation @ SV471 )
| ~ ( ~ ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3587,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3588,plain,
! [SV472: $i] :
( ( ! [SY7033: $i] :
( ~ ( function @ SY7033 )
| ~ ( relation @ SY7033 )
| ~ ( ~ ! [SY7034: $i] :
( ~ ( function @ SY7034 )
| ~ ( relation @ SY7034 )
| ~ ( ~ ( in @ ( sK62_D @ SY7034 @ SY7033 @ SV472 ) @ ( relation_dom @ SY7033 ) )
| ~ ( ( ( apply @ SY7033 @ ( sK62_D @ SY7034 @ SY7033 @ SV472 ) )
!= ( apply @ SY7034 @ ( sK62_D @ SY7034 @ SY7033 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SY7033 )
!= ( set_intersection2 @ ( relation_dom @ SY7034 ) @ SV472 ) )
| ( SY7033
= ( relation_dom_restriction @ SY7034 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7035: $i] :
( ~ ( function @ SY7035 )
| ~ ( relation @ SY7035 )
| ( SY7033
!= ( relation_dom_restriction @ SY7035 @ SV472 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY7033 ) )
| ( ( apply @ SY7033 @ SX3 )
= ( apply @ SY7035 @ SX3 ) ) ) )
| ~ ! [SY7037: $i] :
( ~ ( function @ SY7037 )
| ~ ( relation @ SY7037 )
| ( SY7033
!= ( relation_dom_restriction @ SY7037 @ SV472 ) )
| ( ( relation_dom @ SY7033 )
= ( set_intersection2 @ ( relation_dom @ SY7037 ) @ SV472 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3589,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3590,plain,
! [SV473: $i] :
( ( ~ ( relation @ SV473 )
| ~ ( ~ ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) )
| ~ ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3591,plain,
! [SV474: $i] :
( ( ~ ( relation @ SV474 )
| ~ ( ~ ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) )
| ~ ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(3592,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_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)],[3471]) ).
thf(3593,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
| ~ ( ordinal @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3594,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3595,plain,
! [SV475: $i] :
( ( ~ ( ~ ! [SY7048: $i,SY7049: $i] :
( ~ ( relation @ SY7049 )
| ! [SY7050: $i] :
( ~ ( in @ SY7050 @ ( relation_rng @ SY7049 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7050 ) @ SY7049 )
| ~ ( in @ SY7050 @ SY7048 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SY7049 @ SY7048 ) ) )
| ~ ! [SY7051: $i,SY7052: $i] :
( ~ ( relation @ SY7052 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SY7052 @ SY7051 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ ( relation_rng @ SY7052 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) ) @ SY7052 ) )
| ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ SY7051 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3596,plain,
! [SV476: $i] :
( ( ~ ( ~ ! [SY7053: $i,SY7054: $i] :
( ~ ( relation @ SY7054 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7053 ) @ SY7054 )
| ( in @ SV476 @ ( relation_field @ SY7054 ) ) )
| ~ ! [SY7055: $i,SY7056: $i] :
( ~ ( relation @ SY7056 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7055 ) @ SY7056 )
| ( in @ SY7055 @ ( relation_field @ SY7056 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3597,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3598,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3599,plain,
! [SV477: $i] :
( ( ~ ( ~ ! [SY7057: $i,SY7058: $i] :
( ~ ( relation @ SY7058 )
| ~ ( in @ SV477 @ SY7057 )
| ~ ( in @ SV477 @ ( relation_rng @ SY7058 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7057 @ SY7058 ) ) ) )
| ~ ~ ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) )
| ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3600,plain,
! [SV478: $i] :
( ( ~ ( relation @ SV478 )
| ~ ( ~ ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) )
| ~ ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3601,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3602,plain,
! [SV479: $i] :
( ( ~ ( relation @ SV479 )
| ~ ( ~ ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) )
| ~ ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3603,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3604,plain,
! [SV480: $i] :
( ( ! [SY7079: $i] :
( ~ ( relation @ SY7079 )
| ~ ( ~ ! [SY7080: $i] :
( ~ ( relation @ SY7080 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7080 @ SY7079 @ SV480 ) @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) ) @ SY7079 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7080 @ SY7079 @ SV480 ) @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) ) @ SY7080 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7080 @ SY7079 @ SV480 ) @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) ) @ SY7080 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7080 @ SY7079 @ SV480 ) @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) ) @ SY7079 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7080 @ SY7079 @ SV480 ) @ ( sK54_SY6456 @ SY7080 @ SY7079 @ SV480 ) ) @ SY7080 ) ) ) )
| ( SY7080
= ( relation_rng_restriction @ SV480 @ SY7079 ) ) )
| ~ ! [SY7081: $i] :
( ~ ( relation @ SY7081 )
| ( SY7081
!= ( relation_rng_restriction @ SV480 @ SY7079 ) )
| ~ ( ~ ! [SY7082: $i,SY7083: $i] :
( ~ ( in @ SY7083 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7082 @ SY7083 ) @ SY7079 )
| ( in @ ( ordered_pair @ SY7082 @ SY7083 ) @ SY7081 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7081 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7081 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7079 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(3605,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3606,plain,
! [SV481: $i] :
( ( ~ ( relation @ SV481 )
| ~ ( ~ ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) )
| ~ ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(3607,plain,
! [SV482: $i] :
( ( ~ ( function @ SV482 )
| ~ ( relation @ SV482 )
| ~ ( one_to_one @ SV482 )
| ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(3608,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3609,plain,
( ( ~ ( relation @ sK3_A )
| ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3610,plain,
! [SV483: $i] :
( ( ! [SY7105: $i] :
~ ( ~ ! [SY7106: $i,SY7107: $i] :
( ~ ( relation @ SY7107 )
| ~ ( in @ SV483 @ SY7106 )
| ~ ( in @ ( ordered_pair @ SV483 @ SY7105 ) @ SY7107 )
| ( in @ ( ordered_pair @ SV483 @ SY7105 ) @ ( relation_composition @ ( identity_relation @ SY7106 ) @ SY7107 ) ) )
| ~ ~ ( ~ ! [SY7108: $i,SY7109: $i] :
( ~ ( relation @ SY7109 )
| ~ ( in @ ( ordered_pair @ SV483 @ SY7105 ) @ ( relation_composition @ ( identity_relation @ SY7108 ) @ SY7109 ) )
| ( in @ SV483 @ SY7108 ) )
| ~ ! [SY7110: $i,SY7111: $i] :
( ~ ( relation @ SY7111 )
| ~ ( in @ ( ordered_pair @ SV483 @ SY7105 ) @ ( relation_composition @ ( identity_relation @ SY7110 ) @ SY7111 ) )
| ( in @ ( ordered_pair @ SV483 @ SY7105 ) @ SY7111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3611,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3612,plain,
! [SV484: $i] :
( ( ~ ( ~ ! [SY7112: $i,SY7113: $i] :
( ~ ( function @ SY7113 )
| ~ ( relation @ SY7113 )
| ( SY7112
!= ( apply @ SY7113 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SY7113 ) )
| ( in @ ( ordered_pair @ SV484 @ SY7112 ) @ SY7113 ) )
| ~ ~ ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) )
| ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(3613,plain,
! [SV485: $i] :
( ( ~ ( ~ ! [SY7118: $i,SY7119: $i] :
( ~ ( relation @ SY7119 )
| ~ ( in @ SV485 @ SY7118 )
| ~ ( in @ SV485 @ ( relation_dom @ SY7119 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7119 @ SY7118 ) ) ) )
| ~ ~ ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) )
| ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(3614,plain,
! [SV486: $i] :
( ( ~ ( relation @ SV486 )
| ~ ( ~ ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) )
| ~ ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(3615,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ 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)],[3494]) ).
thf(3616,plain,
! [SV487: $i] :
( ( ~ ( ~ ! [SY7127: $i,SY7128: $i] :
( ~ ( relation @ SY7128 )
| ! [SY7129: $i] :
( ~ ( in @ SY7129 @ ( relation_dom @ SY7128 ) )
| ~ ( in @ ( ordered_pair @ SY7129 @ SV487 ) @ SY7128 )
| ~ ( in @ SY7129 @ SY7127 ) )
| ( in @ SV487 @ ( relation_image @ SY7128 @ SY7127 ) ) )
| ~ ! [SY7130: $i,SY7131: $i] :
( ~ ( relation @ SY7131 )
| ~ ( in @ SV487 @ ( relation_image @ SY7131 @ SY7130 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ ( relation_dom @ SY7131 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SV487 ) @ SY7131 ) )
| ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SY7130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3617,plain,
! [SV488: $i] :
( ( ~ ( relation @ SV488 )
| ~ ( ~ ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) )
| ~ ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(3618,plain,
! [SV489: $i] :
( ( ~ ( relation @ SV489 )
| ~ ( ~ ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) )
| ~ ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(3619,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
| ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3620,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_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)],[3499]) ).
thf(3621,plain,
! [SV490: $i] :
( ( ! [SY7138: $i] :
( ~ ( function @ SY7138 )
| ~ ( relation @ SY7138 )
| ~ ( ~ ! [SY7139: $i] :
( ~ ( function @ SY7139 )
| ~ ( relation @ SY7139 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7139 ) )
| ~ ( in @ ( apply @ SY7139 @ SV490 ) @ ( relation_dom @ SY7138 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7139 @ SY7138 ) ) ) )
| ~ ~ ( ~ ! [SY7140: $i] :
( ~ ( function @ SY7140 )
| ~ ( relation @ SY7140 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7140 @ SY7138 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7140 ) ) )
| ~ ! [SY7141: $i] :
( ~ ( function @ SY7141 )
| ~ ( relation @ SY7141 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7141 @ SY7138 ) ) )
| ( in @ ( apply @ SY7141 @ SV490 ) @ ( relation_dom @ SY7138 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(3622,plain,
( ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3623,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3624,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
| ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3625,plain,
( ( ~ ( well_ordering @ sK1_A )
| ~ ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3626,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3627,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3628,plain,
! [SV491: $i] :
( ( ~ ( relation @ SV491 )
| ~ ( ~ ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) )
| ~ ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(3629,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ 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)],[3508]) ).
thf(3630,plain,
! [SV492: $i] :
( ( ~ ( ~ ! [SY7146: $i,SY7147: $i] :
( ~ ( function @ SY7147 )
| ~ ( relation @ SY7147 )
| ~ ( in @ SY7146 @ ( relation_dom @ SY7147 ) )
| ~ ( in @ SY7146 @ SV492 )
| ( in @ SY7146 @ ( relation_dom @ ( relation_dom_restriction @ SY7147 @ SV492 ) ) ) )
| ~ ~ ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) )
| ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(3631,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
| ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3632,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3633,plain,
! [SV493: $i] :
( ( ~ ( function @ SV493 )
| ~ ( relation @ SV493 )
| ~ ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(3634,plain,
! [SV494: $i] :
( ( ~ ( relation @ SV494 )
| ! [SY7158: $i] :
( ~ ( relation @ SY7158 )
| ~ ( ~ ! [SY7159: $i] :
( ~ ( relation @ SY7159 )
| ~ ( ~ ( ! [SY7160: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ SY7160 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7160 @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) ) )
| ( SY7159
= ( relation_composition @ SV494 @ SY7158 ) ) )
| ~ ! [SY7161: $i] :
( ~ ( relation @ SY7161 )
| ( SY7161
!= ( relation_composition @ SV494 @ SY7158 ) )
| ~ ( ~ ! [SY7162: $i,SY7163: $i] :
( ! [SY7164: $i] :
( ~ ( in @ ( ordered_pair @ SY7162 @ SY7164 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7164 @ SY7163 ) @ SY7158 ) )
| ( in @ ( ordered_pair @ SY7162 @ SY7163 ) @ SY7161 ) )
| ~ ! [SY7165: $i,SY7166: $i] :
( ~ ( in @ ( ordered_pair @ SY7165 @ SY7166 ) @ SY7161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7165 @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) @ SY7166 ) @ SY7158 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(3635,plain,
! [SV495: $i] :
( ( ~ ( ~ ! [SY7167: $i,SY7168: $i] :
( ~ ( relation @ SY7168 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7167 ) @ SY7168 )
| ( in @ SV495 @ ( relation_dom @ SY7168 ) ) )
| ~ ! [SY7169: $i,SY7170: $i] :
( ~ ( relation @ SY7170 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7169 ) @ SY7170 )
| ( in @ SY7169 @ ( relation_rng @ SY7170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(3636,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3515]) ).
thf(3637,plain,
( ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
| ~ ( one_to_one @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3638,plain,
! [SV496: $i] :
( ( ~ ( relation @ SV496 )
| ~ ( ~ ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) )
| ~ ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(3639,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ 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)],[3518]) ).
thf(3640,plain,
! [SV497: $i] :
( ( ~ ( relation @ SV497 )
| ~ ( ~ ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) )
| ~ ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(3641,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3642,plain,
! [SV498: $i] :
( ( ~ ( function @ SV498 )
| ~ ( relation @ SV498 )
| ~ ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(3643,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3644,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3645,plain,
! [SV499: $i] :
( ( ~ ( relation @ SV499 )
| ~ ( ~ ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) )
| ~ ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3646,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3525]) ).
thf(3647,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3526]) ).
thf(3648,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3649,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3650,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3651,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3652,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3531]) ).
thf(3653,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3532]) ).
thf(3654,plain,
! [SV423: $i,SV500: $i] :
( ( ~ ( relation @ SV500 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV423 @ SV500 ) ) @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3655,plain,
! [SV424: $i,SV501: $i] :
( ( ~ ( relation @ SV501 )
| ( subset @ ( relation_rng_restriction @ SV424 @ SV501 ) @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(3656,plain,
! [SV425: $i,SV502: $i] :
( ( ~ ( relation @ SV502 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV425 @ SV502 ) ) @ ( relation_rng @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3657,plain,
! [SV426: $i,SV503: $i] :
( ( ~ ( relation @ SV503 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV426 @ SV503 ) )
= ( set_intersection2 @ ( relation_rng @ SV503 ) @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(3658,plain,
! [SV504: $i,SV427: $i] :
( ( ! [SY7197: $i] :
( ~ ( relation @ SY7197 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV427 @ SY7197 ) @ SV504 )
= ( relation_rng_restriction @ SV427 @ ( relation_dom_restriction @ SY7197 @ SV504 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3659,plain,
! [SV428: $i,SV505: $i] :
( ( ~ ( relation @ SV505 )
| ( subset @ ( relation_image @ SV505 @ SV428 ) @ ( relation_rng @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(3660,plain,
! [SV429: $i,SV506: $i] :
( ( ~ ( function @ SV506 )
| ~ ( relation @ SV506 )
| ( subset @ ( relation_image @ SV506 @ ( relation_inverse_image @ SV506 @ SV429 ) ) @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3661,plain,
! [SV430: $i,SV507: $i] :
( ( ~ ( relation @ SV507 )
| ( ( relation_image @ SV507 @ SV430 )
= ( relation_image @ SV507 @ ( set_intersection2 @ ( relation_dom @ SV507 ) @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(3662,plain,
! [SV431: $i,SV508: $i] :
( ( ~ ( relation @ SV508 )
| ~ ( subset @ SV431 @ ( relation_dom @ SV508 ) )
| ( subset @ SV431 @ ( relation_inverse_image @ SV508 @ ( relation_image @ SV508 @ SV431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(3663,plain,
! [SV432: $i] :
( ( ( ~ ( relation @ SV432 ) )
= $true )
| ( ( ( relation_image @ SV432 @ ( relation_dom @ SV432 ) )
= ( relation_rng @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(3664,plain,
! [SV433: $i,SV509: $i] :
( ( ~ ( function @ SV509 )
| ~ ( relation @ SV509 )
| ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) )
| ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(3665,plain,
! [SV434: $i] :
( ( ( ~ ( relation @ SV434 ) )
= $true )
| ( ( ! [SY6972: $i] :
( ~ ( relation @ SY6972 )
| ( ( relation_rng @ ( relation_composition @ SV434 @ SY6972 ) )
= ( relation_image @ SY6972 @ ( relation_rng @ SV434 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3666,plain,
! [SV435: $i,SV510: $i] :
( ( ~ ( relation @ SV510 )
| ( subset @ ( relation_inverse_image @ SV510 @ SV435 ) @ ( relation_dom @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(3667,plain,
! [SV436: $i,SV511: $i] :
( ( ~ ( relation @ SV511 )
| ( SV436 = empty_set )
| ~ ( subset @ SV436 @ ( relation_rng @ SV511 ) )
| ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(3668,plain,
! [SV512: $i,SV437: $i] :
( ( ! [SY7198: $i] :
( ~ ( relation @ SY7198 )
| ~ ( subset @ SV437 @ SV512 )
| ( subset @ ( relation_inverse_image @ SY7198 @ SV437 ) @ ( relation_inverse_image @ SY7198 @ SV512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3669,plain,
! [SV438: $i] :
( ( ( ~ ( relation @ SV438 ) )
= $true )
| ( ( subset @ SV438 @ ( cartesian_product2 @ ( relation_dom @ SV438 ) @ ( relation_rng @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(3670,plain,
! [SV439: $i,SV513: $i] :
( ( ~ ( function @ SV513 )
| ~ ( relation @ SV513 )
| ! [SY7199: $i] :
( ~ ( function @ SY7199 )
| ~ ( relation @ SY7199 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY7199 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SY7199 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SY7199 @ SV439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(3671,plain,
! [SV440: $i,SV514: $i] :
( ( ~ ( function @ SV514 )
| ~ ( relation @ SV514 )
| ! [SY7200: $i] :
( ~ ( function @ SY7200 )
| ~ ( relation @ SY7200 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SY7200 ) @ SV440 )
= ( apply @ SY7200 @ ( apply @ SV514 @ SV440 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3672,plain,
! [SV441: $i] :
( ( ( ~ ( relation @ SV441 ) )
= $true )
| ( ( ! [SY6981: $i] :
( ~ ( relation @ SY6981 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SY6981 ) ) @ ( relation_dom @ SV441 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3551]) ).
thf(3673,plain,
! [SV442: $i] :
( ( ( ~ ( relation @ SV442 ) )
= $true )
| ( ( ! [SY6982: $i] :
( ~ ( relation @ SY6982 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SY6982 ) ) @ ( relation_rng @ SY6982 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3674,plain,
! [SV443: $i] :
( ( ( ~ ( relation @ SV443 ) )
= $true )
| ( ( ! [SY6983: $i] :
( ~ ( relation @ SY6983 )
| ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SY6983 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SY6983 ) )
= ( relation_dom @ SV443 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3675,plain,
! [SV444: $i] :
( ( ( ~ ( relation @ SV444 ) )
= $true )
| ( ( ! [SY6984: $i] :
( ~ ( relation @ SY6984 )
| ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SY6984 ) )
| ( ( relation_rng @ ( relation_composition @ SY6984 @ SV444 ) )
= ( relation_rng @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3676,plain,
! [SV445: $i] :
( ( ( ~ ( relation @ SV445 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK63_B @ SV445 ) @ ( sK64_SY6461 @ SV445 ) ) @ SV445 )
| ( SV445 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3677,plain,
! [SV446: $i] :
( ( ( ~ ( function @ SV446 )
| ~ ( relation @ SV446 ) )
= $true )
| ( ( ~ ( one_to_one @ SV446 )
| ( one_to_one @ ( function_inverse @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3678,plain,
! [SV447: $i,SV515: $i] :
( ( ! [SY7201: $i] :
( ~ ( function @ SY7201 )
| ~ ( relation @ SY7201 )
| ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SY7201 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY7201 @ SV447 ) @ SV515 )
= ( apply @ SY7201 @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(3679,plain,
! [SV448: $i,SV516: $i] :
( ( ! [SY7202: $i] :
( ~ ( function @ SY7202 )
| ~ ( relation @ SY7202 )
| ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SY7202 @ SV448 ) @ SV516 )
= ( apply @ SY7202 @ SV516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(3680,plain,
! [SV449: $i,SV517: $i] :
( ( ~ ( relation @ SV517 )
| ( subset @ ( relation_dom_restriction @ SV517 @ SV449 ) @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(3681,plain,
! [SV450: $i,SV518: $i] :
( ( ~ ( relation @ SV518 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV518 @ SV450 ) )
= ( set_intersection2 @ ( relation_dom @ SV518 ) @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(3682,plain,
! [SV451: $i,SV519: $i] :
( ( ~ ( relation @ SV519 )
| ( ( relation_dom_restriction @ SV519 @ SV451 )
= ( relation_composition @ ( identity_relation @ SV451 ) @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(3683,plain,
! [SV452: $i,SV520: $i] :
( ( ~ ( relation @ SV520 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV520 @ SV452 ) ) @ ( relation_rng @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3684,plain,
! [SV453: $i] :
( ( ( ~ ( empty @ SV453 ) )
= $true )
| ( ( relation @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3563]) ).
thf(3685,plain,
! [SV454: $i] :
( ( ( ~ ( relation @ SV454 ) )
= $true )
| ( ( ( relation_field @ SV454 )
= ( set_union2 @ ( relation_dom @ SV454 ) @ ( relation_rng @ SV454 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3686,plain,
! [SV455: $i] :
( ( ( ~ ( function @ SV455 )
| ~ ( relation @ SV455 ) )
= $true )
| ( ( ~ ( one_to_one @ SV455 )
| ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(3687,plain,
! [SV456: $i] :
( ( ( ~ ( relation @ SV456 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3688,plain,
! [SV521: $i,SV457: $i] :
( ( ~ ( relation @ SV457 )
| ~ ( relation @ SV521 )
| ( relation @ ( relation_composition @ SV457 @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(3689,plain,
! [SV459: $i] :
( ( ( ~ ( relation @ SV459 ) )
= $true )
| ( ( ! [SY6994: $i] : ( relation @ ( relation_dom_restriction @ SV459 @ SY6994 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(3690,plain,
! [SV460: $i,SV522: $i] :
( ( ~ ( relation @ SV522 )
| ( relation @ ( relation_rng_restriction @ SV460 @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(3691,plain,
! [SV523: $i,SV461: $i] :
( ( ~ ( relation @ SV461 )
| ~ ( relation @ SV523 )
| ( relation @ ( set_intersection2 @ SV461 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(3692,plain,
! [SV524: $i,SV462: $i] :
( ( ~ ( relation @ SV462 )
| ~ ( relation @ SV524 )
| ( relation @ ( set_union2 @ SV462 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(3693,plain,
! [SV525: $i,SV463: $i] :
( ( ~ ( relation @ SV463 )
| ~ ( relation @ SV525 )
| ( relation @ ( set_difference @ SV463 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(3694,plain,
! [SV464: $i] :
( ( ( ( empty @ SV464 )
| ~ ( relation @ SV464 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3574]) ).
thf(3695,plain,
! [SV465: $i] :
( ( ( ( empty @ SV465 )
| ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3575]) ).
thf(3696,plain,
! [SV466: $i] :
( ( ( ~ ( relation @ SV466 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV466 ) )
= SV466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3576]) ).
thf(3697,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3698,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3699,plain,
! [SV467: $i] :
( ( ( ~ ( relation @ SV467 ) )
= $true )
| ( ( ~ ( ~ ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) )
| ~ ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3578]) ).
thf(3700,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3701,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3702,plain,
! [SV468: $i] :
( ( ( ~ ( relation @ SV468 ) )
= $true )
| ( ( ~ ( ~ ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) )
| ~ ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3703,plain,
! [SV469: $i] :
( ( ( ~ ( function @ SV469 )
| ~ ( relation @ SV469 ) )
= $true )
| ( ( ~ ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3704,plain,
! [SV470: $i] :
( ( ( ~ ( function @ SV470 )
| ~ ( relation @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3705,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3706,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3707,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3708,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3709,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3710,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3711,plain,
! [SV471: $i] :
( ( ( ~ ( relation @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(3712,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3587]) ).
thf(3713,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3587]) ).
thf(3714,plain,
! [SV472: $i,SV526: $i] :
( ( ~ ( function @ SV526 )
| ~ ( relation @ SV526 )
| ~ ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(3715,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3716,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3717,plain,
! [SV473: $i] :
( ( ( ~ ( relation @ SV473 ) )
= $true )
| ( ( ~ ( ~ ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) )
| ~ ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3590]) ).
thf(3718,plain,
! [SV474: $i] :
( ( ( ~ ( relation @ SV474 ) )
= $true )
| ( ( ~ ( ~ ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) )
| ~ ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3719,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3592]) ).
thf(3720,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)],[3592]) ).
thf(3721,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3722,plain,
( ( ~ ( ordinal @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3723,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3594]) ).
thf(3724,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3594]) ).
thf(3725,plain,
! [SV475: $i] :
( ( ~ ! [SY7048: $i,SY7049: $i] :
( ~ ( relation @ SY7049 )
| ! [SY7050: $i] :
( ~ ( in @ SY7050 @ ( relation_rng @ SY7049 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7050 ) @ SY7049 )
| ~ ( in @ SY7050 @ SY7048 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SY7049 @ SY7048 ) ) )
| ~ ! [SY7051: $i,SY7052: $i] :
( ~ ( relation @ SY7052 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SY7052 @ SY7051 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ ( relation_rng @ SY7052 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) ) @ SY7052 ) )
| ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ SY7051 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3595]) ).
thf(3726,plain,
! [SV476: $i] :
( ( ~ ! [SY7053: $i,SY7054: $i] :
( ~ ( relation @ SY7054 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7053 ) @ SY7054 )
| ( in @ SV476 @ ( relation_field @ SY7054 ) ) )
| ~ ! [SY7055: $i,SY7056: $i] :
( ~ ( relation @ SY7056 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7055 ) @ SY7056 )
| ( in @ SY7055 @ ( relation_field @ SY7056 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3596]) ).
thf(3727,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3597]) ).
thf(3728,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3597]) ).
thf(3729,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3598]) ).
thf(3730,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3598]) ).
thf(3731,plain,
! [SV477: $i] :
( ( ~ ! [SY7057: $i,SY7058: $i] :
( ~ ( relation @ SY7058 )
| ~ ( in @ SV477 @ SY7057 )
| ~ ( in @ SV477 @ ( relation_rng @ SY7058 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7057 @ SY7058 ) ) ) )
| ~ ~ ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) )
| ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3732,plain,
! [SV478: $i] :
( ( ( ~ ( relation @ SV478 ) )
= $true )
| ( ( ~ ( ~ ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) )
| ~ ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(3733,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3734,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3601]) ).
thf(3735,plain,
! [SV479: $i] :
( ( ( ~ ( relation @ SV479 ) )
= $true )
| ( ( ~ ( ~ ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) )
| ~ ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(3736,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3737,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3738,plain,
! [SV480: $i,SV527: $i] :
( ( ~ ( relation @ SV527 )
| ~ ( ~ ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
| ~ ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(3739,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3605]) ).
thf(3740,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3605]) ).
thf(3741,plain,
! [SV481: $i] :
( ( ( ~ ( relation @ SV481 ) )
= $true )
| ( ( ~ ( ~ ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) )
| ~ ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(3742,plain,
! [SV482: $i] :
( ( ( ~ ( function @ SV482 )
| ~ ( relation @ SV482 ) )
= $true )
| ( ( ~ ( one_to_one @ SV482 )
| ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3743,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3608]) ).
thf(3744,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3608]) ).
thf(3745,plain,
( ( ~ ( relation @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3609]) ).
thf(3746,plain,
( ( ~ ( relation_empty_yielding @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3609]) ).
thf(3747,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ( ~ ! [SY7215: $i,SY7216: $i] :
( ~ ( relation @ SY7216 )
| ~ ( in @ SV483 @ SY7215 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7216 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7215 ) @ SY7216 ) ) )
| ~ ~ ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) )
| ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(3748,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3611]) ).
thf(3749,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3611]) ).
thf(3750,plain,
! [SV484: $i] :
( ( ~ ! [SY7112: $i,SY7113: $i] :
( ~ ( function @ SY7113 )
| ~ ( relation @ SY7113 )
| ( SY7112
!= ( apply @ SY7113 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SY7113 ) )
| ( in @ ( ordered_pair @ SV484 @ SY7112 ) @ SY7113 ) )
| ~ ~ ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) )
| ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3751,plain,
! [SV485: $i] :
( ( ~ ! [SY7118: $i,SY7119: $i] :
( ~ ( relation @ SY7119 )
| ~ ( in @ SV485 @ SY7118 )
| ~ ( in @ SV485 @ ( relation_dom @ SY7119 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7119 @ SY7118 ) ) ) )
| ~ ~ ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) )
| ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3752,plain,
! [SV486: $i] :
( ( ( ~ ( relation @ SV486 ) )
= $true )
| ( ( ~ ( ~ ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) )
| ~ ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(3753,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3615]) ).
thf(3754,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)],[3615]) ).
thf(3755,plain,
! [SV487: $i] :
( ( ~ ! [SY7127: $i,SY7128: $i] :
( ~ ( relation @ SY7128 )
| ! [SY7129: $i] :
( ~ ( in @ SY7129 @ ( relation_dom @ SY7128 ) )
| ~ ( in @ ( ordered_pair @ SY7129 @ SV487 ) @ SY7128 )
| ~ ( in @ SY7129 @ SY7127 ) )
| ( in @ SV487 @ ( relation_image @ SY7128 @ SY7127 ) ) )
| ~ ! [SY7130: $i,SY7131: $i] :
( ~ ( relation @ SY7131 )
| ~ ( in @ SV487 @ ( relation_image @ SY7131 @ SY7130 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ ( relation_dom @ SY7131 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SV487 ) @ SY7131 ) )
| ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SY7130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(3756,plain,
! [SV488: $i] :
( ( ( ~ ( relation @ SV488 ) )
= $true )
| ( ( ~ ( ~ ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) )
| ~ ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(3757,plain,
! [SV489: $i] :
( ( ( ~ ( relation @ SV489 ) )
= $true )
| ( ( ~ ( ~ ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) )
| ~ ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3618]) ).
thf(3758,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3619]) ).
thf(3759,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3619]) ).
thf(3760,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3620]) ).
thf(3761,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)],[3620]) ).
thf(3762,plain,
! [SV490: $i,SV529: $i] :
( ( ~ ( function @ SV529 )
| ~ ( relation @ SV529 )
| ~ ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(3763,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3622]) ).
thf(3764,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3622]) ).
thf(3765,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3766,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3767,plain,
( ( ~ ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3624]) ).
thf(3768,plain,
( ( ~ ( function @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3624]) ).
thf(3769,plain,
( ( ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3770,plain,
( ( ~ ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3625]) ).
thf(3771,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(3772,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(3773,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3774,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3775,plain,
! [SV491: $i] :
( ( ( ~ ( relation @ SV491 ) )
= $true )
| ( ( ~ ( ~ ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) )
| ~ ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(3776,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3629]) ).
thf(3777,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)],[3629]) ).
thf(3778,plain,
! [SV492: $i] :
( ( ~ ! [SY7146: $i,SY7147: $i] :
( ~ ( function @ SY7147 )
| ~ ( relation @ SY7147 )
| ~ ( in @ SY7146 @ ( relation_dom @ SY7147 ) )
| ~ ( in @ SY7146 @ SV492 )
| ( in @ SY7146 @ ( relation_dom @ ( relation_dom_restriction @ SY7147 @ SV492 ) ) ) )
| ~ ~ ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) )
| ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3779,plain,
( ( ~ ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3780,plain,
( ( ~ ( function @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3781,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3782,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3783,plain,
! [SV493: $i] :
( ( ( ~ ( function @ SV493 )
| ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3784,plain,
! [SV494: $i] :
( ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ! [SY7158: $i] :
( ~ ( relation @ SY7158 )
| ~ ( ~ ! [SY7159: $i] :
( ~ ( relation @ SY7159 )
| ~ ( ~ ( ! [SY7160: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ SY7160 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7160 @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) ) )
| ( SY7159
= ( relation_composition @ SV494 @ SY7158 ) ) )
| ~ ! [SY7161: $i] :
( ~ ( relation @ SY7161 )
| ( SY7161
!= ( relation_composition @ SV494 @ SY7158 ) )
| ~ ( ~ ! [SY7162: $i,SY7163: $i] :
( ! [SY7164: $i] :
( ~ ( in @ ( ordered_pair @ SY7162 @ SY7164 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7164 @ SY7163 ) @ SY7158 ) )
| ( in @ ( ordered_pair @ SY7162 @ SY7163 ) @ SY7161 ) )
| ~ ! [SY7165: $i,SY7166: $i] :
( ~ ( in @ ( ordered_pair @ SY7165 @ SY7166 ) @ SY7161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7165 @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) @ SY7166 ) @ SY7158 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(3785,plain,
! [SV495: $i] :
( ( ~ ! [SY7167: $i,SY7168: $i] :
( ~ ( relation @ SY7168 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7167 ) @ SY7168 )
| ( in @ SV495 @ ( relation_dom @ SY7168 ) ) )
| ~ ! [SY7169: $i,SY7170: $i] :
( ~ ( relation @ SY7170 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7169 ) @ SY7170 )
| ( in @ SY7169 @ ( relation_rng @ SY7170 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3786,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3787,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3788,plain,
( ( ~ ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3789,plain,
( ( ~ ( one_to_one @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3790,plain,
! [SV496: $i] :
( ( ( ~ ( relation @ SV496 ) )
= $true )
| ( ( ~ ( ~ ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) )
| ~ ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(3791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3639]) ).
thf(3792,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)],[3639]) ).
thf(3793,plain,
! [SV497: $i] :
( ( ( ~ ( relation @ SV497 ) )
= $true )
| ( ( ~ ( ~ ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) )
| ~ ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3794,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3795,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3796,plain,
! [SV498: $i] :
( ( ( ~ ( function @ SV498 )
| ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3642]) ).
thf(3797,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3798,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3799,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3644]) ).
thf(3800,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3644]) ).
thf(3801,plain,
! [SV499: $i] :
( ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( ~ ( ~ ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) )
| ~ ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(3802,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3646]) ).
thf(3803,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3646]) ).
thf(3804,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3805,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3806,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3648]) ).
thf(3807,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3648]) ).
thf(3808,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3809,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3810,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3811,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3812,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3651]) ).
thf(3813,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3651]) ).
thf(3814,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3652]) ).
thf(3815,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3652]) ).
thf(3816,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3653]) ).
thf(3817,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3653]) ).
thf(3818,plain,
! [SV423: $i,SV500: $i] :
( ( ( ~ ( relation @ SV500 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV423 @ SV500 ) ) @ SV423 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(3819,plain,
! [SV424: $i,SV501: $i] :
( ( ( ~ ( relation @ SV501 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV424 @ SV501 ) @ SV501 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3820,plain,
! [SV425: $i,SV502: $i] :
( ( ( ~ ( relation @ SV502 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV425 @ SV502 ) ) @ ( relation_rng @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3821,plain,
! [SV426: $i,SV503: $i] :
( ( ( ~ ( relation @ SV503 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV426 @ SV503 ) )
= ( set_intersection2 @ ( relation_rng @ SV503 ) @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(3822,plain,
! [SV504: $i,SV427: $i,SV530: $i] :
( ( ~ ( relation @ SV530 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV427 @ SV530 ) @ SV504 )
= ( relation_rng_restriction @ SV427 @ ( relation_dom_restriction @ SV530 @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(3823,plain,
! [SV428: $i,SV505: $i] :
( ( ( ~ ( relation @ SV505 ) )
= $true )
| ( ( subset @ ( relation_image @ SV505 @ SV428 ) @ ( relation_rng @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3659]) ).
thf(3824,plain,
! [SV429: $i,SV506: $i] :
( ( ( ~ ( function @ SV506 )
| ~ ( relation @ SV506 ) )
= $true )
| ( ( subset @ ( relation_image @ SV506 @ ( relation_inverse_image @ SV506 @ SV429 ) ) @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(3825,plain,
! [SV430: $i,SV507: $i] :
( ( ( ~ ( relation @ SV507 ) )
= $true )
| ( ( ( relation_image @ SV507 @ SV430 )
= ( relation_image @ SV507 @ ( set_intersection2 @ ( relation_dom @ SV507 ) @ SV430 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(3826,plain,
! [SV431: $i,SV508: $i] :
( ( ( ~ ( relation @ SV508 ) )
= $true )
| ( ( ~ ( subset @ SV431 @ ( relation_dom @ SV508 ) )
| ( subset @ SV431 @ ( relation_inverse_image @ SV508 @ ( relation_image @ SV508 @ SV431 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(3827,plain,
! [SV432: $i] :
( ( ( relation @ SV432 )
= $false )
| ( ( ( relation_image @ SV432 @ ( relation_dom @ SV432 ) )
= ( relation_rng @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3828,plain,
! [SV433: $i,SV509: $i] :
( ( ( ~ ( function @ SV509 )
| ~ ( relation @ SV509 ) )
= $true )
| ( ( ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) )
| ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(3829,plain,
! [SV434: $i] :
( ( ( relation @ SV434 )
= $false )
| ( ( ! [SY6972: $i] :
( ~ ( relation @ SY6972 )
| ( ( relation_rng @ ( relation_composition @ SV434 @ SY6972 ) )
= ( relation_image @ SY6972 @ ( relation_rng @ SV434 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3830,plain,
! [SV435: $i,SV510: $i] :
( ( ( ~ ( relation @ SV510 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV510 @ SV435 ) @ ( relation_dom @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3831,plain,
! [SV436: $i,SV511: $i] :
( ( ( ~ ( relation @ SV511 ) )
= $true )
| ( ( ( SV436 = empty_set )
| ~ ( subset @ SV436 @ ( relation_rng @ SV511 ) )
| ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3667]) ).
thf(3832,plain,
! [SV512: $i,SV437: $i,SV531: $i] :
( ( ~ ( relation @ SV531 )
| ~ ( subset @ SV437 @ SV512 )
| ( subset @ ( relation_inverse_image @ SV531 @ SV437 ) @ ( relation_inverse_image @ SV531 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(3833,plain,
! [SV438: $i] :
( ( ( relation @ SV438 )
= $false )
| ( ( subset @ SV438 @ ( cartesian_product2 @ ( relation_dom @ SV438 ) @ ( relation_rng @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(3834,plain,
! [SV439: $i,SV513: $i] :
( ( ( ~ ( function @ SV513 )
| ~ ( relation @ SV513 ) )
= $true )
| ( ( ! [SY7199: $i] :
( ~ ( function @ SY7199 )
| ~ ( relation @ SY7199 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY7199 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SY7199 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SY7199 @ SV439 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3670]) ).
thf(3835,plain,
! [SV440: $i,SV514: $i] :
( ( ( ~ ( function @ SV514 )
| ~ ( relation @ SV514 ) )
= $true )
| ( ( ! [SY7200: $i] :
( ~ ( function @ SY7200 )
| ~ ( relation @ SY7200 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SY7200 ) @ SV440 )
= ( apply @ SY7200 @ ( apply @ SV514 @ SV440 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(3836,plain,
! [SV441: $i] :
( ( ( relation @ SV441 )
= $false )
| ( ( ! [SY6981: $i] :
( ~ ( relation @ SY6981 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SY6981 ) ) @ ( relation_dom @ SV441 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(3837,plain,
! [SV442: $i] :
( ( ( relation @ SV442 )
= $false )
| ( ( ! [SY6982: $i] :
( ~ ( relation @ SY6982 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SY6982 ) ) @ ( relation_rng @ SY6982 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3838,plain,
! [SV443: $i] :
( ( ( relation @ SV443 )
= $false )
| ( ( ! [SY6983: $i] :
( ~ ( relation @ SY6983 )
| ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SY6983 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SY6983 ) )
= ( relation_dom @ SV443 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(3839,plain,
! [SV444: $i] :
( ( ( relation @ SV444 )
= $false )
| ( ( ! [SY6984: $i] :
( ~ ( relation @ SY6984 )
| ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SY6984 ) )
| ( ( relation_rng @ ( relation_composition @ SY6984 @ SV444 ) )
= ( relation_rng @ SV444 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3675]) ).
thf(3840,plain,
! [SV445: $i] :
( ( ( relation @ SV445 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK63_B @ SV445 ) @ ( sK64_SY6461 @ SV445 ) ) @ SV445 )
| ( SV445 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3841,plain,
! [SV446: $i] :
( ( ( ~ ( function @ SV446 ) )
= $true )
| ( ( ~ ( relation @ SV446 ) )
= $true )
| ( ( ~ ( one_to_one @ SV446 )
| ( one_to_one @ ( function_inverse @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3842,plain,
! [SV447: $i,SV515: $i,SV532: $i] :
( ( ~ ( function @ SV532 )
| ~ ( relation @ SV532 )
| ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(3843,plain,
! [SV448: $i,SV516: $i,SV533: $i] :
( ( ~ ( function @ SV533 )
| ~ ( relation @ SV533 )
| ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(3844,plain,
! [SV449: $i,SV517: $i] :
( ( ( ~ ( relation @ SV517 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV517 @ SV449 ) @ SV517 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3845,plain,
! [SV450: $i,SV518: $i] :
( ( ( ~ ( relation @ SV518 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV518 @ SV450 ) )
= ( set_intersection2 @ ( relation_dom @ SV518 ) @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3846,plain,
! [SV451: $i,SV519: $i] :
( ( ( ~ ( relation @ SV519 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV519 @ SV451 )
= ( relation_composition @ ( identity_relation @ SV451 ) @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3847,plain,
! [SV452: $i,SV520: $i] :
( ( ( ~ ( relation @ SV520 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV520 @ SV452 ) ) @ ( relation_rng @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3848,plain,
! [SV453: $i] :
( ( ( empty @ SV453 )
= $false )
| ( ( relation @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3849,plain,
! [SV454: $i] :
( ( ( relation @ SV454 )
= $false )
| ( ( ( relation_field @ SV454 )
= ( set_union2 @ ( relation_dom @ SV454 ) @ ( relation_rng @ SV454 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3850,plain,
! [SV455: $i] :
( ( ( ~ ( function @ SV455 ) )
= $true )
| ( ( ~ ( relation @ SV455 ) )
= $true )
| ( ( ~ ( one_to_one @ SV455 )
| ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3851,plain,
! [SV456: $i] :
( ( ( relation @ SV456 )
= $false )
| ( ( relation @ ( relation_inverse @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(3852,plain,
! [SV521: $i,SV457: $i] :
( ( ( ~ ( relation @ SV457 )
| ~ ( relation @ SV521 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV457 @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3853,plain,
! [SV459: $i] :
( ( ( relation @ SV459 )
= $false )
| ( ( ! [SY6994: $i] : ( relation @ ( relation_dom_restriction @ SV459 @ SY6994 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(3854,plain,
! [SV460: $i,SV522: $i] :
( ( ( ~ ( relation @ SV522 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV460 @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(3855,plain,
! [SV523: $i,SV461: $i] :
( ( ( ~ ( relation @ SV461 )
| ~ ( relation @ SV523 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV461 @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(3856,plain,
! [SV524: $i,SV462: $i] :
( ( ( ~ ( relation @ SV462 )
| ~ ( relation @ SV524 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV462 @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3857,plain,
! [SV525: $i,SV463: $i] :
( ( ( ~ ( relation @ SV463 )
| ~ ( relation @ SV525 ) )
= $true )
| ( ( relation @ ( set_difference @ SV463 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(3858,plain,
! [SV464: $i] :
( ( ( empty @ SV464 )
= $true )
| ( ( ~ ( relation @ SV464 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(3859,plain,
! [SV465: $i] :
( ( ( empty @ SV465 )
= $true )
| ( ( ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(3860,plain,
! [SV466: $i] :
( ( ( relation @ SV466 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV466 ) )
= SV466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3861,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3697]) ).
thf(3862,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3698]) ).
thf(3863,plain,
! [SV467: $i] :
( ( ( relation @ SV467 )
= $false )
| ( ( ~ ( ~ ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) )
| ~ ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(3864,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3700]) ).
thf(3865,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3701]) ).
thf(3866,plain,
! [SV468: $i] :
( ( ( relation @ SV468 )
= $false )
| ( ( ~ ( ~ ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) )
| ~ ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3867,plain,
! [SV469: $i] :
( ( ( ~ ( function @ SV469 ) )
= $true )
| ( ( ~ ( relation @ SV469 ) )
= $true )
| ( ( ~ ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3703]) ).
thf(3868,plain,
! [SV470: $i] :
( ( ( ~ ( function @ SV470 ) )
= $true )
| ( ( ~ ( relation @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3704]) ).
thf(3869,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK45_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK45_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3870,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK43_C @ SX1 @ SX0 ) @ ( sK44_SY6449 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3706]) ).
thf(3871,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3707]) ).
thf(3872,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3708]) ).
thf(3873,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3874,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3875,plain,
! [SV471: $i] :
( ( ( relation @ SV471 )
= $false )
| ( ( ~ ( ~ ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3876,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3712]) ).
thf(3877,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3878,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ( function @ SV526 )
| ~ ( relation @ SV526 ) )
= $true )
| ( ( ~ ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(3879,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(3880,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3716]) ).
thf(3881,plain,
! [SV473: $i] :
( ( ( relation @ SV473 )
= $false )
| ( ( ~ ( ~ ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) )
| ~ ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(3882,plain,
! [SV474: $i] :
( ( ( relation @ SV474 )
= $false )
| ( ( ~ ( ~ ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) )
| ~ ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3883,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SX0 )
!= ( sK71_SY6463 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK71_SY6463 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SX0 ) @ ( sK71_SY6463 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SX0 ) @ ( sK70_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3884,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)],[3720]) ).
thf(3885,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3721]) ).
thf(3886,plain,
( ( ordinal @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3722]) ).
thf(3887,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(3888,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3724]) ).
thf(3889,plain,
! [SV475: $i] :
( ( ~ ! [SY7048: $i,SY7049: $i] :
( ~ ( relation @ SY7049 )
| ! [SY7050: $i] :
( ~ ( in @ SY7050 @ ( relation_rng @ SY7049 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7050 ) @ SY7049 )
| ~ ( in @ SY7050 @ SY7048 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SY7049 @ SY7048 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3725]) ).
thf(3890,plain,
! [SV475: $i] :
( ( ~ ! [SY7051: $i,SY7052: $i] :
( ~ ( relation @ SY7052 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SY7052 @ SY7051 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ ( relation_rng @ SY7052 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) ) @ SY7052 ) )
| ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ SY7051 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3725]) ).
thf(3891,plain,
! [SV476: $i] :
( ( ~ ! [SY7053: $i,SY7054: $i] :
( ~ ( relation @ SY7054 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7053 ) @ SY7054 )
| ( in @ SV476 @ ( relation_field @ SY7054 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3892,plain,
! [SV476: $i] :
( ( ~ ! [SY7055: $i,SY7056: $i] :
( ~ ( relation @ SY7056 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7055 ) @ SY7056 )
| ( in @ SY7055 @ ( relation_field @ SY7056 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3893,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3727]) ).
thf(3894,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3728]) ).
thf(3895,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3896,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( function @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3730]) ).
thf(3897,plain,
! [SV477: $i] :
( ( ~ ! [SY7057: $i,SY7058: $i] :
( ~ ( relation @ SY7058 )
| ~ ( in @ SV477 @ SY7057 )
| ~ ( in @ SV477 @ ( relation_rng @ SY7058 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7057 @ SY7058 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3731]) ).
thf(3898,plain,
! [SV477: $i] :
( ( ~ ~ ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) )
| ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3731]) ).
thf(3899,plain,
! [SV478: $i] :
( ( ( relation @ SV478 )
= $false )
| ( ( ~ ( ~ ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) )
| ~ ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3732]) ).
thf(3900,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ SX1 @ ( apply @ ( function_inverse @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3733]) ).
thf(3901,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ~ ( one_to_one @ SX1 )
| ( SX0
= ( apply @ ( relation_composition @ ( function_inverse @ SX1 ) @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3734]) ).
thf(3902,plain,
! [SV479: $i] :
( ( ( relation @ SV479 )
= $false )
| ( ( ~ ( ~ ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) )
| ~ ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3903,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3736]) ).
thf(3904,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(3905,plain,
! [SV480: $i,SV527: $i] :
( ( ( ~ ( relation @ SV527 ) )
= $true )
| ( ( ~ ( ~ ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
| ~ ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(3906,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3739]) ).
thf(3907,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(3908,plain,
! [SV481: $i] :
( ( ( relation @ SV481 )
= $false )
| ( ( ~ ( ~ ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) )
| ~ ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3909,plain,
! [SV482: $i] :
( ( ( ~ ( function @ SV482 ) )
= $true )
| ( ( ~ ( relation @ SV482 ) )
= $true )
| ( ( ~ ( one_to_one @ SV482 )
| ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3910,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3743]) ).
thf(3911,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3744]) ).
thf(3912,plain,
( ( relation @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3745]) ).
thf(3913,plain,
( ( relation_empty_yielding @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3746]) ).
thf(3914,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ! [SY7215: $i,SY7216: $i] :
( ~ ( relation @ SY7216 )
| ~ ( in @ SV483 @ SY7215 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7216 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7215 ) @ SY7216 ) ) )
| ~ ~ ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) )
| ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(3915,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3748]) ).
thf(3916,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3917,plain,
! [SV484: $i] :
( ( ~ ! [SY7112: $i,SY7113: $i] :
( ~ ( function @ SY7113 )
| ~ ( relation @ SY7113 )
| ( SY7112
!= ( apply @ SY7113 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SY7113 ) )
| ( in @ ( ordered_pair @ SV484 @ SY7112 ) @ SY7113 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3918,plain,
! [SV484: $i] :
( ( ~ ~ ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) )
| ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3919,plain,
! [SV485: $i] :
( ( ~ ! [SY7118: $i,SY7119: $i] :
( ~ ( relation @ SY7119 )
| ~ ( in @ SV485 @ SY7118 )
| ~ ( in @ SV485 @ ( relation_dom @ SY7119 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7119 @ SY7118 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3920,plain,
! [SV485: $i] :
( ( ~ ~ ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) )
| ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3921,plain,
! [SV486: $i] :
( ( ( relation @ SV486 )
= $false )
| ( ( ~ ( ~ ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) )
| ~ ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3922,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK75_SY6465 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SX0 ) @ ( sK76_SY6467 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3753]) ).
thf(3923,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)],[3754]) ).
thf(3924,plain,
! [SV487: $i] :
( ( ~ ! [SY7127: $i,SY7128: $i] :
( ~ ( relation @ SY7128 )
| ! [SY7129: $i] :
( ~ ( in @ SY7129 @ ( relation_dom @ SY7128 ) )
| ~ ( in @ ( ordered_pair @ SY7129 @ SV487 ) @ SY7128 )
| ~ ( in @ SY7129 @ SY7127 ) )
| ( in @ SV487 @ ( relation_image @ SY7128 @ SY7127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3925,plain,
! [SV487: $i] :
( ( ~ ! [SY7130: $i,SY7131: $i] :
( ~ ( relation @ SY7131 )
| ~ ( in @ SV487 @ ( relation_image @ SY7131 @ SY7130 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ ( relation_dom @ SY7131 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SV487 ) @ SY7131 ) )
| ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SY7130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3926,plain,
! [SV488: $i] :
( ( ( relation @ SV488 )
= $false )
| ( ( ~ ( ~ ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) )
| ~ ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3927,plain,
! [SV489: $i] :
( ( ( relation @ SV489 )
= $false )
| ( ( ~ ( ~ ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) )
| ~ ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(3928,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3758]) ).
thf(3929,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(3930,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK77_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3760]) ).
thf(3931,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)],[3761]) ).
thf(3932,plain,
! [SV490: $i,SV529: $i] :
( ( ( ~ ( function @ SV529 )
| ~ ( relation @ SV529 ) )
= $true )
| ( ( ~ ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(3933,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3763]) ).
thf(3934,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3764]) ).
thf(3935,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3765]) ).
thf(3936,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(3937,plain,
( ( ~ ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3767]) ).
thf(3938,plain,
( ( function @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3768]) ).
thf(3939,plain,
( ( well_ordering @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(3940,plain,
( ( ~ ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3770]) ).
thf(3941,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(3942,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3772]) ).
thf(3943,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3773]) ).
thf(3944,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3774]) ).
thf(3945,plain,
! [SV491: $i] :
( ( ( relation @ SV491 )
= $false )
| ( ( ~ ( ~ ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) )
| ~ ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3946,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SX0 ) @ ( sK73_SY6464 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SX0 ) @ ( sK72_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK72_B @ SX0 )
!= ( sK73_SY6464 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3776]) ).
thf(3947,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)],[3777]) ).
thf(3948,plain,
! [SV492: $i] :
( ( ~ ! [SY7146: $i,SY7147: $i] :
( ~ ( function @ SY7147 )
| ~ ( relation @ SY7147 )
| ~ ( in @ SY7146 @ ( relation_dom @ SY7147 ) )
| ~ ( in @ SY7146 @ SV492 )
| ( in @ SY7146 @ ( relation_dom @ ( relation_dom_restriction @ SY7147 @ SV492 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3778]) ).
thf(3949,plain,
! [SV492: $i] :
( ( ~ ~ ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) )
| ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3778]) ).
thf(3950,plain,
( ( ~ ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3779]) ).
thf(3951,plain,
( ( function @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3780]) ).
thf(3952,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(3953,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3782]) ).
thf(3954,plain,
! [SV493: $i] :
( ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3783]) ).
thf(3955,plain,
! [SV494: $i] :
( ( ( relation @ SV494 )
= $false )
| ( ( ! [SY7158: $i] :
( ~ ( relation @ SY7158 )
| ~ ( ~ ! [SY7159: $i] :
( ~ ( relation @ SY7159 )
| ~ ( ~ ( ! [SY7160: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ SY7160 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7160 @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7158 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7159 @ SY7158 @ SV494 ) @ ( sK15_SY6430 @ SY7159 @ SY7158 @ SV494 ) ) @ SY7159 ) ) )
| ( SY7159
= ( relation_composition @ SV494 @ SY7158 ) ) )
| ~ ! [SY7161: $i] :
( ~ ( relation @ SY7161 )
| ( SY7161
!= ( relation_composition @ SV494 @ SY7158 ) )
| ~ ( ~ ! [SY7162: $i,SY7163: $i] :
( ! [SY7164: $i] :
( ~ ( in @ ( ordered_pair @ SY7162 @ SY7164 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7164 @ SY7163 ) @ SY7158 ) )
| ( in @ ( ordered_pair @ SY7162 @ SY7163 ) @ SY7161 ) )
| ~ ! [SY7165: $i,SY7166: $i] :
( ~ ( in @ ( ordered_pair @ SY7165 @ SY7166 ) @ SY7161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7165 @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7166 @ SY7165 @ SY7161 @ SY7158 @ SV494 ) @ SY7166 ) @ SY7158 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(3956,plain,
! [SV495: $i] :
( ( ~ ! [SY7167: $i,SY7168: $i] :
( ~ ( relation @ SY7168 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7167 ) @ SY7168 )
| ( in @ SV495 @ ( relation_dom @ SY7168 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3785]) ).
thf(3957,plain,
! [SV495: $i] :
( ( ~ ! [SY7169: $i,SY7170: $i] :
( ~ ( relation @ SY7170 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7169 ) @ SY7170 )
| ( in @ SY7169 @ ( relation_rng @ SY7170 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3785]) ).
thf(3958,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3786]) ).
thf(3959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3787]) ).
thf(3960,plain,
( ( ~ ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3788]) ).
thf(3961,plain,
( ( one_to_one @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3789]) ).
thf(3962,plain,
! [SV496: $i] :
( ( ( relation @ SV496 )
= $false )
| ( ( ~ ( ~ ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) )
| ~ ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3790]) ).
thf(3963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
!= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SX1 @ SX0 )
= ( sK61_SY6460 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK60_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK60_C @ SX1 @ SX0 ) @ ( sK61_SY6460 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3791]) ).
thf(3964,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)],[3792]) ).
thf(3965,plain,
! [SV497: $i] :
( ( ( relation @ SV497 )
= $false )
| ( ( ~ ( ~ ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) )
| ~ ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3966,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK39_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK39_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3794]) ).
thf(3967,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK38_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3795]) ).
thf(3968,plain,
! [SV498: $i] :
( ( ( ~ ( function @ SV498 ) )
= $true )
| ( ( ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3969,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ~ ( transitive @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ~ ( connected @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( well_ordering @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3797]) ).
thf(3970,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3798]) ).
thf(3971,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK18_SY6435 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK17_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK18_SY6435 @ SX0 ) ) ) )
| ~ ( ( ( sK17_B @ SX0 )
!= ( sK18_SY6435 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3799]) ).
thf(3972,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) )
| ( ( apply @ SX0 @ SX1 )
!= ( apply @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3800]) ).
thf(3973,plain,
! [SV499: $i] :
( ( ( relation @ SV499 )
= $false )
| ( ( ~ ( ~ ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) )
| ~ ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3974,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3802]) ).
thf(3975,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3803]) ).
thf(3976,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3804]) ).
thf(3977,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3805]) ).
thf(3978,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK67_C @ SX1 @ SX0 ) )
!= ( sK67_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3806]) ).
thf(3979,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3807]) ).
thf(3980,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3808]) ).
thf(3981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(3982,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3810]) ).
thf(3983,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3811]) ).
thf(3984,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3812]) ).
thf(3985,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3813]) ).
thf(3986,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(3987,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3815]) ).
thf(3988,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3816]) ).
thf(3989,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3817]) ).
thf(3990,plain,
! [SV423: $i,SV500: $i] :
( ( ( relation @ SV500 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV423 @ SV500 ) ) @ SV423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(3991,plain,
! [SV424: $i,SV501: $i] :
( ( ( relation @ SV501 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV424 @ SV501 ) @ SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(3992,plain,
! [SV425: $i,SV502: $i] :
( ( ( relation @ SV502 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV425 @ SV502 ) ) @ ( relation_rng @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(3993,plain,
! [SV426: $i,SV503: $i] :
( ( ( relation @ SV503 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV426 @ SV503 ) )
= ( set_intersection2 @ ( relation_rng @ SV503 ) @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3994,plain,
! [SV504: $i,SV427: $i,SV530: $i] :
( ( ( ~ ( relation @ SV530 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV427 @ SV530 ) @ SV504 )
= ( relation_rng_restriction @ SV427 @ ( relation_dom_restriction @ SV530 @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(3995,plain,
! [SV428: $i,SV505: $i] :
( ( ( relation @ SV505 )
= $false )
| ( ( subset @ ( relation_image @ SV505 @ SV428 ) @ ( relation_rng @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(3996,plain,
! [SV429: $i,SV506: $i] :
( ( ( ~ ( function @ SV506 ) )
= $true )
| ( ( ~ ( relation @ SV506 ) )
= $true )
| ( ( subset @ ( relation_image @ SV506 @ ( relation_inverse_image @ SV506 @ SV429 ) ) @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(3997,plain,
! [SV430: $i,SV507: $i] :
( ( ( relation @ SV507 )
= $false )
| ( ( ( relation_image @ SV507 @ SV430 )
= ( relation_image @ SV507 @ ( set_intersection2 @ ( relation_dom @ SV507 ) @ SV430 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3998,plain,
! [SV431: $i,SV508: $i] :
( ( ( relation @ SV508 )
= $false )
| ( ( ~ ( subset @ SV431 @ ( relation_dom @ SV508 ) )
| ( subset @ SV431 @ ( relation_inverse_image @ SV508 @ ( relation_image @ SV508 @ SV431 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3999,plain,
! [SV433: $i,SV509: $i] :
( ( ( ~ ( function @ SV509 ) )
= $true )
| ( ( ~ ( relation @ SV509 ) )
= $true )
| ( ( ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) )
| ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(4000,plain,
! [SV434: $i,SV534: $i] :
( ( ( ~ ( relation @ SV534 )
| ( ( relation_rng @ ( relation_composition @ SV434 @ SV534 ) )
= ( relation_image @ SV534 @ ( relation_rng @ SV434 ) ) ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4001,plain,
! [SV435: $i,SV510: $i] :
( ( ( relation @ SV510 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV510 @ SV435 ) @ ( relation_dom @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(4002,plain,
! [SV436: $i,SV511: $i] :
( ( ( relation @ SV511 )
= $false )
| ( ( ( SV436 = empty_set )
| ~ ( subset @ SV436 @ ( relation_rng @ SV511 ) )
| ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(4003,plain,
! [SV512: $i,SV437: $i,SV531: $i] :
( ( ( ~ ( relation @ SV531 ) )
= $true )
| ( ( ~ ( subset @ SV437 @ SV512 )
| ( subset @ ( relation_inverse_image @ SV531 @ SV437 ) @ ( relation_inverse_image @ SV531 @ SV512 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4004,plain,
! [SV439: $i,SV513: $i] :
( ( ( ~ ( function @ SV513 ) )
= $true )
| ( ( ~ ( relation @ SV513 ) )
= $true )
| ( ( ! [SY7199: $i] :
( ~ ( function @ SY7199 )
| ~ ( relation @ SY7199 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY7199 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SY7199 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SY7199 @ SV439 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(4005,plain,
! [SV440: $i,SV514: $i] :
( ( ( ~ ( function @ SV514 ) )
= $true )
| ( ( ~ ( relation @ SV514 ) )
= $true )
| ( ( ! [SY7200: $i] :
( ~ ( function @ SY7200 )
| ~ ( relation @ SY7200 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SY7200 ) @ SV440 )
= ( apply @ SY7200 @ ( apply @ SV514 @ SV440 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(4006,plain,
! [SV441: $i,SV535: $i] :
( ( ( ~ ( relation @ SV535 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SV535 ) ) @ ( relation_dom @ SV441 ) ) )
= $true )
| ( ( relation @ SV441 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4007,plain,
! [SV442: $i,SV536: $i] :
( ( ( ~ ( relation @ SV536 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SV536 ) ) @ ( relation_rng @ SV536 ) ) )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4008,plain,
! [SV443: $i,SV537: $i] :
( ( ( ~ ( relation @ SV537 )
| ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SV537 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SV537 ) )
= ( relation_dom @ SV443 ) ) )
= $true )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4009,plain,
! [SV444: $i,SV538: $i] :
( ( ( ~ ( relation @ SV538 )
| ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SV538 ) )
| ( ( relation_rng @ ( relation_composition @ SV538 @ SV444 ) )
= ( relation_rng @ SV444 ) ) )
= $true )
| ( ( relation @ SV444 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4010,plain,
! [SV445: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_B @ SV445 ) @ ( sK64_SY6461 @ SV445 ) ) @ SV445 )
= $true )
| ( ( SV445 = empty_set )
= $true )
| ( ( relation @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4011,plain,
! [SV446: $i] :
( ( ( function @ SV446 )
= $false )
| ( ( ~ ( relation @ SV446 ) )
= $true )
| ( ( ~ ( one_to_one @ SV446 )
| ( one_to_one @ ( function_inverse @ SV446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(4012,plain,
! [SV447: $i,SV515: $i,SV532: $i] :
( ( ( ~ ( function @ SV532 )
| ~ ( relation @ SV532 ) )
= $true )
| ( ( ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4013,plain,
! [SV448: $i,SV516: $i,SV533: $i] :
( ( ( ~ ( function @ SV533 )
| ~ ( relation @ SV533 ) )
= $true )
| ( ( ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(4014,plain,
! [SV449: $i,SV517: $i] :
( ( ( relation @ SV517 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV517 @ SV449 ) @ SV517 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4015,plain,
! [SV450: $i,SV518: $i] :
( ( ( relation @ SV518 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV518 @ SV450 ) )
= ( set_intersection2 @ ( relation_dom @ SV518 ) @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4016,plain,
! [SV451: $i,SV519: $i] :
( ( ( relation @ SV519 )
= $false )
| ( ( ( relation_dom_restriction @ SV519 @ SV451 )
= ( relation_composition @ ( identity_relation @ SV451 ) @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(4017,plain,
! [SV452: $i,SV520: $i] :
( ( ( relation @ SV520 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV520 @ SV452 ) ) @ ( relation_rng @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4018,plain,
! [SV455: $i] :
( ( ( function @ SV455 )
= $false )
| ( ( ~ ( relation @ SV455 ) )
= $true )
| ( ( ~ ( one_to_one @ SV455 )
| ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(4019,plain,
! [SV521: $i,SV457: $i] :
( ( ( ~ ( relation @ SV457 ) )
= $true )
| ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV457 @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4020,plain,
! [SV539: $i,SV459: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV459 @ SV539 ) )
= $true )
| ( ( relation @ SV459 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4021,plain,
! [SV460: $i,SV522: $i] :
( ( ( relation @ SV522 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV460 @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(4022,plain,
! [SV523: $i,SV461: $i] :
( ( ( ~ ( relation @ SV461 ) )
= $true )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV461 @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4023,plain,
! [SV524: $i,SV462: $i] :
( ( ( ~ ( relation @ SV462 ) )
= $true )
| ( ( ~ ( relation @ SV524 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV462 @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3856]) ).
thf(4024,plain,
! [SV525: $i,SV463: $i] :
( ( ( ~ ( relation @ SV463 ) )
= $true )
| ( ( ~ ( relation @ SV525 ) )
= $true )
| ( ( relation @ ( set_difference @ SV463 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(4025,plain,
! [SV464: $i] :
( ( ( relation @ SV464 )
= $false )
| ( ( empty @ SV464 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4026,plain,
! [SV465: $i] :
( ( ( relation @ SV465 )
= $false )
| ( ( empty @ SV465 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(4027,plain,
! [SV540: $i] :
( ( ~ ( relation @ SV540 )
| ~ ( is_transitive_in @ SV540 @ ( relation_field @ SV540 ) )
| ( transitive @ SV540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4028,plain,
! [SV541: $i] :
( ( ~ ( relation @ SV541 )
| ~ ( transitive @ SV541 )
| ( is_transitive_in @ SV541 @ ( relation_field @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(4029,plain,
! [SV467: $i] :
( ( ( ~ ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) )
| ~ ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(4030,plain,
! [SV542: $i] :
( ( ~ ( function @ SV542 )
| ~ ( relation @ SV542 )
| ! [SY7224: $i] : ( function @ ( relation_dom_restriction @ SV542 @ SY7224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4031,plain,
! [SV543: $i] :
( ( ~ ( function @ SV543 )
| ~ ( relation @ SV543 )
| ! [SY7225: $i] : ( relation @ ( relation_dom_restriction @ SV543 @ SY7225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4032,plain,
! [SV468: $i] :
( ( ( ~ ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) )
| ~ ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3866]) ).
thf(4033,plain,
! [SV469: $i] :
( ( ( function @ SV469 )
= $false )
| ( ( ~ ( relation @ SV469 ) )
= $true )
| ( ( ~ ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4034,plain,
! [SV470: $i] :
( ( ( function @ SV470 )
= $false )
| ( ( ~ ( relation @ SV470 ) )
= $true )
| ( ( ~ ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(4035,plain,
! [SV544: $i] :
( ( ~ ( ~ ! [SY7226: $i,SY7227: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SY7226 @ SY7227 ) )
| ~ ( in @ ( sK45_B @ SV544 ) @ SV544 ) )
| ( relation @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4036,plain,
! [SV545: $i] :
( ( ~ ( relation @ SV545 )
| ! [SY7228: $i] :
( ( SY7228
= ( ordered_pair @ ( sK43_C @ SY7228 @ SV545 ) @ ( sK44_SY6449 @ SY7228 @ SV545 ) ) )
| ~ ( in @ SY7228 @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(4037,plain,
! [SV546: $i] :
( ( ~ ( relation @ SV546 )
| ~ ( relation_empty_yielding @ SV546 )
| ! [SY7229: $i] : ( relation @ ( relation_dom_restriction @ SV546 @ SY7229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(4038,plain,
! [SV547: $i] :
( ( ~ ( relation @ SV547 )
| ~ ( relation_empty_yielding @ SV547 )
| ! [SY7230: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SY7230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3872]) ).
thf(4039,plain,
! [SV548: $i] :
( ( ~ ( empty @ SV548 )
| ( empty @ ( relation_rng @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4040,plain,
! [SV549: $i] :
( ( ~ ( empty @ SV549 )
| ( relation @ ( relation_rng @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4041,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4042,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4043,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ( function @ SV526 ) )
= $true )
| ( ( ~ ( relation @ SV526 ) )
= $true )
| ( ( ~ ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4044,plain,
! [SV550: $i] :
( ( ~ ( relation @ SV550 )
| ~ ( is_reflexive_in @ SV550 @ ( relation_field @ SV550 ) )
| ( reflexive @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(4045,plain,
! [SV551: $i] :
( ( ~ ( relation @ SV551 )
| ~ ( reflexive @ SV551 )
| ( is_reflexive_in @ SV551 @ ( relation_field @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(4046,plain,
! [SV473: $i] :
( ( ( ~ ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) )
| ~ ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(4047,plain,
! [SV474: $i] :
( ( ( ~ ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) )
| ~ ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(4048,plain,
! [SV552: $i] :
( ( ~ ( relation @ SV552 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
| ( connected @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4049,plain,
! [SV553: $i] :
( ( ~ ( relation @ SV553 )
| ~ ( connected @ SV553 )
| ! [SY7231: $i,SY7232: $i] :
( ( SY7231 = SY7232 )
| ~ ( in @ SY7231 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7232 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SY7231 @ SY7232 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7232 @ SY7231 ) @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4050,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
| ~ ( epsilon_connected @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4051,plain,
! [SV475: $i] :
( ( ! [SY7048: $i,SY7049: $i] :
( ~ ( relation @ SY7049 )
| ! [SY7050: $i] :
( ~ ( in @ SY7050 @ ( relation_rng @ SY7049 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7050 ) @ SY7049 )
| ~ ( in @ SY7050 @ SY7048 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SY7049 @ SY7048 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3889]) ).
thf(4052,plain,
! [SV475: $i] :
( ( ! [SY7051: $i,SY7052: $i] :
( ~ ( relation @ SY7052 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SY7052 @ SY7051 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ ( relation_rng @ SY7052 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) ) @ SY7052 ) )
| ~ ( in @ ( sK68_D @ SY7052 @ SY7051 @ SV475 ) @ SY7051 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3890]) ).
thf(4053,plain,
! [SV476: $i] :
( ( ! [SY7053: $i,SY7054: $i] :
( ~ ( relation @ SY7054 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7053 ) @ SY7054 )
| ( in @ SV476 @ ( relation_field @ SY7054 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3891]) ).
thf(4054,plain,
! [SV476: $i] :
( ( ! [SY7055: $i,SY7056: $i] :
( ~ ( relation @ SY7056 )
| ~ ( in @ ( ordered_pair @ SV476 @ SY7055 ) @ SY7056 )
| ( in @ SY7055 @ ( relation_field @ SY7056 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3892]) ).
thf(4055,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(4056,plain,
! [SV554: $i] :
( ( ~ ( empty @ SV554 )
| ~ ( relation @ SV554 )
| ~ ( function @ SV554 )
| ( one_to_one @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4057,plain,
! [SV555: $i] :
( ( ! [SY7233: $i] :
( ~ ( function @ SV555 )
| ~ ( relation @ SV555 )
| ~ ( relation @ SY7233 )
| ~ ( function @ SY7233 )
| ( function @ ( relation_composition @ SV555 @ SY7233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4058,plain,
! [SV556: $i] :
( ( ! [SY7234: $i] :
( ~ ( function @ SV556 )
| ~ ( relation @ SV556 )
| ~ ( relation @ SY7234 )
| ~ ( function @ SY7234 )
| ( relation @ ( relation_composition @ SV556 @ SY7234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4059,plain,
! [SV477: $i] :
( ( ! [SY7057: $i,SY7058: $i] :
( ~ ( relation @ SY7058 )
| ~ ( in @ SV477 @ SY7057 )
| ~ ( in @ SV477 @ ( relation_rng @ SY7058 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7057 @ SY7058 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3897]) ).
thf(4060,plain,
! [SV477: $i] :
( ( ~ ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) )
| ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3898]) ).
thf(4061,plain,
! [SV478: $i] :
( ( ( ~ ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) )
| ~ ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(4062,plain,
! [SV557: $i] :
( ( ! [SY7235: $i] :
( ~ ( function @ SY7235 )
| ~ ( relation @ SY7235 )
| ~ ( in @ SV557 @ ( relation_rng @ SY7235 ) )
| ~ ( one_to_one @ SY7235 )
| ( SV557
= ( apply @ SY7235 @ ( apply @ ( function_inverse @ SY7235 ) @ SV557 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4063,plain,
! [SV558: $i] :
( ( ! [SY7236: $i] :
( ~ ( function @ SY7236 )
| ~ ( relation @ SY7236 )
| ~ ( in @ SV558 @ ( relation_rng @ SY7236 ) )
| ~ ( one_to_one @ SY7236 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SY7236 ) @ SY7236 ) @ SV558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4064,plain,
! [SV479: $i] :
( ( ( ~ ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) )
| ~ ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4065,plain,
! [SV559: $i] :
( ( ~ ( empty @ SV559 )
| ( empty @ ( relation_inverse @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4066,plain,
! [SV560: $i] :
( ( ~ ( empty @ SV560 )
| ( relation @ ( relation_inverse @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4067,plain,
! [SV480: $i,SV527: $i] :
( ( ( relation @ SV527 )
= $false )
| ( ( ~ ( ~ ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
| ~ ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4068,plain,
! [SV561: $i] :
( ( ~ ( relation @ SV561 )
| ( ( relation_dom @ SV561 )
!= empty_set )
| ( SV561 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3906]) ).
thf(4069,plain,
! [SV562: $i] :
( ( ~ ( relation @ SV562 )
| ( ( relation_rng @ SV562 )
!= empty_set )
| ( SV562 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3907]) ).
thf(4070,plain,
! [SV481: $i] :
( ( ( ~ ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) )
| ~ ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4071,plain,
! [SV482: $i] :
( ( ( function @ SV482 )
= $false )
| ( ( ~ ( relation @ SV482 ) )
= $true )
| ( ( ~ ( one_to_one @ SV482 )
| ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4072,plain,
! [SV563: $i] :
( ( ~ ( function @ SV563 )
| ~ ( relation @ SV563 )
| ~ ( one_to_one @ SV563 )
| ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4073,plain,
! [SV564: $i] :
( ( ~ ( function @ SV564 )
| ~ ( relation @ SV564 )
| ~ ( one_to_one @ SV564 )
| ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4074,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ! [SY7215: $i,SY7216: $i] :
( ~ ( relation @ SY7216 )
| ~ ( in @ SV483 @ SY7215 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7216 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7215 ) @ SY7216 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4075,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ~ ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) )
| ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4076,plain,
! [SV565: $i] :
( ( ~ ( function @ SV565 )
| ~ ( relation @ SV565 )
| ( function @ ( function_inverse @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4077,plain,
! [SV566: $i] :
( ( ~ ( function @ SV566 )
| ~ ( relation @ SV566 )
| ( relation @ ( function_inverse @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4078,plain,
! [SV484: $i] :
( ( ! [SY7112: $i,SY7113: $i] :
( ~ ( function @ SY7113 )
| ~ ( relation @ SY7113 )
| ( SY7112
!= ( apply @ SY7113 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SY7113 ) )
| ( in @ ( ordered_pair @ SV484 @ SY7112 ) @ SY7113 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3917]) ).
thf(4079,plain,
! [SV484: $i] :
( ( ~ ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) )
| ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3918]) ).
thf(4080,plain,
! [SV485: $i] :
( ( ! [SY7118: $i,SY7119: $i] :
( ~ ( relation @ SY7119 )
| ~ ( in @ SV485 @ SY7118 )
| ~ ( in @ SV485 @ ( relation_dom @ SY7119 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7119 @ SY7118 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3919]) ).
thf(4081,plain,
! [SV485: $i] :
( ( ~ ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) )
| ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3920]) ).
thf(4082,plain,
! [SV486: $i] :
( ( ( ~ ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) )
| ~ ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(4083,plain,
! [SV567: $i] :
( ( ~ ( relation @ SV567 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ( transitive @ SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4084,plain,
! [SV568: $i] :
( ( ~ ( relation @ SV568 )
| ~ ( transitive @ SV568 )
| ! [SY7237: $i,SY7238: $i,SY7239: $i] :
( ~ ( in @ ( ordered_pair @ SY7237 @ SY7238 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7238 @ SY7239 ) @ SV568 )
| ( in @ ( ordered_pair @ SY7237 @ SY7239 ) @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4085,plain,
! [SV487: $i] :
( ( ! [SY7127: $i,SY7128: $i] :
( ~ ( relation @ SY7128 )
| ! [SY7129: $i] :
( ~ ( in @ SY7129 @ ( relation_dom @ SY7128 ) )
| ~ ( in @ ( ordered_pair @ SY7129 @ SV487 ) @ SY7128 )
| ~ ( in @ SY7129 @ SY7127 ) )
| ( in @ SV487 @ ( relation_image @ SY7128 @ SY7127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3924]) ).
thf(4086,plain,
! [SV487: $i] :
( ( ! [SY7130: $i,SY7131: $i] :
( ~ ( relation @ SY7131 )
| ~ ( in @ SV487 @ ( relation_image @ SY7131 @ SY7130 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ ( relation_dom @ SY7131 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SV487 ) @ SY7131 ) )
| ~ ( in @ ( sK69_D @ SY7131 @ SY7130 @ SV487 ) @ SY7130 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(4087,plain,
! [SV488: $i] :
( ( ( ~ ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) )
| ~ ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3926]) ).
thf(4088,plain,
! [SV489: $i] :
( ( ( ~ ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) )
| ~ ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4089,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
| ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(4090,plain,
! [SV569: $i] :
( ( ~ ( relation @ SV569 )
| ~ ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
| ( reflexive @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4091,plain,
! [SV570: $i] :
( ( ~ ( relation @ SV570 )
| ~ ( reflexive @ SV570 )
| ! [SY7240: $i] :
( ~ ( in @ SY7240 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SY7240 @ SY7240 ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4092,plain,
! [SV490: $i,SV529: $i] :
( ( ( ~ ( function @ SV529 ) )
= $true )
| ( ( ~ ( relation @ SV529 ) )
= $true )
| ( ( ~ ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3932]) ).
thf(4093,plain,
( ( ~ ( relation @ sK2_A )
| ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(4094,plain,
( ( well_orders @ sK1_A @ ( relation_field @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3940]) ).
thf(4095,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4096,plain,
! [SV571: $i] :
( ( ~ ( relation @ SV571 )
| ~ ( is_well_founded_in @ SV571 @ ( relation_field @ SV571 ) )
| ( well_founded_relation @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4097,plain,
! [SV572: $i] :
( ( ~ ( relation @ SV572 )
| ~ ( well_founded_relation @ SV572 )
| ( is_well_founded_in @ SV572 @ ( relation_field @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4098,plain,
! [SV491: $i] :
( ( ( ~ ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) )
| ~ ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4099,plain,
! [SV573: $i] :
( ( ~ ( relation @ SV573 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
| ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) )
| ( antisymmetric @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3946]) ).
thf(4100,plain,
! [SV574: $i] :
( ( ~ ( relation @ SV574 )
| ~ ( antisymmetric @ SV574 )
| ! [SY7241: $i,SY7242: $i] :
( ~ ( in @ ( ordered_pair @ SY7241 @ SY7242 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7242 @ SY7241 ) @ SV574 )
| ( SY7241 = SY7242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4101,plain,
! [SV492: $i] :
( ( ! [SY7146: $i,SY7147: $i] :
( ~ ( function @ SY7147 )
| ~ ( relation @ SY7147 )
| ~ ( in @ SY7146 @ ( relation_dom @ SY7147 ) )
| ~ ( in @ SY7146 @ SV492 )
| ( in @ SY7146 @ ( relation_dom @ ( relation_dom_restriction @ SY7147 @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3948]) ).
thf(4102,plain,
! [SV492: $i] :
( ( ~ ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) )
| ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3949]) ).
thf(4103,plain,
( ( ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4104,plain,
! [SV575: $i] :
( ( ~ ( relation @ SV575 )
| ( ( relation_dom @ SV575 )
!= empty_set )
| ( ( relation_rng @ SV575 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4105,plain,
! [SV576: $i] :
( ( ~ ( relation @ SV576 )
| ( ( relation_rng @ SV576 )
!= empty_set )
| ( ( relation_dom @ SV576 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4106,plain,
! [SV493: $i] :
( ( ( function @ SV493 )
= $false )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4107,plain,
! [SV494: $i,SV577: $i] :
( ( ( ~ ( relation @ SV577 )
| ~ ( ~ ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) )
| ~ ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4108,plain,
! [SV495: $i] :
( ( ! [SY7167: $i,SY7168: $i] :
( ~ ( relation @ SY7168 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7167 ) @ SY7168 )
| ( in @ SV495 @ ( relation_dom @ SY7168 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3956]) ).
thf(4109,plain,
! [SV495: $i] :
( ( ! [SY7169: $i,SY7170: $i] :
( ~ ( relation @ SY7170 )
| ~ ( in @ ( ordered_pair @ SV495 @ SY7169 ) @ SY7170 )
| ( in @ SY7169 @ ( relation_rng @ SY7170 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3957]) ).
thf(4110,plain,
! [SV578: $i] :
( ( ! [SY7251: $i] :
( ~ ( empty @ SV578 )
| ~ ( relation @ SY7251 )
| ( empty @ ( relation_composition @ SY7251 @ SV578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4111,plain,
! [SV579: $i] :
( ( ! [SY7252: $i] :
( ~ ( empty @ SV579 )
| ~ ( relation @ SY7252 )
| ( relation @ ( relation_composition @ SY7252 @ SV579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4112,plain,
( ( ~ ( function @ sK4_A )
| ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4113,plain,
! [SV496: $i] :
( ( ( ~ ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) )
| ~ ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4114,plain,
! [SV580: $i] :
( ( ! [SY7253: $i] :
( ~ ( relation @ SY7253 )
| ~ ( ~ ( ( ( sK60_C @ SY7253 @ SV580 )
!= ( sK61_SY6460 @ SY7253 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SY7253 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SY7253 @ SV580 ) @ ( sK61_SY6460 @ SY7253 @ SV580 ) ) @ SY7253 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SY7253 @ SV580 )
= ( sK61_SY6460 @ SY7253 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SY7253 @ SV580 ) @ ( sK61_SY6460 @ SY7253 @ SV580 ) ) @ SY7253 ) )
| ~ ( ( in @ ( sK60_C @ SY7253 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SY7253 @ SV580 ) @ ( sK61_SY6460 @ SY7253 @ SV580 ) ) @ SY7253 ) ) ) )
| ( SY7253
= ( identity_relation @ SV580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4115,plain,
! [SV581: $i] :
( ( ! [SY7254: $i] :
( ~ ( relation @ SY7254 )
| ( SY7254
!= ( identity_relation @ SV581 ) )
| ~ ( ~ ! [SY7255: $i,SY7256: $i] :
( ( SY7255 != SY7256 )
| ~ ( in @ SY7255 @ SV581 )
| ( in @ ( ordered_pair @ SY7255 @ SY7256 ) @ SY7254 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY7254 )
| ( SX2 = SX3 ) )
| ~ ! [SY7259: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY7259 @ SX3 ) @ SY7254 )
| ( in @ SY7259 @ SV581 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4116,plain,
! [SV497: $i] :
( ( ( ~ ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) )
| ~ ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4117,plain,
! [SV582: $i] :
( ( ~ ( relation @ SV582 )
| ~ ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
| ( well_founded_relation @ SV582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3966]) ).
thf(4118,plain,
! [SV583: $i] :
( ( ~ ( relation @ SV583 )
| ~ ( well_founded_relation @ SV583 )
| ! [SY7262: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SY7262 @ SV583 ) ) @ SY7262 )
| ~ ( in @ ( sK38_C @ SY7262 @ SV583 ) @ SY7262 ) )
| ( SY7262 = empty_set )
| ~ ( subset @ SY7262 @ ( relation_field @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4119,plain,
! [SV498: $i] :
( ( ( function @ SV498 )
= $false )
| ( ( ~ ( relation @ SV498 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3968]) ).
thf(4120,plain,
! [SV584: $i] :
( ( ~ ( relation @ SV584 )
| ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 )
| ~ ( connected @ SV584 )
| ~ ( well_founded_relation @ SV584 )
| ( well_ordering @ SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3969]) ).
thf(4121,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4122,plain,
! [SV585: $i] :
( ( ~ ( function @ SV585 )
| ~ ( relation @ SV585 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
| ( one_to_one @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4123,plain,
! [SV586: $i] :
( ( ~ ( function @ SV586 )
| ~ ( relation @ SV586 )
| ~ ( one_to_one @ SV586 )
| ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4124,plain,
! [SV499: $i] :
( ( ( ~ ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) )
| ~ ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4125,plain,
! [SV587: $i] :
( ( ~ ( relation @ SV587 )
| ( ( relation_rng @ SV587 )
= ( relation_dom @ ( relation_inverse @ SV587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4126,plain,
! [SV588: $i] :
( ( ~ ( relation @ SV588 )
| ( ( relation_dom @ SV588 )
= ( relation_rng @ ( relation_inverse @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4127,plain,
! [SV589: $i] :
( ( ~ ( relation @ SV589 )
| ~ ( antisymmetric @ SV589 )
| ( is_antisymmetric_in @ SV589 @ ( relation_field @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4128,plain,
! [SV590: $i] :
( ( ~ ( relation @ SV590 )
| ~ ( is_antisymmetric_in @ SV590 @ ( relation_field @ SV590 ) )
| ( antisymmetric @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4129,plain,
! [SV591: $i] :
( ( ! [SY7265: $i] :
( ~ ( function @ SY7265 )
| ~ ( relation @ SY7265 )
| ~ ( ~ ( in @ ( sK67_C @ SY7265 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SY7265 @ ( sK67_C @ SY7265 @ SV591 ) )
!= ( sK67_C @ SY7265 @ SV591 ) ) ) )
| ( ( relation_dom @ SY7265 )
!= SV591 )
| ( SY7265
= ( identity_relation @ SV591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4130,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4131,plain,
! [SV592: $i] :
( ( ! [SY7266: $i] :
( ~ ( empty @ SV592 )
| ~ ( relation @ SY7266 )
| ( empty @ ( relation_composition @ SV592 @ SY7266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4132,plain,
! [SV593: $i] :
( ( ! [SY7267: $i] :
( ~ ( empty @ SV593 )
| ~ ( relation @ SY7267 )
| ( relation @ ( relation_composition @ SV593 @ SY7267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4133,plain,
! [SV594: $i] :
( ( ~ ( relation @ SV594 )
| ~ ( connected @ SV594 )
| ( is_connected_in @ SV594 @ ( relation_field @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4134,plain,
! [SV595: $i] :
( ( ~ ( relation @ SV595 )
| ~ ( is_connected_in @ SV595 @ ( relation_field @ SV595 ) )
| ( connected @ SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4135,plain,
! [SV596: $i] :
( ( ~ ( function @ SV596 )
| ~ ( relation @ SV596 )
| ~ ( one_to_one @ SV596 )
| ( function @ ( relation_inverse @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3984]) ).
thf(4136,plain,
! [SV597: $i] :
( ( ~ ( function @ SV597 )
| ~ ( relation @ SV597 )
| ~ ( one_to_one @ SV597 )
| ( relation @ ( relation_inverse @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4137,plain,
! [SV598: $i] :
( ( function @ ( identity_relation @ SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4138,plain,
! [SV599: $i] :
( ( relation @ ( identity_relation @ SV599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4139,plain,
! [SV600: $i] :
( ( ~ ( empty @ SV600 )
| ( empty @ ( relation_dom @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4140,plain,
! [SV601: $i] :
( ( ~ ( empty @ SV601 )
| ( relation @ ( relation_dom @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4141,plain,
! [SV504: $i,SV427: $i,SV530: $i] :
( ( ( relation @ SV530 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV427 @ SV530 ) @ SV504 )
= ( relation_rng_restriction @ SV427 @ ( relation_dom_restriction @ SV530 @ SV504 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4142,plain,
! [SV429: $i,SV506: $i] :
( ( ( function @ SV506 )
= $false )
| ( ( ~ ( relation @ SV506 ) )
= $true )
| ( ( subset @ ( relation_image @ SV506 @ ( relation_inverse_image @ SV506 @ SV429 ) ) @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4143,plain,
! [SV508: $i,SV431: $i] :
( ( ( ~ ( subset @ SV431 @ ( relation_dom @ SV508 ) ) )
= $true )
| ( ( subset @ SV431 @ ( relation_inverse_image @ SV508 @ ( relation_image @ SV508 @ SV431 ) ) )
= $true )
| ( ( relation @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3998]) ).
thf(4144,plain,
! [SV433: $i,SV509: $i] :
( ( ( function @ SV509 )
= $false )
| ( ( ~ ( relation @ SV509 ) )
= $true )
| ( ( ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) )
| ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4145,plain,
! [SV434: $i,SV534: $i] :
( ( ( ~ ( relation @ SV534 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV434 @ SV534 ) )
= ( relation_image @ SV534 @ ( relation_rng @ SV434 ) ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4000]) ).
thf(4146,plain,
! [SV511: $i,SV436: $i] :
( ( ( ( SV436 = empty_set )
| ~ ( subset @ SV436 @ ( relation_rng @ SV511 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true )
| ( ( relation @ SV511 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4147,plain,
! [SV512: $i,SV437: $i,SV531: $i] :
( ( ( relation @ SV531 )
= $false )
| ( ( ~ ( subset @ SV437 @ SV512 )
| ( subset @ ( relation_inverse_image @ SV531 @ SV437 ) @ ( relation_inverse_image @ SV531 @ SV512 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4148,plain,
! [SV439: $i,SV513: $i] :
( ( ( function @ SV513 )
= $false )
| ( ( ~ ( relation @ SV513 ) )
= $true )
| ( ( ! [SY7199: $i] :
( ~ ( function @ SY7199 )
| ~ ( relation @ SY7199 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY7199 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SY7199 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SY7199 @ SV439 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4149,plain,
! [SV440: $i,SV514: $i] :
( ( ( function @ SV514 )
= $false )
| ( ( ~ ( relation @ SV514 ) )
= $true )
| ( ( ! [SY7200: $i] :
( ~ ( function @ SY7200 )
| ~ ( relation @ SY7200 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SY7200 ) @ SV440 )
= ( apply @ SY7200 @ ( apply @ SV514 @ SV440 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4150,plain,
! [SV441: $i,SV535: $i] :
( ( ( ~ ( relation @ SV535 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SV535 ) ) @ ( relation_dom @ SV441 ) )
= $true )
| ( ( relation @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4151,plain,
! [SV442: $i,SV536: $i] :
( ( ( ~ ( relation @ SV536 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SV536 ) ) @ ( relation_rng @ SV536 ) )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4152,plain,
! [SV443: $i,SV537: $i] :
( ( ( ~ ( relation @ SV537 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SV537 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SV537 ) )
= ( relation_dom @ SV443 ) ) )
= $true )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4153,plain,
! [SV444: $i,SV538: $i] :
( ( ( ~ ( relation @ SV538 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SV538 ) )
| ( ( relation_rng @ ( relation_composition @ SV538 @ SV444 ) )
= ( relation_rng @ SV444 ) ) )
= $true )
| ( ( relation @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4154,plain,
! [SV446: $i] :
( ( ( relation @ SV446 )
= $false )
| ( ( function @ SV446 )
= $false )
| ( ( ~ ( one_to_one @ SV446 )
| ( one_to_one @ ( function_inverse @ SV446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4155,plain,
! [SV447: $i,SV515: $i,SV532: $i] :
( ( ( ~ ( function @ SV532 ) )
= $true )
| ( ( ~ ( relation @ SV532 ) )
= $true )
| ( ( ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4156,plain,
! [SV448: $i,SV516: $i,SV533: $i] :
( ( ( ~ ( function @ SV533 ) )
= $true )
| ( ( ~ ( relation @ SV533 ) )
= $true )
| ( ( ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4157,plain,
! [SV455: $i] :
( ( ( relation @ SV455 )
= $false )
| ( ( function @ SV455 )
= $false )
| ( ( ~ ( one_to_one @ SV455 )
| ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4158,plain,
! [SV521: $i,SV457: $i] :
( ( ( relation @ SV457 )
= $false )
| ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV457 @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4159,plain,
! [SV523: $i,SV461: $i] :
( ( ( relation @ SV461 )
= $false )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV461 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4160,plain,
! [SV524: $i,SV462: $i] :
( ( ( relation @ SV462 )
= $false )
| ( ( ~ ( relation @ SV524 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV462 @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4023]) ).
thf(4161,plain,
! [SV525: $i,SV463: $i] :
( ( ( relation @ SV463 )
= $false )
| ( ( ~ ( relation @ SV525 ) )
= $true )
| ( ( relation @ ( set_difference @ SV463 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4162,plain,
! [SV464: $i] :
( ( ( empty @ ( relation_dom @ SV464 ) )
= $false )
| ( ( empty @ SV464 )
= $true )
| ( ( relation @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4163,plain,
! [SV465: $i] :
( ( ( empty @ ( relation_rng @ SV465 ) )
= $false )
| ( ( empty @ SV465 )
= $true )
| ( ( relation @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4164,plain,
! [SV540: $i] :
( ( ( ~ ( relation @ SV540 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV540 @ ( relation_field @ SV540 ) )
| ( transitive @ SV540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4165,plain,
! [SV541: $i] :
( ( ( ~ ( relation @ SV541 ) )
= $true )
| ( ( ~ ( transitive @ SV541 )
| ( is_transitive_in @ SV541 @ ( relation_field @ SV541 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4166,plain,
! [SV467: $i] :
( ( ( ~ ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4167,plain,
! [SV467: $i] :
( ( ( ~ ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4168,plain,
! [SV542: $i] :
( ( ( ~ ( function @ SV542 )
| ~ ( relation @ SV542 ) )
= $true )
| ( ( ! [SY7224: $i] : ( function @ ( relation_dom_restriction @ SV542 @ SY7224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4169,plain,
! [SV543: $i] :
( ( ( ~ ( function @ SV543 )
| ~ ( relation @ SV543 ) )
= $true )
| ( ( ! [SY7225: $i] : ( relation @ ( relation_dom_restriction @ SV543 @ SY7225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4170,plain,
! [SV468: $i] :
( ( ( ~ ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) ) )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4032]) ).
thf(4171,plain,
! [SV468: $i] :
( ( ( ~ ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4032]) ).
thf(4172,plain,
! [SV469: $i] :
( ( ( relation @ SV469 )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( ~ ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4173,plain,
! [SV470: $i] :
( ( ( relation @ SV470 )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( ~ ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4174,plain,
! [SV544: $i] :
( ( ( ~ ( ~ ! [SY7226: $i,SY7227: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SY7226 @ SY7227 ) )
| ~ ( in @ ( sK45_B @ SV544 ) @ SV544 ) ) )
= $true )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4175,plain,
! [SV545: $i] :
( ( ( ~ ( relation @ SV545 ) )
= $true )
| ( ( ! [SY7228: $i] :
( ( SY7228
= ( ordered_pair @ ( sK43_C @ SY7228 @ SV545 ) @ ( sK44_SY6449 @ SY7228 @ SV545 ) ) )
| ~ ( in @ SY7228 @ SV545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4036]) ).
thf(4176,plain,
! [SV546: $i] :
( ( ( ~ ( relation @ SV546 )
| ~ ( relation_empty_yielding @ SV546 ) )
= $true )
| ( ( ! [SY7229: $i] : ( relation @ ( relation_dom_restriction @ SV546 @ SY7229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4037]) ).
thf(4177,plain,
! [SV547: $i] :
( ( ( ~ ( relation @ SV547 )
| ~ ( relation_empty_yielding @ SV547 ) )
= $true )
| ( ( ! [SY7230: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SY7230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4178,plain,
! [SV548: $i] :
( ( ( ~ ( empty @ SV548 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4039]) ).
thf(4179,plain,
! [SV549: $i] :
( ( ( ~ ( empty @ SV549 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4180,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4041]) ).
thf(4181,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4041]) ).
thf(4182,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4183,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4184,plain,
! [SV472: $i,SV526: $i] :
( ( ( function @ SV526 )
= $false )
| ( ( ~ ( relation @ SV526 ) )
= $true )
| ( ( ~ ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4185,plain,
! [SV550: $i] :
( ( ( ~ ( relation @ SV550 ) )
= $true )
| ( ( ~ ( is_reflexive_in @ SV550 @ ( relation_field @ SV550 ) )
| ( reflexive @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4044]) ).
thf(4186,plain,
! [SV551: $i] :
( ( ( ~ ( relation @ SV551 ) )
= $true )
| ( ( ~ ( reflexive @ SV551 )
| ( is_reflexive_in @ SV551 @ ( relation_field @ SV551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4045]) ).
thf(4187,plain,
! [SV473: $i] :
( ( ( ~ ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4046]) ).
thf(4188,plain,
! [SV473: $i] :
( ( ( ~ ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4046]) ).
thf(4189,plain,
! [SV474: $i] :
( ( ( ~ ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) ) )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4047]) ).
thf(4190,plain,
! [SV474: $i] :
( ( ( ~ ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4047]) ).
thf(4191,plain,
! [SV552: $i] :
( ( ( ~ ( relation @ SV552 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
| ( connected @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4192,plain,
! [SV553: $i] :
( ( ( ~ ( relation @ SV553 ) )
= $true )
| ( ( ~ ( connected @ SV553 )
| ! [SY7231: $i,SY7232: $i] :
( ( SY7231 = SY7232 )
| ~ ( in @ SY7231 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7232 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SY7231 @ SY7232 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7232 @ SY7231 ) @ SV553 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4049]) ).
thf(4193,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4194,plain,
( ( ~ ( epsilon_connected @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4195,plain,
! [SV602: $i,SV475: $i] :
( ( ! [SY7268: $i] :
( ~ ( relation @ SY7268 )
| ! [SY7269: $i] :
( ~ ( in @ SY7269 @ ( relation_rng @ SY7268 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7269 ) @ SY7268 )
| ~ ( in @ SY7269 @ SV602 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SY7268 @ SV602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4051]) ).
thf(4196,plain,
! [SV603: $i,SV475: $i] :
( ( ! [SY7270: $i] :
( ~ ( relation @ SY7270 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SY7270 @ SV603 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SY7270 @ SV603 @ SV475 ) @ ( relation_rng @ SY7270 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SY7270 @ SV603 @ SV475 ) ) @ SY7270 ) )
| ~ ( in @ ( sK68_D @ SY7270 @ SV603 @ SV475 ) @ SV603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4052]) ).
thf(4197,plain,
! [SV604: $i,SV476: $i] :
( ( ! [SY7271: $i] :
( ~ ( relation @ SY7271 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SY7271 )
| ( in @ SV476 @ ( relation_field @ SY7271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4198,plain,
! [SV605: $i,SV476: $i] :
( ( ! [SY7272: $i] :
( ~ ( relation @ SY7272 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SY7272 )
| ( in @ SV605 @ ( relation_field @ SY7272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4199,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4055]) ).
thf(4200,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4055]) ).
thf(4201,plain,
! [SV554: $i] :
( ( ( ~ ( empty @ SV554 )
| ~ ( relation @ SV554 )
| ~ ( function @ SV554 ) )
= $true )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4202,plain,
! [SV606: $i,SV555: $i] :
( ( ~ ( function @ SV555 )
| ~ ( relation @ SV555 )
| ~ ( relation @ SV606 )
| ~ ( function @ SV606 )
| ( function @ ( relation_composition @ SV555 @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4057]) ).
thf(4203,plain,
! [SV607: $i,SV556: $i] :
( ( ~ ( function @ SV556 )
| ~ ( relation @ SV556 )
| ~ ( relation @ SV607 )
| ~ ( function @ SV607 )
| ( relation @ ( relation_composition @ SV556 @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4204,plain,
! [SV608: $i,SV477: $i] :
( ( ! [SY7273: $i] :
( ~ ( relation @ SY7273 )
| ~ ( in @ SV477 @ SV608 )
| ~ ( in @ SV477 @ ( relation_rng @ SY7273 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SY7273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4205,plain,
! [SV477: $i] :
( ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) )
| ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4206,plain,
! [SV478: $i] :
( ( ( ~ ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) ) )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4061]) ).
thf(4207,plain,
! [SV478: $i] :
( ( ( ~ ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4061]) ).
thf(4208,plain,
! [SV557: $i,SV609: $i] :
( ( ~ ( function @ SV609 )
| ~ ( relation @ SV609 )
| ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 )
| ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4209,plain,
! [SV558: $i,SV610: $i] :
( ( ~ ( function @ SV610 )
| ~ ( relation @ SV610 )
| ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4210,plain,
! [SV479: $i] :
( ( ( ~ ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4064]) ).
thf(4211,plain,
! [SV479: $i] :
( ( ( ~ ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4064]) ).
thf(4212,plain,
! [SV559: $i] :
( ( ( ~ ( empty @ SV559 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4065]) ).
thf(4213,plain,
! [SV560: $i] :
( ( ( ~ ( empty @ SV560 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV560 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4214,plain,
! [SV480: $i,SV527: $i] :
( ( ( ~ ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
| ~ ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4215,plain,
! [SV561: $i] :
( ( ( ~ ( relation @ SV561 ) )
= $true )
| ( ( ( ( relation_dom @ SV561 )
!= empty_set )
| ( SV561 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4216,plain,
! [SV562: $i] :
( ( ( ~ ( relation @ SV562 ) )
= $true )
| ( ( ( ( relation_rng @ SV562 )
!= empty_set )
| ( SV562 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4217,plain,
! [SV481: $i] :
( ( ( ~ ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4218,plain,
! [SV481: $i] :
( ( ( ~ ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4219,plain,
! [SV482: $i] :
( ( ( relation @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( ~ ( one_to_one @ SV482 )
| ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4220,plain,
! [SV563: $i] :
( ( ( ~ ( function @ SV563 )
| ~ ( relation @ SV563 ) )
= $true )
| ( ( ~ ( one_to_one @ SV563 )
| ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4221,plain,
! [SV564: $i] :
( ( ( ~ ( function @ SV564 )
| ~ ( relation @ SV564 ) )
= $true )
| ( ( ~ ( one_to_one @ SV564 )
| ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4222,plain,
! [SV528: $i,SV483: $i] :
( ( ! [SY7215: $i,SY7216: $i] :
( ~ ( relation @ SY7216 )
| ~ ( in @ SV483 @ SY7215 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7216 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7215 ) @ SY7216 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4074]) ).
thf(4223,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) )
| ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4075]) ).
thf(4224,plain,
! [SV565: $i] :
( ( ( ~ ( function @ SV565 )
| ~ ( relation @ SV565 ) )
= $true )
| ( ( function @ ( function_inverse @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4225,plain,
! [SV566: $i] :
( ( ( ~ ( function @ SV566 )
| ~ ( relation @ SV566 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4226,plain,
! [SV484: $i,SV611: $i] :
( ( ! [SY7274: $i] :
( ~ ( function @ SY7274 )
| ~ ( relation @ SY7274 )
| ( SV611
!= ( apply @ SY7274 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SY7274 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SY7274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4227,plain,
! [SV484: $i] :
( ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) )
| ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4228,plain,
! [SV612: $i,SV485: $i] :
( ( ! [SY7275: $i] :
( ~ ( relation @ SY7275 )
| ~ ( in @ SV485 @ SV612 )
| ~ ( in @ SV485 @ ( relation_dom @ SY7275 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7275 @ SV612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4229,plain,
! [SV485: $i] :
( ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) )
| ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4230,plain,
! [SV486: $i] :
( ( ( ~ ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) ) )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4231,plain,
! [SV486: $i] :
( ( ( ~ ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4232,plain,
! [SV567: $i] :
( ( ( ~ ( relation @ SV567 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ( transitive @ SV567 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4083]) ).
thf(4233,plain,
! [SV568: $i] :
( ( ( ~ ( relation @ SV568 ) )
= $true )
| ( ( ~ ( transitive @ SV568 )
| ! [SY7237: $i,SY7238: $i,SY7239: $i] :
( ~ ( in @ ( ordered_pair @ SY7237 @ SY7238 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7238 @ SY7239 ) @ SV568 )
| ( in @ ( ordered_pair @ SY7237 @ SY7239 ) @ SV568 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4234,plain,
! [SV613: $i,SV487: $i] :
( ( ! [SY7276: $i] :
( ~ ( relation @ SY7276 )
| ! [SY7277: $i] :
( ~ ( in @ SY7277 @ ( relation_dom @ SY7276 ) )
| ~ ( in @ ( ordered_pair @ SY7277 @ SV487 ) @ SY7276 )
| ~ ( in @ SY7277 @ SV613 ) )
| ( in @ SV487 @ ( relation_image @ SY7276 @ SV613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4235,plain,
! [SV614: $i,SV487: $i] :
( ( ! [SY7278: $i] :
( ~ ( relation @ SY7278 )
| ~ ( in @ SV487 @ ( relation_image @ SY7278 @ SV614 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SY7278 @ SV614 @ SV487 ) @ ( relation_dom @ SY7278 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SY7278 @ SV614 @ SV487 ) @ SV487 ) @ SY7278 ) )
| ~ ( in @ ( sK69_D @ SY7278 @ SV614 @ SV487 ) @ SV614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4086]) ).
thf(4236,plain,
! [SV488: $i] :
( ( ( ~ ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4237,plain,
! [SV488: $i] :
( ( ( ~ ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4238,plain,
! [SV489: $i] :
( ( ( ~ ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) ) )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4088]) ).
thf(4239,plain,
! [SV489: $i] :
( ( ( ~ ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4088]) ).
thf(4240,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4089]) ).
thf(4241,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4089]) ).
thf(4242,plain,
! [SV569: $i] :
( ( ( ~ ( relation @ SV569 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
| ( reflexive @ SV569 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4243,plain,
! [SV570: $i] :
( ( ( ~ ( relation @ SV570 ) )
= $true )
| ( ( ~ ( reflexive @ SV570 )
| ! [SY7240: $i] :
( ~ ( in @ SY7240 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SY7240 @ SY7240 ) @ SV570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4244,plain,
! [SV490: $i,SV529: $i] :
( ( ( function @ SV529 )
= $false )
| ( ( ~ ( relation @ SV529 ) )
= $true )
| ( ( ~ ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4245,plain,
( ( ~ ( relation @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4093]) ).
thf(4246,plain,
( ( ~ ( relation_empty_yielding @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4093]) ).
thf(4247,plain,
! [SV571: $i] :
( ( ( ~ ( relation @ SV571 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV571 @ ( relation_field @ SV571 ) )
| ( well_founded_relation @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4096]) ).
thf(4248,plain,
! [SV572: $i] :
( ( ( ~ ( relation @ SV572 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV572 )
| ( is_well_founded_in @ SV572 @ ( relation_field @ SV572 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4097]) ).
thf(4249,plain,
! [SV491: $i] :
( ( ( ~ ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) ) )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4098]) ).
thf(4250,plain,
! [SV491: $i] :
( ( ( ~ ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4098]) ).
thf(4251,plain,
! [SV573: $i] :
( ( ( ~ ( relation @ SV573 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
| ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) )
| ( antisymmetric @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4099]) ).
thf(4252,plain,
! [SV574: $i] :
( ( ( ~ ( relation @ SV574 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV574 )
| ! [SY7241: $i,SY7242: $i] :
( ~ ( in @ ( ordered_pair @ SY7241 @ SY7242 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7242 @ SY7241 ) @ SV574 )
| ( SY7241 = SY7242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4100]) ).
thf(4253,plain,
! [SV492: $i,SV615: $i] :
( ( ! [SY7279: $i] :
( ~ ( function @ SY7279 )
| ~ ( relation @ SY7279 )
| ~ ( in @ SV615 @ ( relation_dom @ SY7279 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SY7279 @ SV492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4254,plain,
! [SV492: $i] :
( ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) )
| ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4255,plain,
( ( ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4256,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4257,plain,
! [SV575: $i] :
( ( ( ~ ( relation @ SV575 ) )
= $true )
| ( ( ( ( relation_dom @ SV575 )
!= empty_set )
| ( ( relation_rng @ SV575 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4258,plain,
! [SV576: $i] :
( ( ( ~ ( relation @ SV576 ) )
= $true )
| ( ( ( ( relation_rng @ SV576 )
!= empty_set )
| ( ( relation_dom @ SV576 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4259,plain,
! [SV493: $i] :
( ( ( relation @ SV493 )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( ~ ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4260,plain,
! [SV494: $i,SV577: $i] :
( ( ( ~ ( relation @ SV577 ) )
= $true )
| ( ( ~ ( ~ ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) )
| ~ ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4107]) ).
thf(4261,plain,
! [SV616: $i,SV495: $i] :
( ( ! [SY7280: $i] :
( ~ ( relation @ SY7280 )
| ~ ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SY7280 )
| ( in @ SV495 @ ( relation_dom @ SY7280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4262,plain,
! [SV617: $i,SV495: $i] :
( ( ! [SY7281: $i] :
( ~ ( relation @ SY7281 )
| ~ ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SY7281 )
| ( in @ SV617 @ ( relation_rng @ SY7281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4263,plain,
! [SV618: $i,SV578: $i] :
( ( ~ ( empty @ SV578 )
| ~ ( relation @ SV618 )
| ( empty @ ( relation_composition @ SV618 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4264,plain,
! [SV619: $i,SV579: $i] :
( ( ~ ( empty @ SV579 )
| ~ ( relation @ SV619 )
| ( relation @ ( relation_composition @ SV619 @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4265,plain,
( ( ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4112]) ).
thf(4266,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4112]) ).
thf(4267,plain,
! [SV496: $i] :
( ( ( ~ ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) ) )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4113]) ).
thf(4268,plain,
! [SV496: $i] :
( ( ( ~ ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4113]) ).
thf(4269,plain,
! [SV580: $i,SV620: $i] :
( ( ~ ( relation @ SV620 )
| ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
| ( SV620
= ( identity_relation @ SV580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4270,plain,
! [SV581: $i,SV621: $i] :
( ( ~ ( relation @ SV621 )
| ( SV621
!= ( identity_relation @ SV581 ) )
| ~ ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4115]) ).
thf(4271,plain,
! [SV497: $i] :
( ( ( ~ ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) ) )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4116]) ).
thf(4272,plain,
! [SV497: $i] :
( ( ( ~ ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4116]) ).
thf(4273,plain,
! [SV582: $i] :
( ( ( ~ ( relation @ SV582 ) )
= $true )
| ( ( ~ ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
| ( well_founded_relation @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4117]) ).
thf(4274,plain,
! [SV583: $i] :
( ( ( ~ ( relation @ SV583 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV583 )
| ! [SY7262: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SY7262 @ SV583 ) ) @ SY7262 )
| ~ ( in @ ( sK38_C @ SY7262 @ SV583 ) @ SY7262 ) )
| ( SY7262 = empty_set )
| ~ ( subset @ SY7262 @ ( relation_field @ SV583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4275,plain,
! [SV498: $i] :
( ( ( relation @ SV498 )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4276,plain,
! [SV584: $i] :
( ( ( ~ ( relation @ SV584 ) )
= $true )
| ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 )
| ~ ( connected @ SV584 )
| ~ ( well_founded_relation @ SV584 )
| ( well_ordering @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4277,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4121]) ).
thf(4278,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4121]) ).
thf(4279,plain,
! [SV585: $i] :
( ( ( ~ ( function @ SV585 )
| ~ ( relation @ SV585 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
| ( one_to_one @ SV585 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4280,plain,
! [SV586: $i] :
( ( ( ~ ( function @ SV586 )
| ~ ( relation @ SV586 ) )
= $true )
| ( ( ~ ( one_to_one @ SV586 )
| ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4281,plain,
! [SV499: $i] :
( ( ( ~ ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4124]) ).
thf(4282,plain,
! [SV499: $i] :
( ( ( ~ ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4124]) ).
thf(4283,plain,
! [SV587: $i] :
( ( ( ~ ( relation @ SV587 ) )
= $true )
| ( ( ( relation_rng @ SV587 )
= ( relation_dom @ ( relation_inverse @ SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4125]) ).
thf(4284,plain,
! [SV588: $i] :
( ( ( ~ ( relation @ SV588 ) )
= $true )
| ( ( ( relation_dom @ SV588 )
= ( relation_rng @ ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4285,plain,
! [SV589: $i] :
( ( ( ~ ( relation @ SV589 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV589 )
| ( is_antisymmetric_in @ SV589 @ ( relation_field @ SV589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4286,plain,
! [SV590: $i] :
( ( ( ~ ( relation @ SV590 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV590 @ ( relation_field @ SV590 ) )
| ( antisymmetric @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4287,plain,
! [SV591: $i,SV622: $i] :
( ( ~ ( function @ SV622 )
| ~ ( relation @ SV622 )
| ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 )
| ( SV622
= ( identity_relation @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4288,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4130]) ).
thf(4289,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4130]) ).
thf(4290,plain,
! [SV623: $i,SV592: $i] :
( ( ~ ( empty @ SV592 )
| ~ ( relation @ SV623 )
| ( empty @ ( relation_composition @ SV592 @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4291,plain,
! [SV624: $i,SV593: $i] :
( ( ~ ( empty @ SV593 )
| ~ ( relation @ SV624 )
| ( relation @ ( relation_composition @ SV593 @ SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4292,plain,
! [SV594: $i] :
( ( ( ~ ( relation @ SV594 ) )
= $true )
| ( ( ~ ( connected @ SV594 )
| ( is_connected_in @ SV594 @ ( relation_field @ SV594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4293,plain,
! [SV595: $i] :
( ( ( ~ ( relation @ SV595 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV595 @ ( relation_field @ SV595 ) )
| ( connected @ SV595 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4294,plain,
! [SV596: $i] :
( ( ( ~ ( function @ SV596 )
| ~ ( relation @ SV596 )
| ~ ( one_to_one @ SV596 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4135]) ).
thf(4295,plain,
! [SV597: $i] :
( ( ( ~ ( function @ SV597 )
| ~ ( relation @ SV597 )
| ~ ( one_to_one @ SV597 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4296,plain,
! [SV600: $i] :
( ( ( ~ ( empty @ SV600 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4297,plain,
! [SV601: $i] :
( ( ( ~ ( empty @ SV601 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4140]) ).
thf(4298,plain,
! [SV429: $i,SV506: $i] :
( ( ( relation @ SV506 )
= $false )
| ( ( function @ SV506 )
= $false )
| ( ( subset @ ( relation_image @ SV506 @ ( relation_inverse_image @ SV506 @ SV429 ) ) @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4299,plain,
! [SV508: $i,SV431: $i] :
( ( ( subset @ SV431 @ ( relation_dom @ SV508 ) )
= $false )
| ( ( subset @ SV431 @ ( relation_inverse_image @ SV508 @ ( relation_image @ SV508 @ SV431 ) ) )
= $true )
| ( ( relation @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4300,plain,
! [SV433: $i,SV509: $i] :
( ( ( relation @ SV509 )
= $false )
| ( ( function @ SV509 )
= $false )
| ( ( ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) )
| ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4301,plain,
! [SV434: $i,SV534: $i] :
( ( ( relation @ SV534 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV434 @ SV534 ) )
= ( relation_image @ SV534 @ ( relation_rng @ SV434 ) ) )
= $true )
| ( ( relation @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4302,plain,
! [SV511: $i,SV436: $i] :
( ( ( SV436 = empty_set )
= $true )
| ( ( ~ ( subset @ SV436 @ ( relation_rng @ SV511 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true )
| ( ( relation @ SV511 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4303,plain,
! [SV531: $i,SV512: $i,SV437: $i] :
( ( ( ~ ( subset @ SV437 @ SV512 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV531 @ SV437 ) @ ( relation_inverse_image @ SV531 @ SV512 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4147]) ).
thf(4304,plain,
! [SV439: $i,SV513: $i] :
( ( ( relation @ SV513 )
= $false )
| ( ( function @ SV513 )
= $false )
| ( ( ! [SY7199: $i] :
( ~ ( function @ SY7199 )
| ~ ( relation @ SY7199 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SY7199 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SY7199 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SY7199 @ SV439 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4305,plain,
! [SV440: $i,SV514: $i] :
( ( ( relation @ SV514 )
= $false )
| ( ( function @ SV514 )
= $false )
| ( ( ! [SY7200: $i] :
( ~ ( function @ SY7200 )
| ~ ( relation @ SY7200 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SY7200 ) @ SV440 )
= ( apply @ SY7200 @ ( apply @ SV514 @ SV440 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4306,plain,
! [SV441: $i,SV535: $i] :
( ( ( relation @ SV535 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV441 @ SV535 ) ) @ ( relation_dom @ SV441 ) )
= $true )
| ( ( relation @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4307,plain,
! [SV442: $i,SV536: $i] :
( ( ( relation @ SV536 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV442 @ SV536 ) ) @ ( relation_rng @ SV536 ) )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4151]) ).
thf(4308,plain,
! [SV443: $i,SV537: $i] :
( ( ( relation @ SV537 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SV537 ) )
| ( ( relation_dom @ ( relation_composition @ SV443 @ SV537 ) )
= ( relation_dom @ SV443 ) ) )
= $true )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4309,plain,
! [SV444: $i,SV538: $i] :
( ( ( relation @ SV538 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SV538 ) )
| ( ( relation_rng @ ( relation_composition @ SV538 @ SV444 ) )
= ( relation_rng @ SV444 ) ) )
= $true )
| ( ( relation @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4310,plain,
! [SV446: $i] :
( ( ( ~ ( one_to_one @ SV446 ) )
= $true )
| ( ( one_to_one @ ( function_inverse @ SV446 ) )
= $true )
| ( ( function @ SV446 )
= $false )
| ( ( relation @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4311,plain,
! [SV447: $i,SV515: $i,SV532: $i] :
( ( ( function @ SV532 )
= $false )
| ( ( ~ ( relation @ SV532 ) )
= $true )
| ( ( ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4155]) ).
thf(4312,plain,
! [SV448: $i,SV516: $i,SV533: $i] :
( ( ( function @ SV533 )
= $false )
| ( ( ~ ( relation @ SV533 ) )
= $true )
| ( ( ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4313,plain,
! [SV455: $i] :
( ( ( ~ ( one_to_one @ SV455 ) )
= $true )
| ( ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) )
= $true )
| ( ( function @ SV455 )
= $false )
| ( ( relation @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4157]) ).
thf(4314,plain,
! [SV457: $i,SV521: $i] :
( ( ( relation @ SV521 )
= $false )
| ( ( relation @ SV457 )
= $false )
| ( ( relation @ ( relation_composition @ SV457 @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4315,plain,
! [SV461: $i,SV523: $i] :
( ( ( relation @ SV523 )
= $false )
| ( ( relation @ SV461 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV461 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4316,plain,
! [SV462: $i,SV524: $i] :
( ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV462 )
= $false )
| ( ( relation @ ( set_union2 @ SV462 @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4317,plain,
! [SV463: $i,SV525: $i] :
( ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV463 )
= $false )
| ( ( relation @ ( set_difference @ SV463 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4318,plain,
! [SV540: $i] :
( ( ( relation @ SV540 )
= $false )
| ( ( ~ ( is_transitive_in @ SV540 @ ( relation_field @ SV540 ) )
| ( transitive @ SV540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4164]) ).
thf(4319,plain,
! [SV541: $i] :
( ( ( relation @ SV541 )
= $false )
| ( ( ~ ( transitive @ SV541 )
| ( is_transitive_in @ SV541 @ ( relation_field @ SV541 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4165]) ).
thf(4320,plain,
! [SV467: $i] :
( ( ( ! [SY6999: $i,SY7000: $i] :
( ~ ( ~ ( ! [SY7001: $i] :
( ~ ( in @ ( ordered_pair @ SY7001 @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7001 @ SY6999 ) )
| ~ ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7000 @ SY6999 @ SV467 ) @ SY6999 ) )
| ( in @ ( sK50_D @ SY7000 @ SY6999 @ SV467 ) @ SY7000 ) ) )
| ( SY7000
= ( relation_image @ SV467 @ SY6999 ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4321,plain,
! [SV467: $i] :
( ( ( ! [SY7002: $i,SY7003: $i] :
( ( SY7003
!= ( relation_image @ SV467 @ SY7002 ) )
| ~ ( ~ ! [SY7004: $i] :
( ! [SY7005: $i] :
( ~ ( in @ ( ordered_pair @ SY7005 @ SY7004 ) @ SV467 )
| ~ ( in @ SY7005 @ SY7002 ) )
| ( in @ SY7004 @ SY7003 ) )
| ~ ! [SY7006: $i] :
( ~ ( in @ SY7006 @ SY7003 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7006 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7006 @ SY7003 @ SY7002 @ SV467 ) @ SY7002 ) ) ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4167]) ).
thf(4322,plain,
! [SV542: $i] :
( ( ( ~ ( function @ SV542 ) )
= $true )
| ( ( ~ ( relation @ SV542 ) )
= $true )
| ( ( ! [SY7224: $i] : ( function @ ( relation_dom_restriction @ SV542 @ SY7224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4323,plain,
! [SV543: $i] :
( ( ( ~ ( function @ SV543 ) )
= $true )
| ( ( ~ ( relation @ SV543 ) )
= $true )
| ( ( ! [SY7225: $i] : ( relation @ ( relation_dom_restriction @ SV543 @ SY7225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4324,plain,
! [SV468: $i] :
( ( ( ! [SY7007: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SY7007 @ SV468 ) @ SY7007 )
| ~ ( in @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( sK12_SY6429 @ SY7007 @ SV468 ) @ SY7007 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK11_SY6427 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SY7007 @ SV468 ) @ ( sK12_SY6429 @ SY7007 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SY7007 ) ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4170]) ).
thf(4325,plain,
! [SV468: $i] :
( ( ( ! [SY7008: $i] :
( ~ ( is_transitive_in @ SV468 @ SY7008 )
| ! [SY7009: $i,SY7010: $i,SY7011: $i] :
( ~ ( in @ SY7009 @ SY7008 )
| ~ ( in @ SY7010 @ SY7008 )
| ~ ( in @ SY7011 @ SY7008 )
| ~ ( in @ ( ordered_pair @ SY7009 @ SY7010 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7010 @ SY7011 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7009 @ SY7011 ) @ SV468 ) ) ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4171]) ).
thf(4326,plain,
! [SV469: $i] :
( ( ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) )
| ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4327,plain,
! [SV470: $i] :
( ( ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) )
| ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4328,plain,
! [SV544: $i] :
( ( ( ~ ! [SY7226: $i,SY7227: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SY7226 @ SY7227 ) )
| ~ ( in @ ( sK45_B @ SV544 ) @ SV544 ) )
= $false )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4329,plain,
! [SV545: $i] :
( ( ( relation @ SV545 )
= $false )
| ( ( ! [SY7228: $i] :
( ( SY7228
= ( ordered_pair @ ( sK43_C @ SY7228 @ SV545 ) @ ( sK44_SY6449 @ SY7228 @ SV545 ) ) )
| ~ ( in @ SY7228 @ SV545 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4330,plain,
! [SV546: $i] :
( ( ( ~ ( relation @ SV546 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV546 ) )
= $true )
| ( ( ! [SY7229: $i] : ( relation @ ( relation_dom_restriction @ SV546 @ SY7229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4331,plain,
! [SV547: $i] :
( ( ( ~ ( relation @ SV547 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV547 ) )
= $true )
| ( ( ! [SY7230: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SY7230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4177]) ).
thf(4332,plain,
! [SV548: $i] :
( ( ( empty @ SV548 )
= $false )
| ( ( empty @ ( relation_rng @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4333,plain,
! [SV549: $i] :
( ( ( empty @ SV549 )
= $false )
| ( ( relation @ ( relation_rng @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4179]) ).
thf(4334,plain,
! [SV471: $i] :
( ( ( ! [SY7027: $i] :
( ~ ( is_reflexive_in @ SV471 @ SY7027 )
| ~ ( is_transitive_in @ SV471 @ SY7027 )
| ~ ( is_antisymmetric_in @ SV471 @ SY7027 )
| ~ ( is_connected_in @ SV471 @ SY7027 )
| ~ ( is_well_founded_in @ SV471 @ SY7027 )
| ( well_orders @ SV471 @ SY7027 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4180]) ).
thf(4335,plain,
! [SV471: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4181]) ).
thf(4336,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4182]) ).
thf(4337,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4183]) ).
thf(4338,plain,
! [SV472: $i,SV526: $i] :
( ( ( relation @ SV526 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( ~ ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4339,plain,
! [SV550: $i] :
( ( ( relation @ SV550 )
= $false )
| ( ( ~ ( is_reflexive_in @ SV550 @ ( relation_field @ SV550 ) )
| ( reflexive @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4340,plain,
! [SV551: $i] :
( ( ( relation @ SV551 )
= $false )
| ( ( ~ ( reflexive @ SV551 )
| ( is_reflexive_in @ SV551 @ ( relation_field @ SV551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4186]) ).
thf(4341,plain,
! [SV473: $i] :
( ( ( ! [SY7038: $i] :
( ~ ( ~ ( ! [SY7039: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ SY7039 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SY7038 @ SV473 ) @ ( sK33_SY6444 @ SY7038 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SY7038 @ SV473 ) @ SY7038 ) ) )
| ( SY7038
= ( relation_dom @ SV473 ) ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4187]) ).
thf(4342,plain,
! [SV473: $i] :
( ( ( ! [SY7040: $i] :
( ( SY7040
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7041: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7041 @ SY7042 ) @ SV473 )
| ( in @ SY7041 @ SY7040 ) )
| ~ ! [SY7043: $i] :
( ~ ( in @ SY7043 @ SY7040 )
| ( in @ ( ordered_pair @ SY7043 @ ( sK31_D @ SY7043 @ SY7040 @ SV473 ) ) @ SV473 ) ) ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4188]) ).
thf(4343,plain,
! [SV474: $i] :
( ( ( ! [SY7044: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SY7044 @ SV474 ) @ SY7044 )
| ~ ( in @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ SY7044 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SY7044 @ SV474 ) @ ( sK30_SY6442 @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SY7044 @ SV474 ) @ ( sK29_C @ SY7044 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SY7044 @ SV474 )
!= ( sK30_SY6442 @ SY7044 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SY7044 ) ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4189]) ).
thf(4344,plain,
! [SV474: $i] :
( ( ( ! [SY7045: $i] :
( ~ ( is_antisymmetric_in @ SV474 @ SY7045 )
| ! [SY7046: $i,SY7047: $i] :
( ~ ( in @ SY7046 @ SY7045 )
| ~ ( in @ SY7047 @ SY7045 )
| ~ ( in @ ( ordered_pair @ SY7046 @ SY7047 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7047 @ SY7046 ) @ SV474 )
| ( SY7046 = SY7047 ) ) ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4190]) ).
thf(4345,plain,
! [SV552: $i] :
( ( ( relation @ SV552 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
| ( connected @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4191]) ).
thf(4346,plain,
! [SV553: $i] :
( ( ( relation @ SV553 )
= $false )
| ( ( ~ ( connected @ SV553 )
| ! [SY7231: $i,SY7232: $i] :
( ( SY7231 = SY7232 )
| ~ ( in @ SY7231 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7232 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SY7231 @ SY7232 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7232 @ SY7231 ) @ SV553 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4347,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4193]) ).
thf(4348,plain,
( ( epsilon_connected @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4194]) ).
thf(4349,plain,
! [SV602: $i,SV475: $i,SV625: $i] :
( ( ~ ( relation @ SV625 )
| ! [SY7288: $i] :
( ~ ( in @ SY7288 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7288 ) @ SV625 )
| ~ ( in @ SY7288 @ SV602 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4350,plain,
! [SV603: $i,SV475: $i,SV626: $i] :
( ( ~ ( relation @ SV626 )
| ~ ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4351,plain,
! [SV604: $i,SV476: $i,SV627: $i] :
( ( ~ ( relation @ SV627 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SV627 )
| ( in @ SV476 @ ( relation_field @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(4352,plain,
! [SV605: $i,SV476: $i,SV628: $i] :
( ( ~ ( relation @ SV628 )
| ~ ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SV628 )
| ( in @ SV605 @ ( relation_field @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4353,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4199]) ).
thf(4354,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4200]) ).
thf(4355,plain,
! [SV554: $i] :
( ( ( ~ ( empty @ SV554 )
| ~ ( relation @ SV554 ) )
= $true )
| ( ( ~ ( function @ SV554 ) )
= $true )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4201]) ).
thf(4356,plain,
! [SV606: $i,SV555: $i] :
( ( ( ~ ( function @ SV555 )
| ~ ( relation @ SV555 )
| ~ ( relation @ SV606 )
| ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4357,plain,
! [SV607: $i,SV556: $i] :
( ( ( ~ ( function @ SV556 )
| ~ ( relation @ SV556 )
| ~ ( relation @ SV607 )
| ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4358,plain,
! [SV608: $i,SV477: $i,SV629: $i] :
( ( ~ ( relation @ SV629 )
| ~ ( in @ SV477 @ SV608 )
| ~ ( in @ SV477 @ ( relation_rng @ SV629 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4204]) ).
thf(4359,plain,
! [SV477: $i] :
( ( ~ ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4205]) ).
thf(4360,plain,
! [SV477: $i] :
( ( ~ ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4205]) ).
thf(4361,plain,
! [SV478: $i] :
( ( ( ! [SY7063: $i,SY7064: $i] :
( ~ ( relation @ SY7064 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ SY7063 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7064 @ SY7063 @ SV478 ) @ ( sK59_SY6459 @ SY7064 @ SY7063 @ SV478 ) ) @ SY7064 ) ) ) )
| ( SY7064
= ( relation_dom_restriction @ SV478 @ SY7063 ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4206]) ).
thf(4362,plain,
! [SV478: $i] :
( ( ( ! [SY7065: $i,SY7066: $i] :
( ~ ( relation @ SY7066 )
| ( SY7066
!= ( relation_dom_restriction @ SV478 @ SY7065 ) )
| ~ ( ~ ! [SY7067: $i,SY7068: $i] :
( ~ ( in @ SY7067 @ SY7065 )
| ~ ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7067 @ SY7068 ) @ SY7066 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY7066 )
| ( in @ SX3 @ SY7065 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7066 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4207]) ).
thf(4363,plain,
! [SV557: $i,SV609: $i] :
( ( ( ~ ( function @ SV609 )
| ~ ( relation @ SV609 ) )
= $true )
| ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 )
| ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4364,plain,
! [SV558: $i,SV610: $i] :
( ( ( ~ ( function @ SV610 )
| ~ ( relation @ SV610 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4365,plain,
! [SV479: $i] :
( ( ( ! [SY7073: $i] :
( ~ ( ~ ( ! [SY7074: $i] :
~ ( in @ ( ordered_pair @ SY7074 @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SY7073 @ SV479 ) @ ( sK24_C @ SY7073 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SY7073 @ SV479 ) @ SY7073 ) ) )
| ( SY7073
= ( relation_rng @ SV479 ) ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4210]) ).
thf(4366,plain,
! [SV479: $i] :
( ( ( ! [SY7075: $i] :
( ( SY7075
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7076: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7076 ) @ SV479 )
| ( in @ SY7076 @ SY7075 ) )
| ~ ! [SY7078: $i] :
( ~ ( in @ SY7078 @ SY7075 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7078 @ SY7075 @ SV479 ) @ SY7078 ) @ SV479 ) ) ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4211]) ).
thf(4367,plain,
! [SV559: $i] :
( ( ( empty @ SV559 )
= $false )
| ( ( empty @ ( relation_inverse @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4368,plain,
! [SV560: $i] :
( ( ( empty @ SV560 )
= $false )
| ( ( relation @ ( relation_inverse @ SV560 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4369,plain,
! [SV480: $i,SV527: $i] :
( ( ( ~ ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) ) )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4214]) ).
thf(4370,plain,
! [SV527: $i,SV480: $i] :
( ( ( ~ ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4214]) ).
thf(4371,plain,
! [SV561: $i] :
( ( ( relation @ SV561 )
= $false )
| ( ( ( ( relation_dom @ SV561 )
!= empty_set )
| ( SV561 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4372,plain,
! [SV562: $i] :
( ( ( relation @ SV562 )
= $false )
| ( ( ( ( relation_rng @ SV562 )
!= empty_set )
| ( SV562 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4373,plain,
! [SV481: $i] :
( ( ( ! [SY7088: $i] :
( ~ ( relation @ SY7088 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SY7088 @ SV481 ) @ ( sK41_SY6448 @ SY7088 @ SV481 ) ) @ SY7088 ) ) )
| ( SV481 = SY7088 ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4217]) ).
thf(4374,plain,
! [SV481: $i] :
( ( ( ! [SY7089: $i] :
( ~ ( relation @ SY7089 )
| ( SV481 != SY7089 )
| ~ ( ~ ! [SY7090: $i,SY7091: $i] :
( ~ ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7090 @ SY7091 ) @ SY7089 ) )
| ~ ! [SY7092: $i,SY7093: $i] :
( ~ ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SY7089 )
| ( in @ ( ordered_pair @ SY7092 @ SY7093 ) @ SV481 ) ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4218]) ).
thf(4375,plain,
! [SV482: $i] :
( ( ( ~ ( one_to_one @ SV482 ) )
= $true )
| ( ( ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4376,plain,
! [SV563: $i] :
( ( ( ~ ( function @ SV563 ) )
= $true )
| ( ( ~ ( relation @ SV563 ) )
= $true )
| ( ( ~ ( one_to_one @ SV563 )
| ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4377,plain,
! [SV564: $i] :
( ( ( ~ ( function @ SV564 ) )
= $true )
| ( ( ~ ( relation @ SV564 ) )
= $true )
| ( ( ~ ( one_to_one @ SV564 )
| ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4378,plain,
! [SV528: $i,SV630: $i,SV483: $i] :
( ( ! [SY7289: $i] :
( ~ ( relation @ SY7289 )
| ~ ( in @ SV483 @ SV630 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7289 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SY7289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4379,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) )
| ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4380,plain,
! [SV565: $i] :
( ( ( ~ ( function @ SV565 ) )
= $true )
| ( ( ~ ( relation @ SV565 ) )
= $true )
| ( ( function @ ( function_inverse @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4381,plain,
! [SV566: $i] :
( ( ( ~ ( function @ SV566 ) )
= $true )
| ( ( ~ ( relation @ SV566 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4382,plain,
! [SV484: $i,SV611: $i,SV631: $i] :
( ( ~ ( function @ SV631 )
| ~ ( relation @ SV631 )
| ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(4383,plain,
! [SV484: $i] :
( ( ~ ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4227]) ).
thf(4384,plain,
! [SV484: $i] :
( ( ~ ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4227]) ).
thf(4385,plain,
! [SV612: $i,SV485: $i,SV632: $i] :
( ( ~ ( relation @ SV632 )
| ~ ( in @ SV485 @ SV612 )
| ~ ( in @ SV485 @ ( relation_dom @ SV632 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4386,plain,
! [SV485: $i] :
( ( ~ ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4229]) ).
thf(4387,plain,
! [SV485: $i] :
( ( ~ ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4229]) ).
thf(4388,plain,
! [SV486: $i] :
( ( ( ! [SY7124: $i] :
( ~ ( ~ ( in @ ( sK42_C @ SY7124 @ SV486 ) @ SY7124 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SY7124 @ SV486 ) @ ( sK42_C @ SY7124 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SY7124 ) ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4230]) ).
thf(4389,plain,
! [SV486: $i] :
( ( ( ! [SY7125: $i] :
( ~ ( is_reflexive_in @ SV486 @ SY7125 )
| ! [SY7126: $i] :
( ~ ( in @ SY7126 @ SY7125 )
| ( in @ ( ordered_pair @ SY7126 @ SY7126 ) @ SV486 ) ) ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4231]) ).
thf(4390,plain,
! [SV567: $i] :
( ( ( relation @ SV567 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ( transitive @ SV567 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4391,plain,
! [SV568: $i] :
( ( ( relation @ SV568 )
= $false )
| ( ( ~ ( transitive @ SV568 )
| ! [SY7237: $i,SY7238: $i,SY7239: $i] :
( ~ ( in @ ( ordered_pair @ SY7237 @ SY7238 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7238 @ SY7239 ) @ SV568 )
| ( in @ ( ordered_pair @ SY7237 @ SY7239 ) @ SV568 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4392,plain,
! [SV613: $i,SV487: $i,SV633: $i] :
( ( ~ ( relation @ SV633 )
| ! [SY7290: $i] :
( ~ ( in @ SY7290 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SY7290 @ SV487 ) @ SV633 )
| ~ ( in @ SY7290 @ SV613 ) )
| ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(4393,plain,
! [SV614: $i,SV487: $i,SV634: $i] :
( ( ~ ( relation @ SV634 )
| ~ ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4235]) ).
thf(4394,plain,
! [SV488: $i] :
( ( ( ! [SY7132: $i] :
( ~ ( ~ ! [SY7133: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7133 ) @ ( sK35_C @ SY7132 @ SV488 ) )
| ~ ( in @ SY7133 @ ( sK35_C @ SY7132 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SY7132 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SY7132 @ SV488 ) @ SY7132 ) ) )
| ( is_well_founded_in @ SV488 @ SY7132 ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4236]) ).
thf(4395,plain,
! [SV488: $i] :
( ( ( ! [SY7134: $i] :
( ~ ( is_well_founded_in @ SV488 @ SY7134 )
| ! [SY7135: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) ) @ SY7135 )
| ~ ( in @ ( sK34_D @ SY7135 @ SY7134 @ SV488 ) @ SY7135 ) )
| ( SY7135 = empty_set )
| ~ ( subset @ SY7135 @ SY7134 ) ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4237]) ).
thf(4396,plain,
! [SV489: $i] :
( ( ( ! [SY7136: $i] :
( ~ ( relation @ SY7136 )
| ~ ( subset @ SV489 @ SY7136 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SY7136 ) ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4238]) ).
thf(4397,plain,
! [SV489: $i] :
( ( ( ! [SY7137: $i] :
( ~ ( relation @ SY7137 )
| ~ ( subset @ SV489 @ SY7137 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SY7137 ) ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4239]) ).
thf(4398,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4240]) ).
thf(4399,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4241]) ).
thf(4400,plain,
! [SV569: $i] :
( ( ( relation @ SV569 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
| ( reflexive @ SV569 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4401,plain,
! [SV570: $i] :
( ( ( relation @ SV570 )
= $false )
| ( ( ~ ( reflexive @ SV570 )
| ! [SY7240: $i] :
( ~ ( in @ SY7240 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SY7240 @ SY7240 ) @ SV570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4243]) ).
thf(4402,plain,
! [SV490: $i,SV529: $i] :
( ( ( relation @ SV529 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( ~ ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4403,plain,
( ( relation @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4245]) ).
thf(4404,plain,
( ( relation_empty_yielding @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4246]) ).
thf(4405,plain,
! [SV571: $i] :
( ( ( relation @ SV571 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV571 @ ( relation_field @ SV571 ) )
| ( well_founded_relation @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4406,plain,
! [SV572: $i] :
( ( ( relation @ SV572 )
= $false )
| ( ( ~ ( well_founded_relation @ SV572 )
| ( is_well_founded_in @ SV572 @ ( relation_field @ SV572 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4407,plain,
! [SV491: $i] :
( ( ( ! [SY7142: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SY7142 @ SV491 )
!= ( sK22_SY6437 @ SY7142 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SY7142 @ SV491 ) @ SY7142 )
| ~ ( in @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ SY7142 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SY7142 @ SV491 ) @ ( sK22_SY6437 @ SY7142 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SY7142 @ SV491 ) @ ( sK21_C @ SY7142 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SY7142 ) ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4249]) ).
thf(4408,plain,
! [SV491: $i] :
( ( ( ! [SY7143: $i] :
( ~ ( is_connected_in @ SV491 @ SY7143 )
| ! [SY7144: $i,SY7145: $i] :
( ( SY7144 = SY7145 )
| ~ ( in @ SY7144 @ SY7143 )
| ~ ( in @ SY7145 @ SY7143 )
| ( in @ ( ordered_pair @ SY7144 @ SY7145 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7145 @ SY7144 ) @ SV491 ) ) ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4250]) ).
thf(4409,plain,
! [SV573: $i] :
( ( ( relation @ SV573 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
| ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) )
| ( antisymmetric @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4251]) ).
thf(4410,plain,
! [SV574: $i] :
( ( ( relation @ SV574 )
= $false )
| ( ( ~ ( antisymmetric @ SV574 )
| ! [SY7241: $i,SY7242: $i] :
( ~ ( in @ ( ordered_pair @ SY7241 @ SY7242 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7242 @ SY7241 ) @ SV574 )
| ( SY7241 = SY7242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4252]) ).
thf(4411,plain,
! [SV492: $i,SV615: $i,SV635: $i] :
( ( ~ ( function @ SV635 )
| ~ ( relation @ SV635 )
| ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(4412,plain,
! [SV492: $i] :
( ( ~ ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4254]) ).
thf(4413,plain,
! [SV492: $i] :
( ( ~ ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4254]) ).
thf(4414,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4255]) ).
thf(4415,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4256]) ).
thf(4416,plain,
! [SV575: $i] :
( ( ( relation @ SV575 )
= $false )
| ( ( ( ( relation_dom @ SV575 )
!= empty_set )
| ( ( relation_rng @ SV575 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4257]) ).
thf(4417,plain,
! [SV576: $i] :
( ( ( relation @ SV576 )
= $false )
| ( ( ( ( relation_rng @ SV576 )
!= empty_set )
| ( ( relation_dom @ SV576 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4418,plain,
! [SV493: $i] :
( ( ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) )
| ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4419,plain,
! [SV494: $i,SV577: $i] :
( ( ( relation @ SV577 )
= $false )
| ( ( ~ ( ~ ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) )
| ~ ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4420,plain,
! [SV616: $i,SV495: $i,SV636: $i] :
( ( ~ ( relation @ SV636 )
| ~ ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SV636 )
| ( in @ SV495 @ ( relation_dom @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(4421,plain,
! [SV617: $i,SV495: $i,SV637: $i] :
( ( ~ ( relation @ SV637 )
| ~ ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SV637 )
| ( in @ SV617 @ ( relation_rng @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(4422,plain,
! [SV618: $i,SV578: $i] :
( ( ( ~ ( empty @ SV578 )
| ~ ( relation @ SV618 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV618 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4423,plain,
! [SV619: $i,SV579: $i] :
( ( ( ~ ( empty @ SV579 )
| ~ ( relation @ SV619 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV619 @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4424,plain,
( ( function @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4265]) ).
thf(4425,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4266]) ).
thf(4426,plain,
! [SV496: $i] :
( ( ( ! [SY7171: $i] :
( ~ ( relation @ SY7171 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SY7171 @ SV496 ) @ ( sK20_SY6436 @ SY7171 @ SV496 ) ) @ SY7171 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SY7171 @ SV496 ) @ ( sK19_C @ SY7171 @ SV496 ) ) @ SV496 ) ) )
| ( SY7171
= ( relation_inverse @ SV496 ) ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4267]) ).
thf(4427,plain,
! [SV496: $i] :
( ( ( ! [SY7172: $i] :
( ~ ( relation @ SY7172 )
| ( SY7172
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7173: $i,SY7174: $i] :
( ~ ( in @ ( ordered_pair @ SY7173 @ SY7174 ) @ SY7172 )
| ( in @ ( ordered_pair @ SY7174 @ SY7173 ) @ SV496 ) )
| ~ ! [SY7175: $i,SY7176: $i] :
( ~ ( in @ ( ordered_pair @ SY7176 @ SY7175 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7175 @ SY7176 ) @ SY7172 ) ) ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4268]) ).
thf(4428,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( relation @ SV620 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
| ( SV620
= ( identity_relation @ SV580 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4429,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ( relation @ SV621 ) )
= $true )
| ( ( ( SV621
!= ( identity_relation @ SV581 ) )
| ~ ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4430,plain,
! [SV497: $i] :
( ( ( ! [SY7177: $i] :
( ~ ( relation @ SY7177 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY7177 @ SV497 ) @ ( sK37_SY6446 @ SY7177 @ SV497 ) ) @ SY7177 ) )
| ( subset @ SV497 @ SY7177 ) ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4271]) ).
thf(4431,plain,
! [SV497: $i] :
( ( ( ! [SY7178: $i] :
( ~ ( relation @ SY7178 )
| ~ ( subset @ SV497 @ SY7178 )
| ! [SY7179: $i,SY7180: $i] :
( ~ ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7179 @ SY7180 ) @ SY7178 ) ) ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4272]) ).
thf(4432,plain,
! [SV582: $i] :
( ( ( relation @ SV582 )
= $false )
| ( ( ~ ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
| ( well_founded_relation @ SV582 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4433,plain,
! [SV583: $i] :
( ( ( relation @ SV583 )
= $false )
| ( ( ~ ( well_founded_relation @ SV583 )
| ! [SY7262: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SY7262 @ SV583 ) ) @ SY7262 )
| ~ ( in @ ( sK38_C @ SY7262 @ SV583 ) @ SY7262 ) )
| ( SY7262 = empty_set )
| ~ ( subset @ SY7262 @ ( relation_field @ SV583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4274]) ).
thf(4434,plain,
! [SV498: $i] :
( ( ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
| ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4275]) ).
thf(4435,plain,
! [SV584: $i] :
( ( ( relation @ SV584 )
= $false )
| ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 )
| ~ ( connected @ SV584 )
| ~ ( well_founded_relation @ SV584 )
| ( well_ordering @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4436,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4437,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4278]) ).
thf(4438,plain,
! [SV585: $i] :
( ( ( ~ ( function @ SV585 ) )
= $true )
| ( ( ~ ( relation @ SV585 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
| ( one_to_one @ SV585 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4439,plain,
! [SV586: $i] :
( ( ( ~ ( function @ SV586 ) )
= $true )
| ( ( ~ ( relation @ SV586 ) )
= $true )
| ( ( ~ ( one_to_one @ SV586 )
| ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4440,plain,
! [SV499: $i] :
( ( ( ! [SY7189: $i,SY7190: $i] :
( ~ ( ~ ( ! [SY7191: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7191 ) @ SV499 )
| ~ ( in @ SY7191 @ SY7189 ) )
| ~ ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7190 @ SY7189 @ SV499 ) @ SY7189 ) )
| ( in @ ( sK47_D @ SY7190 @ SY7189 @ SV499 ) @ SY7190 ) ) )
| ( SY7190
= ( relation_inverse_image @ SV499 @ SY7189 ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4281]) ).
thf(4441,plain,
! [SV499: $i] :
( ( ( ! [SY7192: $i,SY7193: $i] :
( ( SY7193
!= ( relation_inverse_image @ SV499 @ SY7192 ) )
| ~ ( ~ ! [SY7194: $i] :
( ! [SY7195: $i] :
( ~ ( in @ ( ordered_pair @ SY7194 @ SY7195 ) @ SV499 )
| ~ ( in @ SY7195 @ SY7192 ) )
| ( in @ SY7194 @ SY7193 ) )
| ~ ! [SY7196: $i] :
( ~ ( in @ SY7196 @ SY7193 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7196 @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7196 @ SY7193 @ SY7192 @ SV499 ) @ SY7192 ) ) ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4282]) ).
thf(4442,plain,
! [SV587: $i] :
( ( ( relation @ SV587 )
= $false )
| ( ( ( relation_rng @ SV587 )
= ( relation_dom @ ( relation_inverse @ SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4443,plain,
! [SV588: $i] :
( ( ( relation @ SV588 )
= $false )
| ( ( ( relation_dom @ SV588 )
= ( relation_rng @ ( relation_inverse @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4284]) ).
thf(4444,plain,
! [SV589: $i] :
( ( ( relation @ SV589 )
= $false )
| ( ( ~ ( antisymmetric @ SV589 )
| ( is_antisymmetric_in @ SV589 @ ( relation_field @ SV589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4445,plain,
! [SV590: $i] :
( ( ( relation @ SV590 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV590 @ ( relation_field @ SV590 ) )
| ( antisymmetric @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4446,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( function @ SV622 )
| ~ ( relation @ SV622 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 )
| ( SV622
= ( identity_relation @ SV591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4287]) ).
thf(4447,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( ( apply @ SX1 @ SX2 )
= SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4288]) ).
thf(4448,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4289]) ).
thf(4449,plain,
! [SV623: $i,SV592: $i] :
( ( ( ~ ( empty @ SV592 )
| ~ ( relation @ SV623 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV592 @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4450,plain,
! [SV624: $i,SV593: $i] :
( ( ( ~ ( empty @ SV593 )
| ~ ( relation @ SV624 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV593 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4291]) ).
thf(4451,plain,
! [SV594: $i] :
( ( ( relation @ SV594 )
= $false )
| ( ( ~ ( connected @ SV594 )
| ( is_connected_in @ SV594 @ ( relation_field @ SV594 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4452,plain,
! [SV595: $i] :
( ( ( relation @ SV595 )
= $false )
| ( ( ~ ( is_connected_in @ SV595 @ ( relation_field @ SV595 ) )
| ( connected @ SV595 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4453,plain,
! [SV596: $i] :
( ( ( ~ ( function @ SV596 )
| ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( one_to_one @ SV596 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4294]) ).
thf(4454,plain,
! [SV597: $i] :
( ( ( ~ ( function @ SV597 )
| ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( one_to_one @ SV597 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4295]) ).
thf(4455,plain,
! [SV600: $i] :
( ( ( empty @ SV600 )
= $false )
| ( ( empty @ ( relation_dom @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4456,plain,
! [SV601: $i] :
( ( ( empty @ SV601 )
= $false )
| ( ( relation @ ( relation_dom @ SV601 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4457,plain,
! [SV509: $i,SV433: $i] :
( ( ( ~ ( subset @ SV433 @ ( relation_rng @ SV509 ) ) )
= $true )
| ( ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 )
= $true )
| ( ( function @ SV509 )
= $false )
| ( ( relation @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4458,plain,
! [SV511: $i,SV436: $i] :
( ( ( subset @ SV436 @ ( relation_rng @ SV511 ) )
= $false )
| ( ( SV436 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV511 @ SV436 )
!= empty_set ) )
= $true )
| ( ( relation @ SV511 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4459,plain,
! [SV531: $i,SV512: $i,SV437: $i] :
( ( ( subset @ SV437 @ SV512 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV531 @ SV437 ) @ ( relation_inverse_image @ SV531 @ SV512 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4303]) ).
thf(4460,plain,
! [SV513: $i,SV439: $i,SV638: $i] :
( ( ( ~ ( function @ SV638 )
| ~ ( relation @ SV638 )
| ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) ) )
= $true )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(4461,plain,
! [SV514: $i,SV440: $i,SV639: $i] :
( ( ( ~ ( function @ SV639 )
| ~ ( relation @ SV639 )
| ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) ) )
= $true )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4305]) ).
thf(4462,plain,
! [SV537: $i,SV443: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SV537 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV443 @ SV537 ) )
= ( relation_dom @ SV443 ) )
= $true )
| ( ( relation @ SV537 )
= $false )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(4463,plain,
! [SV538: $i,SV444: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SV538 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV538 @ SV444 ) )
= ( relation_rng @ SV444 ) )
= $true )
| ( ( relation @ SV538 )
= $false )
| ( ( relation @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4464,plain,
! [SV446: $i] :
( ( ( one_to_one @ SV446 )
= $false )
| ( ( one_to_one @ ( function_inverse @ SV446 ) )
= $true )
| ( ( function @ SV446 )
= $false )
| ( ( relation @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4465,plain,
! [SV447: $i,SV515: $i,SV532: $i] :
( ( ( relation @ SV532 )
= $false )
| ( ( function @ SV532 )
= $false )
| ( ( ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4466,plain,
! [SV448: $i,SV516: $i,SV533: $i] :
( ( ( relation @ SV533 )
= $false )
| ( ( function @ SV533 )
= $false )
| ( ( ~ ( in @ SV516 @ SV448 )
| ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4467,plain,
! [SV455: $i] :
( ( ( one_to_one @ SV455 )
= $false )
| ( ( ( function_inverse @ SV455 )
= ( relation_inverse @ SV455 ) )
= $true )
| ( ( function @ SV455 )
= $false )
| ( ( relation @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4468,plain,
! [SV540: $i] :
( ( ( ~ ( is_transitive_in @ SV540 @ ( relation_field @ SV540 ) ) )
= $true )
| ( ( transitive @ SV540 )
= $true )
| ( ( relation @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(4469,plain,
! [SV541: $i] :
( ( ( ~ ( transitive @ SV541 ) )
= $true )
| ( ( is_transitive_in @ SV541 @ ( relation_field @ SV541 ) )
= $true )
| ( ( relation @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4470,plain,
! [SV467: $i,SV640: $i] :
( ( ( ! [SY7291: $i] :
( ~ ( ~ ( ! [SY7292: $i] :
( ~ ( in @ ( ordered_pair @ SY7292 @ ( sK50_D @ SY7291 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7292 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SY7291 @ SV640 @ SV467 ) @ SY7291 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SY7291 @ SV640 @ SV467 ) @ ( sK50_D @ SY7291 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SY7291 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SY7291 @ SV640 @ SV467 ) @ SY7291 ) ) )
| ( SY7291
= ( relation_image @ SV467 @ SV640 ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4320]) ).
thf(4471,plain,
! [SV641: $i,SV467: $i] :
( ( ( ! [SY7293: $i] :
( ( SY7293
!= ( relation_image @ SV467 @ SV641 ) )
| ~ ( ~ ! [SY7294: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7294 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7294 @ SY7293 ) )
| ~ ! [SY7296: $i] :
( ~ ( in @ SY7296 @ SY7293 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7296 @ SY7293 @ SV641 @ SV467 ) @ SY7296 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7296 @ SY7293 @ SV641 @ SV467 ) @ SV641 ) ) ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4321]) ).
thf(4472,plain,
! [SV542: $i] :
( ( ( function @ SV542 )
= $false )
| ( ( ~ ( relation @ SV542 ) )
= $true )
| ( ( ! [SY7224: $i] : ( function @ ( relation_dom_restriction @ SV542 @ SY7224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4473,plain,
! [SV543: $i] :
( ( ( function @ SV543 )
= $false )
| ( ( ~ ( relation @ SV543 ) )
= $true )
| ( ( ! [SY7225: $i] : ( relation @ ( relation_dom_restriction @ SV543 @ SY7225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4474,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
| ( is_transitive_in @ SV468 @ SV642 ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4475,plain,
! [SV643: $i,SV468: $i] :
( ( ( ~ ( is_transitive_in @ SV468 @ SV643 )
| ! [SY7297: $i,SY7298: $i,SY7299: $i] :
( ~ ( in @ SY7297 @ SV643 )
| ~ ( in @ SY7298 @ SV643 )
| ~ ( in @ SY7299 @ SV643 )
| ~ ( in @ ( ordered_pair @ SY7297 @ SY7298 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7298 @ SY7299 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7297 @ SY7299 ) @ SV468 ) ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4476,plain,
! [SV469: $i] :
( ( ( ~ ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4326]) ).
thf(4477,plain,
! [SV469: $i] :
( ( ( ~ ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4326]) ).
thf(4478,plain,
! [SV470: $i] :
( ( ( ~ ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4327]) ).
thf(4479,plain,
! [SV470: $i] :
( ( ( ~ ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4327]) ).
thf(4480,plain,
! [SV544: $i] :
( ( ( ~ ! [SY7226: $i,SY7227: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SY7226 @ SY7227 ) ) )
= $false )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4328]) ).
thf(4481,plain,
! [SV544: $i] :
( ( ( ~ ( in @ ( sK45_B @ SV544 ) @ SV544 ) )
= $false )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4328]) ).
thf(4482,plain,
! [SV545: $i,SV644: $i] :
( ( ( ( SV644
= ( ordered_pair @ ( sK43_C @ SV644 @ SV545 ) @ ( sK44_SY6449 @ SV644 @ SV545 ) ) )
| ~ ( in @ SV644 @ SV545 ) )
= $true )
| ( ( relation @ SV545 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(4483,plain,
! [SV546: $i] :
( ( ( relation @ SV546 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV546 ) )
= $true )
| ( ( ! [SY7229: $i] : ( relation @ ( relation_dom_restriction @ SV546 @ SY7229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4330]) ).
thf(4484,plain,
! [SV547: $i] :
( ( ( relation @ SV547 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV547 ) )
= $true )
| ( ( ! [SY7230: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SY7230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4485,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 )
| ~ ( is_transitive_in @ SV471 @ SV645 )
| ~ ( is_antisymmetric_in @ SV471 @ SV645 )
| ~ ( is_connected_in @ SV471 @ SV645 )
| ~ ( is_well_founded_in @ SV471 @ SV645 )
| ( well_orders @ SV471 @ SV645 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4486,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
| ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4335]) ).
thf(4487,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) )
| ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4488,plain,
! [SV550: $i] :
( ( ( ~ ( is_reflexive_in @ SV550 @ ( relation_field @ SV550 ) ) )
= $true )
| ( ( reflexive @ SV550 )
= $true )
| ( ( relation @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4339]) ).
thf(4489,plain,
! [SV551: $i] :
( ( ( ~ ( reflexive @ SV551 ) )
= $true )
| ( ( is_reflexive_in @ SV551 @ ( relation_field @ SV551 ) )
= $true )
| ( ( relation @ SV551 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4340]) ).
thf(4490,plain,
! [SV473: $i,SV646: $i] :
( ( ( ~ ( ~ ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) ) )
| ( SV646
= ( relation_dom @ SV473 ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4491,plain,
! [SV473: $i,SV647: $i] :
( ( ( ( SV647
!= ( relation_dom @ SV473 ) )
| ~ ( ~ ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) )
| ~ ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4492,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SV648 @ SV474 )
!= ( sK30_SY6442 @ SV648 @ SV474 ) ) ) )
| ( is_antisymmetric_in @ SV474 @ SV648 ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4493,plain,
! [SV649: $i,SV474: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV474 @ SV649 )
| ! [SY7304: $i,SY7305: $i] :
( ~ ( in @ SY7304 @ SV649 )
| ~ ( in @ SY7305 @ SV649 )
| ~ ( in @ ( ordered_pair @ SY7304 @ SY7305 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7305 @ SY7304 ) @ SV474 )
| ( SY7304 = SY7305 ) ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4494,plain,
! [SV552: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4495,plain,
! [SV553: $i] :
( ( ( ~ ( connected @ SV553 ) )
= $true )
| ( ( ! [SY7231: $i,SY7232: $i] :
( ( SY7231 = SY7232 )
| ~ ( in @ SY7231 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7232 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SY7231 @ SY7232 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7232 @ SY7231 ) @ SV553 ) ) )
= $true )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4496,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
| ~ ( epsilon_transitive @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4497,plain,
! [SV602: $i,SV475: $i,SV625: $i] :
( ( ( ~ ( relation @ SV625 ) )
= $true )
| ( ( ! [SY7288: $i] :
( ~ ( in @ SY7288 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7288 ) @ SV625 )
| ~ ( in @ SY7288 @ SV602 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4498,plain,
! [SV603: $i,SV475: $i,SV626: $i] :
( ( ( ~ ( relation @ SV626 ) )
= $true )
| ( ( ~ ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4499,plain,
! [SV604: $i,SV476: $i,SV627: $i] :
( ( ( ~ ( relation @ SV627 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SV627 )
| ( in @ SV476 @ ( relation_field @ SV627 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4500,plain,
! [SV605: $i,SV476: $i,SV628: $i] :
( ( ( ~ ( relation @ SV628 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SV628 )
| ( in @ SV605 @ ( relation_field @ SV628 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4501,plain,
! [SV650: $i] :
( ( ~ ( empty @ SV650 )
| ~ ( relation @ SV650 )
| ~ ( function @ SV650 )
| ( function @ SV650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(4502,plain,
! [SV651: $i] :
( ( ~ ( empty @ SV651 )
| ~ ( relation @ SV651 )
| ~ ( function @ SV651 )
| ( relation @ SV651 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(4503,plain,
! [SV554: $i] :
( ( ( ~ ( empty @ SV554 ) )
= $true )
| ( ( ~ ( relation @ SV554 ) )
= $true )
| ( ( ~ ( function @ SV554 ) )
= $true )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4355]) ).
thf(4504,plain,
! [SV606: $i,SV555: $i] :
( ( ( ~ ( function @ SV555 )
| ~ ( relation @ SV555 )
| ~ ( relation @ SV606 ) )
= $true )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4505,plain,
! [SV607: $i,SV556: $i] :
( ( ( ~ ( function @ SV556 )
| ~ ( relation @ SV556 )
| ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4506,plain,
! [SV608: $i,SV477: $i,SV629: $i] :
( ( ( ~ ( relation @ SV629 ) )
= $true )
| ( ( ~ ( in @ SV477 @ SV608 )
| ~ ( in @ SV477 @ ( relation_rng @ SV629 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4358]) ).
thf(4507,plain,
! [SV477: $i] :
( ( ! [SY7059: $i,SY7060: $i] :
( ~ ( relation @ SY7060 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7059 @ SY7060 ) ) )
| ( in @ SV477 @ SY7059 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4359]) ).
thf(4508,plain,
! [SV477: $i] :
( ( ! [SY7061: $i,SY7062: $i] :
( ~ ( relation @ SY7062 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SY7061 @ SY7062 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7062 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4360]) ).
thf(4509,plain,
! [SV478: $i,SV652: $i] :
( ( ( ! [SY7306: $i] :
( ~ ( relation @ SY7306 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SY7306 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SY7306 @ SV652 @ SV478 ) ) @ SY7306 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SY7306 @ SV652 @ SV478 ) ) @ SY7306 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SY7306 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY7306 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SY7306 @ SV652 @ SV478 ) ) @ SY7306 ) ) ) )
| ( SY7306
= ( relation_dom_restriction @ SV478 @ SV652 ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4510,plain,
! [SV653: $i,SV478: $i] :
( ( ( ! [SY7307: $i] :
( ~ ( relation @ SY7307 )
| ( SY7307
!= ( relation_dom_restriction @ SV478 @ SV653 ) )
| ~ ( ~ ! [SY7308: $i,SY7309: $i] :
( ~ ( in @ SY7308 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7308 @ SY7309 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7308 @ SY7309 ) @ SY7307 ) )
| ~ ~ ( ~ ! [SY7310: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY7310 @ SX4 ) @ SY7307 )
| ( in @ SY7310 @ SV653 ) )
| ~ ! [SY7071: $i,SY7072: $i] :
( ~ ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SY7307 )
| ( in @ ( ordered_pair @ SY7071 @ SY7072 ) @ SV478 ) ) ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4511,plain,
! [SV557: $i,SV609: $i] :
( ( ( ~ ( function @ SV609 ) )
= $true )
| ( ( ~ ( relation @ SV609 ) )
= $true )
| ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 )
| ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4512,plain,
! [SV558: $i,SV610: $i] :
( ( ( ~ ( function @ SV610 ) )
= $true )
| ( ( ~ ( relation @ SV610 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4513,plain,
! [SV479: $i,SV654: $i] :
( ( ( ~ ( ~ ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) ) )
| ( SV654
= ( relation_rng @ SV479 ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4514,plain,
! [SV479: $i,SV655: $i] :
( ( ( ( SV655
!= ( relation_rng @ SV479 ) )
| ~ ( ~ ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) )
| ~ ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(4515,plain,
! [SV480: $i,SV527: $i] :
( ( ( ! [SY7207: $i] :
( ~ ( relation @ SY7207 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SY7207 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SY7207 @ SV527 @ SV480 ) ) @ SY7207 ) ) ) )
| ( SY7207
= ( relation_rng_restriction @ SV480 @ SV527 ) ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4369]) ).
thf(4516,plain,
! [SV527: $i,SV480: $i] :
( ( ( ! [SY7208: $i] :
( ~ ( relation @ SY7208 )
| ( SY7208
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7209: $i,SY7210: $i] :
( ~ ( in @ SY7210 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7209 @ SY7210 ) @ SY7208 ) )
| ~ ~ ( ~ ! [SY7084: $i,SY7085: $i] :
( ~ ( in @ ( ordered_pair @ SY7084 @ SY7085 ) @ SY7208 )
| ( in @ SY7085 @ SV480 ) )
| ~ ! [SY7213: $i,SY7214: $i] :
( ~ ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SY7208 )
| ( in @ ( ordered_pair @ SY7213 @ SY7214 ) @ SV527 ) ) ) ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4370]) ).
thf(4517,plain,
! [SV561: $i] :
( ( ( ( ( relation_dom @ SV561 )
!= empty_set ) )
= $true )
| ( ( SV561 = empty_set )
= $true )
| ( ( relation @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(4518,plain,
! [SV562: $i] :
( ( ( ( ( relation_rng @ SV562 )
!= empty_set ) )
= $true )
| ( ( SV562 = empty_set )
= $true )
| ( ( relation @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4372]) ).
thf(4519,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( relation @ SV656 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
| ( SV481 = SV656 ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(4520,plain,
! [SV481: $i,SV657: $i] :
( ( ( ~ ( relation @ SV657 )
| ( SV481 != SV657 )
| ~ ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4521,plain,
! [SV482: $i] :
( ( ( one_to_one @ SV482 )
= $false )
| ( ( ~ ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4522,plain,
! [SV563: $i] :
( ( ( function @ SV563 )
= $false )
| ( ( ~ ( relation @ SV563 ) )
= $true )
| ( ( ~ ( one_to_one @ SV563 )
| ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4523,plain,
! [SV564: $i] :
( ( ( function @ SV564 )
= $false )
| ( ( ~ ( relation @ SV564 ) )
= $true )
| ( ( ~ ( one_to_one @ SV564 )
| ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4524,plain,
! [SV528: $i,SV630: $i,SV483: $i,SV658: $i] :
( ( ~ ( relation @ SV658 )
| ~ ( in @ SV483 @ SV630 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4378]) ).
thf(4525,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4379]) ).
thf(4526,plain,
! [SV528: $i,SV483: $i] :
( ( ~ ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4379]) ).
thf(4527,plain,
! [SV565: $i] :
( ( ( function @ SV565 )
= $false )
| ( ( ~ ( relation @ SV565 ) )
= $true )
| ( ( function @ ( function_inverse @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4528,plain,
! [SV566: $i] :
( ( ( function @ SV566 )
= $false )
| ( ( ~ ( relation @ SV566 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4529,plain,
! [SV484: $i,SV611: $i,SV631: $i] :
( ( ( ~ ( function @ SV631 )
| ~ ( relation @ SV631 ) )
= $true )
| ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4530,plain,
! [SV484: $i] :
( ( ! [SY7114: $i,SY7115: $i] :
( ~ ( function @ SY7115 )
| ~ ( relation @ SY7115 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7114 ) @ SY7115 )
| ( SY7114
= ( apply @ SY7115 @ SV484 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4383]) ).
thf(4531,plain,
! [SV484: $i] :
( ( ! [SY7116: $i,SY7117: $i] :
( ~ ( function @ SY7117 )
| ~ ( relation @ SY7117 )
| ~ ( in @ ( ordered_pair @ SV484 @ SY7116 ) @ SY7117 )
| ( in @ SV484 @ ( relation_dom @ SY7117 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4384]) ).
thf(4532,plain,
! [SV612: $i,SV485: $i,SV632: $i] :
( ( ( ~ ( relation @ SV632 ) )
= $true )
| ( ( ~ ( in @ SV485 @ SV612 )
| ~ ( in @ SV485 @ ( relation_dom @ SV632 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4533,plain,
! [SV485: $i] :
( ( ! [SY7120: $i,SY7121: $i] :
( ~ ( relation @ SY7121 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7121 @ SY7120 ) ) )
| ( in @ SV485 @ SY7120 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4386]) ).
thf(4534,plain,
! [SV485: $i] :
( ( ! [SY7122: $i,SY7123: $i] :
( ~ ( relation @ SY7123 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7123 @ SY7122 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7123 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4387]) ).
thf(4535,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_C @ SV659 @ SV486 ) @ SV659 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 ) )
| ( is_reflexive_in @ SV486 @ SV659 ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(4536,plain,
! [SV660: $i,SV486: $i] :
( ( ( ~ ( is_reflexive_in @ SV486 @ SV660 )
| ! [SY7322: $i] :
( ~ ( in @ SY7322 @ SV660 )
| ( in @ ( ordered_pair @ SY7322 @ SY7322 ) @ SV486 ) ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(4537,plain,
! [SV567: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) ) )
= $true )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4538,plain,
! [SV568: $i] :
( ( ( ~ ( transitive @ SV568 ) )
= $true )
| ( ( ! [SY7237: $i,SY7238: $i,SY7239: $i] :
( ~ ( in @ ( ordered_pair @ SY7237 @ SY7238 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7238 @ SY7239 ) @ SV568 )
| ( in @ ( ordered_pair @ SY7237 @ SY7239 ) @ SV568 ) ) )
= $true )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4391]) ).
thf(4539,plain,
! [SV613: $i,SV487: $i,SV633: $i] :
( ( ( ~ ( relation @ SV633 ) )
= $true )
| ( ( ! [SY7290: $i] :
( ~ ( in @ SY7290 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SY7290 @ SV487 ) @ SV633 )
| ~ ( in @ SY7290 @ SV613 ) )
| ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4392]) ).
thf(4540,plain,
! [SV614: $i,SV487: $i,SV634: $i] :
( ( ( ~ ( relation @ SV634 ) )
= $true )
| ( ( ~ ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4541,plain,
! [SV661: $i,SV488: $i] :
( ( ( ~ ( ~ ! [SY7323: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7323 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SY7323 @ ( sK35_C @ SV661 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) ) )
| ( is_well_founded_in @ SV488 @ SV661 ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(4542,plain,
! [SV662: $i,SV488: $i] :
( ( ( ~ ( is_well_founded_in @ SV488 @ SV662 )
| ! [SY7324: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) ) @ SY7324 )
| ~ ( in @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) @ SY7324 ) )
| ( SY7324 = empty_set )
| ~ ( subset @ SY7324 @ SV662 ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(4543,plain,
! [SV489: $i,SV663: $i] :
( ( ( ~ ( relation @ SV663 )
| ~ ( subset @ SV489 @ SV663 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SV663 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(4544,plain,
! [SV489: $i,SV664: $i] :
( ( ( ~ ( relation @ SV664 )
| ~ ( subset @ SV489 @ SV664 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SV664 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(4545,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
| ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4398]) ).
thf(4546,plain,
! [SV569: $i] :
( ( ( ~ ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) ) )
= $true )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4547,plain,
! [SV570: $i] :
( ( ( ~ ( reflexive @ SV570 ) )
= $true )
| ( ( ! [SY7240: $i] :
( ~ ( in @ SY7240 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SY7240 @ SY7240 ) @ SV570 ) ) )
= $true )
| ( ( relation @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4548,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) )
| ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4549,plain,
! [SV571: $i] :
( ( ( ~ ( is_well_founded_in @ SV571 @ ( relation_field @ SV571 ) ) )
= $true )
| ( ( well_founded_relation @ SV571 )
= $true )
| ( ( relation @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4405]) ).
thf(4550,plain,
! [SV572: $i] :
( ( ( ~ ( well_founded_relation @ SV572 ) )
= $true )
| ( ( is_well_founded_in @ SV572 @ ( relation_field @ SV572 ) )
= $true )
| ( ( relation @ SV572 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4551,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 ) )
| ( is_connected_in @ SV491 @ SV665 ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(4552,plain,
! [SV666: $i,SV491: $i] :
( ( ( ~ ( is_connected_in @ SV491 @ SV666 )
| ! [SY7325: $i,SY7326: $i] :
( ( SY7325 = SY7326 )
| ~ ( in @ SY7325 @ SV666 )
| ~ ( in @ SY7326 @ SV666 )
| ( in @ ( ordered_pair @ SY7325 @ SY7326 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7326 @ SY7325 ) @ SV491 ) ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(4553,plain,
! [SV573: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
| ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(4554,plain,
! [SV574: $i] :
( ( ( ~ ( antisymmetric @ SV574 ) )
= $true )
| ( ( ! [SY7241: $i,SY7242: $i] :
( ~ ( in @ ( ordered_pair @ SY7241 @ SY7242 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7242 @ SY7241 ) @ SV574 )
| ( SY7241 = SY7242 ) ) )
= $true )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(4555,plain,
! [SV492: $i,SV615: $i,SV635: $i] :
( ( ( ~ ( function @ SV635 )
| ~ ( relation @ SV635 ) )
= $true )
| ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4411]) ).
thf(4556,plain,
! [SV492: $i] :
( ( ! [SY7148: $i,SY7149: $i] :
( ~ ( function @ SY7149 )
| ~ ( relation @ SY7149 )
| ~ ( in @ SY7148 @ ( relation_dom @ ( relation_dom_restriction @ SY7149 @ SV492 ) ) )
| ( in @ SY7148 @ ( relation_dom @ SY7149 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4557,plain,
! [SV492: $i] :
( ( ! [SY7150: $i,SY7151: $i] :
( ~ ( function @ SY7151 )
| ~ ( relation @ SY7151 )
| ~ ( in @ SY7150 @ ( relation_dom @ ( relation_dom_restriction @ SY7151 @ SV492 ) ) )
| ( in @ SY7150 @ SV492 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4413]) ).
thf(4558,plain,
! [SV575: $i] :
( ( ( ( ( relation_dom @ SV575 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV575 )
= empty_set )
= $true )
| ( ( relation @ SV575 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4559,plain,
! [SV576: $i] :
( ( ( ( ( relation_rng @ SV576 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV576 )
= empty_set )
= $true )
| ( ( relation @ SV576 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4560,plain,
! [SV493: $i] :
( ( ( ~ ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4418]) ).
thf(4561,plain,
! [SV493: $i] :
( ( ( ~ ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4418]) ).
thf(4562,plain,
! [SV494: $i,SV577: $i] :
( ( ( ~ ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) )
| ~ ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4419]) ).
thf(4563,plain,
! [SV616: $i,SV495: $i,SV636: $i] :
( ( ( ~ ( relation @ SV636 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SV636 )
| ( in @ SV495 @ ( relation_dom @ SV636 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4564,plain,
! [SV617: $i,SV495: $i,SV637: $i] :
( ( ( ~ ( relation @ SV637 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SV637 )
| ( in @ SV617 @ ( relation_rng @ SV637 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(4565,plain,
! [SV618: $i,SV578: $i] :
( ( ( ~ ( empty @ SV578 ) )
= $true )
| ( ( ~ ( relation @ SV618 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV618 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(4566,plain,
! [SV619: $i,SV579: $i] :
( ( ( ~ ( empty @ SV579 ) )
= $true )
| ( ( ~ ( relation @ SV619 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV619 @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(4567,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( relation @ SV667 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
| ( SV667
= ( relation_inverse @ SV496 ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(4568,plain,
! [SV496: $i,SV668: $i] :
( ( ( ~ ( relation @ SV668 )
| ( SV668
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(4569,plain,
! [SV580: $i,SV620: $i] :
( ( ( relation @ SV620 )
= $false )
| ( ( ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
| ( SV620
= ( identity_relation @ SV580 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4570,plain,
! [SV581: $i,SV621: $i] :
( ( ( relation @ SV621 )
= $false )
| ( ( ( SV621
!= ( identity_relation @ SV581 ) )
| ~ ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(4571,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( relation @ SV669 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
| ( subset @ SV497 @ SV669 ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4430]) ).
thf(4572,plain,
! [SV497: $i,SV670: $i] :
( ( ( ~ ( relation @ SV670 )
| ~ ( subset @ SV497 @ SV670 )
| ! [SY7331: $i,SY7332: $i] :
( ~ ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV670 ) ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(4573,plain,
! [SV582: $i] :
( ( ( ~ ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(4574,plain,
! [SV583: $i] :
( ( ( ~ ( well_founded_relation @ SV583 ) )
= $true )
| ( ( ! [SY7262: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SY7262 @ SV583 ) ) @ SY7262 )
| ~ ( in @ ( sK38_C @ SY7262 @ SV583 ) @ SY7262 ) )
| ( SY7262 = empty_set )
| ~ ( subset @ SY7262 @ ( relation_field @ SV583 ) ) ) )
= $true )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4575,plain,
! [SV498: $i] :
( ( ( ~ ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4576,plain,
! [SV498: $i] :
( ( ( ~ ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4577,plain,
! [SV584: $i] :
( ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 )
| ~ ( connected @ SV584 )
| ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4578,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(4579,plain,
! [SV671: $i] :
( ( ~ ( relation @ SV671 )
| ~ ( well_ordering @ SV671 )
| ( well_founded_relation @ SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4437]) ).
thf(4580,plain,
! [SV585: $i] :
( ( ( function @ SV585 )
= $false )
| ( ( ~ ( relation @ SV585 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
| ( one_to_one @ SV585 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4438]) ).
thf(4581,plain,
! [SV586: $i] :
( ( ( function @ SV586 )
= $false )
| ( ( ~ ( relation @ SV586 ) )
= $true )
| ( ( ~ ( one_to_one @ SV586 )
| ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4439]) ).
thf(4582,plain,
! [SV499: $i,SV672: $i] :
( ( ( ! [SY7333: $i] :
( ~ ( ~ ( ! [SY7334: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7333 @ SV672 @ SV499 ) @ SY7334 ) @ SV499 )
| ~ ( in @ SY7334 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SY7333 @ SV672 @ SV499 ) @ SY7333 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SY7333 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SY7333 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SY7333 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SY7333 @ SV672 @ SV499 ) @ SY7333 ) ) )
| ( SY7333
= ( relation_inverse_image @ SV499 @ SV672 ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(4583,plain,
! [SV673: $i,SV499: $i] :
( ( ( ! [SY7335: $i] :
( ( SY7335
!= ( relation_inverse_image @ SV499 @ SV673 ) )
| ~ ( ~ ! [SY7336: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7336 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7336 @ SY7335 ) )
| ~ ! [SY7338: $i] :
( ~ ( in @ SY7338 @ SY7335 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7338 @ ( sK46_E @ SY7338 @ SY7335 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7338 @ SY7335 @ SV673 @ SV499 ) @ SV673 ) ) ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(4584,plain,
! [SV589: $i] :
( ( ( ~ ( antisymmetric @ SV589 ) )
= $true )
| ( ( is_antisymmetric_in @ SV589 @ ( relation_field @ SV589 ) )
= $true )
| ( ( relation @ SV589 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(4585,plain,
! [SV590: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV590 @ ( relation_field @ SV590 ) ) )
= $true )
| ( ( antisymmetric @ SV590 )
= $true )
| ( ( relation @ SV590 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(4586,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( function @ SV622 ) )
= $true )
| ( ( ~ ( relation @ SV622 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 )
| ( SV622
= ( identity_relation @ SV591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(4587,plain,
! [SV674: $i] :
( ( ! [SY7339: $i] :
( ~ ( function @ SY7339 )
| ~ ( relation @ SY7339 )
| ( SY7339
!= ( identity_relation @ SV674 ) )
| ! [SY7340: $i] :
( ~ ( in @ SY7340 @ SV674 )
| ( ( apply @ SY7339 @ SY7340 )
= SY7340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4447]) ).
thf(4588,plain,
! [SV675: $i] :
( ( ! [SY7341: $i] :
( ~ ( function @ SY7341 )
| ~ ( relation @ SY7341 )
| ( SY7341
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SY7341 )
= SV675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(4589,plain,
! [SV623: $i,SV592: $i] :
( ( ( ~ ( empty @ SV592 ) )
= $true )
| ( ( ~ ( relation @ SV623 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV592 @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4590,plain,
! [SV624: $i,SV593: $i] :
( ( ( ~ ( empty @ SV593 ) )
= $true )
| ( ( ~ ( relation @ SV624 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV593 @ SV624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4450]) ).
thf(4591,plain,
! [SV594: $i] :
( ( ( ~ ( connected @ SV594 ) )
= $true )
| ( ( is_connected_in @ SV594 @ ( relation_field @ SV594 ) )
= $true )
| ( ( relation @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(4592,plain,
! [SV595: $i] :
( ( ( ~ ( is_connected_in @ SV595 @ ( relation_field @ SV595 ) ) )
= $true )
| ( ( connected @ SV595 )
= $true )
| ( ( relation @ SV595 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(4593,plain,
! [SV596: $i] :
( ( ( ~ ( function @ SV596 ) )
= $true )
| ( ( ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( one_to_one @ SV596 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(4594,plain,
! [SV597: $i] :
( ( ( ~ ( function @ SV597 ) )
= $true )
| ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( one_to_one @ SV597 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4595,plain,
! [SV509: $i,SV433: $i] :
( ( ( subset @ SV433 @ ( relation_rng @ SV509 ) )
= $false )
| ( ( ( relation_image @ SV509 @ ( relation_inverse_image @ SV509 @ SV433 ) )
= SV433 )
= $true )
| ( ( function @ SV509 )
= $false )
| ( ( relation @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(4596,plain,
! [SV436: $i,SV511: $i] :
( ( ( ( relation_inverse_image @ SV511 @ SV436 )
= empty_set )
= $false )
| ( ( SV436 = empty_set )
= $true )
| ( ( subset @ SV436 @ ( relation_rng @ SV511 ) )
= $false )
| ( ( relation @ SV511 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4458]) ).
thf(4597,plain,
! [SV513: $i,SV439: $i,SV638: $i] :
( ( ( ~ ( function @ SV638 )
| ~ ( relation @ SV638 ) )
= $true )
| ( ( ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) ) )
= $true )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(4598,plain,
! [SV514: $i,SV440: $i,SV639: $i] :
( ( ( ~ ( function @ SV639 )
| ~ ( relation @ SV639 ) )
= $true )
| ( ( ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) ) )
= $true )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(4599,plain,
! [SV537: $i,SV443: $i] :
( ( ( subset @ ( relation_rng @ SV443 ) @ ( relation_dom @ SV537 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV443 @ SV537 ) )
= ( relation_dom @ SV443 ) )
= $true )
| ( ( relation @ SV537 )
= $false )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4600,plain,
! [SV538: $i,SV444: $i] :
( ( ( subset @ ( relation_dom @ SV444 ) @ ( relation_rng @ SV538 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV538 @ SV444 ) )
= ( relation_rng @ SV444 ) )
= $true )
| ( ( relation @ SV538 )
= $false )
| ( ( relation @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4601,plain,
! [SV447: $i,SV532: $i,SV515: $i] :
( ( ( ~ ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) )
= $true )
| ( ( function @ SV532 )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4602,plain,
! [SV533: $i,SV448: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ SV448 ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) )
= $true )
| ( ( function @ SV533 )
= $false )
| ( ( relation @ SV533 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4603,plain,
! [SV540: $i] :
( ( ( is_transitive_in @ SV540 @ ( relation_field @ SV540 ) )
= $false )
| ( ( transitive @ SV540 )
= $true )
| ( ( relation @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4604,plain,
! [SV541: $i] :
( ( ( transitive @ SV541 )
= $false )
| ( ( is_transitive_in @ SV541 @ ( relation_field @ SV541 ) )
= $true )
| ( ( relation @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4605,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ~ ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) ) )
| ( SV676
= ( relation_image @ SV467 @ SV640 ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4470]) ).
thf(4606,plain,
! [SV641: $i,SV467: $i,SV677: $i] :
( ( ( ( SV677
!= ( relation_image @ SV467 @ SV641 ) )
| ~ ( ~ ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) )
| ~ ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4471]) ).
thf(4607,plain,
! [SV542: $i] :
( ( ( relation @ SV542 )
= $false )
| ( ( function @ SV542 )
= $false )
| ( ( ! [SY7224: $i] : ( function @ ( relation_dom_restriction @ SV542 @ SY7224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(4608,plain,
! [SV543: $i] :
( ( ( relation @ SV543 )
= $false )
| ( ( function @ SV543 )
= $false )
| ( ( ! [SY7225: $i] : ( relation @ ( relation_dom_restriction @ SV543 @ SY7225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4609,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(4610,plain,
! [SV643: $i,SV468: $i] :
( ( ( ~ ( is_transitive_in @ SV468 @ SV643 ) )
= $true )
| ( ( ! [SY7297: $i,SY7298: $i,SY7299: $i] :
( ~ ( in @ SY7297 @ SV643 )
| ~ ( in @ SY7298 @ SV643 )
| ~ ( in @ SY7299 @ SV643 )
| ~ ( in @ ( ordered_pair @ SY7297 @ SY7298 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7298 @ SY7299 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7297 @ SY7299 ) @ SV468 ) ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4611,plain,
! [SV469: $i] :
( ( ( ! [SY7012: $i,SY7013: $i] :
( ~ ( ~ ( ! [SY7014: $i] :
( ~ ( in @ SY7014 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7014 @ SY7012 )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ SY7014 ) ) )
| ~ ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) @ SY7012 ) )
| ( ( sK56_D @ SY7013 @ SY7012 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7013 @ SY7012 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7013 @ SY7012 @ SV469 ) @ SY7013 ) ) )
| ( SY7013
= ( relation_image @ SV469 @ SY7012 ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4476]) ).
thf(4612,plain,
! [SV469: $i] :
( ( ( ! [SY7015: $i,SY7016: $i] :
( ( SY7016
!= ( relation_image @ SV469 @ SY7015 ) )
| ~ ( ~ ! [SY7017: $i] :
( ! [SY7018: $i] :
( ~ ( in @ SY7018 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7018 @ SY7015 )
| ( SY7017
!= ( apply @ SV469 @ SY7018 ) ) )
| ( in @ SY7017 @ SY7016 ) )
| ~ ! [SY7019: $i] :
( ~ ( in @ SY7019 @ SY7016 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) @ SY7015 ) )
| ( SY7019
!= ( apply @ SV469 @ ( sK55_E @ SY7019 @ SY7016 @ SY7015 @ SV469 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4477]) ).
thf(4613,plain,
! [SV470: $i] :
( ( ( ! [SY7020: $i,SY7021: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ~ ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) ) @ SY7020 )
| ( in @ ( sK52_D @ SY7021 @ SY7020 @ SV470 ) @ SY7021 ) ) ) )
| ( SY7021
= ( relation_inverse_image @ SV470 @ SY7020 ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4478]) ).
thf(4614,plain,
! [SV470: $i] :
( ( ( ! [SY7022: $i,SY7023: $i] :
( ( SY7023
!= ( relation_inverse_image @ SV470 @ SY7022 ) )
| ~ ( ~ ! [SY7024: $i] :
( ~ ( in @ SY7024 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7024 ) @ SY7022 )
| ( in @ SY7024 @ SY7023 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7023 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7026: $i] :
( ~ ( in @ SY7026 @ SY7023 )
| ( in @ ( apply @ SV470 @ SY7026 ) @ SY7022 ) ) ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4479]) ).
thf(4615,plain,
! [SV544: $i] :
( ( ( ! [SY7226: $i,SY7227: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SY7226 @ SY7227 ) ) )
= $true )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4480]) ).
thf(4616,plain,
! [SV544: $i] :
( ( ( in @ ( sK45_B @ SV544 ) @ SV544 )
= $true )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4481]) ).
thf(4617,plain,
! [SV545: $i,SV644: $i] :
( ( ( SV644
= ( ordered_pair @ ( sK43_C @ SV644 @ SV545 ) @ ( sK44_SY6449 @ SV644 @ SV545 ) ) )
= $true )
| ( ( ~ ( in @ SV644 @ SV545 ) )
= $true )
| ( ( relation @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(4618,plain,
! [SV546: $i] :
( ( ( relation_empty_yielding @ SV546 )
= $false )
| ( ( relation @ SV546 )
= $false )
| ( ( ! [SY7229: $i] : ( relation @ ( relation_dom_restriction @ SV546 @ SY7229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4619,plain,
! [SV547: $i] :
( ( ( relation_empty_yielding @ SV547 )
= $false )
| ( ( relation @ SV547 )
= $false )
| ( ( ! [SY7230: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SY7230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4620,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 )
| ~ ( is_transitive_in @ SV471 @ SV645 )
| ~ ( is_antisymmetric_in @ SV471 @ SV645 )
| ~ ( is_connected_in @ SV471 @ SV645 )
| ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(4621,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4622,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4623,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4487]) ).
thf(4624,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4487]) ).
thf(4625,plain,
! [SV550: $i] :
( ( ( is_reflexive_in @ SV550 @ ( relation_field @ SV550 ) )
= $false )
| ( ( reflexive @ SV550 )
= $true )
| ( ( relation @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4626,plain,
! [SV551: $i] :
( ( ( reflexive @ SV551 )
= $false )
| ( ( is_reflexive_in @ SV551 @ ( relation_field @ SV551 ) )
= $true )
| ( ( relation @ SV551 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4627,plain,
! [SV473: $i,SV646: $i] :
( ( ( ~ ( ~ ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) ) ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4490]) ).
thf(4628,plain,
! [SV473: $i,SV647: $i] :
( ( ( ( SV647
!= ( relation_dom @ SV473 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) )
| ~ ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4491]) ).
thf(4629,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SV648 @ SV474 )
!= ( sK30_SY6442 @ SV648 @ SV474 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(4630,plain,
! [SV649: $i,SV474: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV474 @ SV649 ) )
= $true )
| ( ( ! [SY7304: $i,SY7305: $i] :
( ~ ( in @ SY7304 @ SV649 )
| ~ ( in @ SY7305 @ SV649 )
| ~ ( in @ ( ordered_pair @ SY7304 @ SY7305 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7305 @ SY7304 ) @ SV474 )
| ( SY7304 = SY7305 ) ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(4631,plain,
! [SV552: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4632,plain,
! [SV553: $i] :
( ( ( connected @ SV553 )
= $false )
| ( ( ! [SY7231: $i,SY7232: $i] :
( ( SY7231 = SY7232 )
| ~ ( in @ SY7231 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7232 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SY7231 @ SY7232 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7232 @ SY7231 ) @ SV553 ) ) )
= $true )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4633,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4496]) ).
thf(4634,plain,
( ( ~ ( epsilon_transitive @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4496]) ).
thf(4635,plain,
! [SV602: $i,SV475: $i,SV625: $i] :
( ( ( relation @ SV625 )
= $false )
| ( ( ! [SY7288: $i] :
( ~ ( in @ SY7288 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7288 ) @ SV625 )
| ~ ( in @ SY7288 @ SV602 ) )
| ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4636,plain,
! [SV603: $i,SV475: $i,SV626: $i] :
( ( ( relation @ SV626 )
= $false )
| ( ( ~ ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4637,plain,
! [SV604: $i,SV476: $i,SV627: $i] :
( ( ( relation @ SV627 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SV627 )
| ( in @ SV476 @ ( relation_field @ SV627 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4638,plain,
! [SV605: $i,SV476: $i,SV628: $i] :
( ( ( relation @ SV628 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SV628 )
| ( in @ SV605 @ ( relation_field @ SV628 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4639,plain,
! [SV650: $i] :
( ( ( ~ ( empty @ SV650 )
| ~ ( relation @ SV650 )
| ~ ( function @ SV650 ) )
= $true )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(4640,plain,
! [SV651: $i] :
( ( ( ~ ( empty @ SV651 )
| ~ ( relation @ SV651 )
| ~ ( function @ SV651 ) )
= $true )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(4641,plain,
! [SV554: $i] :
( ( ( empty @ SV554 )
= $false )
| ( ( ~ ( relation @ SV554 ) )
= $true )
| ( ( ~ ( function @ SV554 ) )
= $true )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(4642,plain,
! [SV606: $i,SV555: $i] :
( ( ( ~ ( function @ SV555 )
| ~ ( relation @ SV555 ) )
= $true )
| ( ( ~ ( relation @ SV606 ) )
= $true )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4643,plain,
! [SV607: $i,SV556: $i] :
( ( ( ~ ( function @ SV556 )
| ~ ( relation @ SV556 ) )
= $true )
| ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4644,plain,
! [SV608: $i,SV477: $i,SV629: $i] :
( ( ( relation @ SV629 )
= $false )
| ( ( ~ ( in @ SV477 @ SV608 )
| ~ ( in @ SV477 @ ( relation_rng @ SV629 ) )
| ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4506]) ).
thf(4645,plain,
! [SV678: $i,SV477: $i] :
( ( ! [SY7346: $i] :
( ~ ( relation @ SY7346 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SY7346 ) ) )
| ( in @ SV477 @ SV678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4507]) ).
thf(4646,plain,
! [SV679: $i,SV477: $i] :
( ( ! [SY7347: $i] :
( ~ ( relation @ SY7347 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SY7347 ) ) )
| ( in @ SV477 @ ( relation_rng @ SY7347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4508]) ).
thf(4647,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( relation @ SV680 )
| ~ ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
| ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4509]) ).
thf(4648,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( ~ ( relation @ SV681 )
| ( SV681
!= ( relation_dom_restriction @ SV478 @ SV653 ) )
| ~ ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4510]) ).
thf(4649,plain,
! [SV557: $i,SV609: $i] :
( ( ( function @ SV609 )
= $false )
| ( ( ~ ( relation @ SV609 ) )
= $true )
| ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 )
| ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4650,plain,
! [SV558: $i,SV610: $i] :
( ( ( function @ SV610 )
= $false )
| ( ( ~ ( relation @ SV610 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(4651,plain,
! [SV479: $i,SV654: $i] :
( ( ( ~ ( ~ ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) ) ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(4652,plain,
! [SV479: $i,SV655: $i] :
( ( ( ( SV655
!= ( relation_rng @ SV479 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) )
| ~ ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(4653,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( relation @ SV682 )
| ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
| ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4515]) ).
thf(4654,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ( relation @ SV683 )
| ( SV683
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4516]) ).
thf(4655,plain,
! [SV561: $i] :
( ( ( ( relation_dom @ SV561 )
= empty_set )
= $false )
| ( ( SV561 = empty_set )
= $true )
| ( ( relation @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4656,plain,
! [SV562: $i] :
( ( ( ( relation_rng @ SV562 )
= empty_set )
= $false )
| ( ( SV562 = empty_set )
= $true )
| ( ( relation @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(4657,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( relation @ SV656 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
| ( SV481 = SV656 ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4658,plain,
! [SV481: $i,SV657: $i] :
( ( ( ~ ( relation @ SV657 ) )
= $true )
| ( ( ( SV481 != SV657 )
| ~ ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4520]) ).
thf(4659,plain,
! [SV482: $i] :
( ( ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) )
| ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4660,plain,
! [SV563: $i] :
( ( ( relation @ SV563 )
= $false )
| ( ( function @ SV563 )
= $false )
| ( ( ~ ( one_to_one @ SV563 )
| ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(4661,plain,
! [SV564: $i] :
( ( ( relation @ SV564 )
= $false )
| ( ( function @ SV564 )
= $false )
| ( ( ~ ( one_to_one @ SV564 )
| ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4662,plain,
! [SV528: $i,SV630: $i,SV483: $i,SV658: $i] :
( ( ( ~ ( relation @ SV658 ) )
= $true )
| ( ( ~ ( in @ SV483 @ SV630 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4663,plain,
! [SV528: $i,SV483: $i] :
( ( ! [SY7217: $i,SY7218: $i] :
( ~ ( relation @ SY7218 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7217 ) @ SY7218 ) )
| ( in @ SV483 @ SY7217 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4525]) ).
thf(4664,plain,
! [SV528: $i,SV483: $i] :
( ( ! [SY7219: $i,SY7220: $i] :
( ~ ( relation @ SY7220 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SY7219 ) @ SY7220 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7220 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4526]) ).
thf(4665,plain,
! [SV565: $i] :
( ( ( relation @ SV565 )
= $false )
| ( ( function @ SV565 )
= $false )
| ( ( function @ ( function_inverse @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(4666,plain,
! [SV566: $i] :
( ( ( relation @ SV566 )
= $false )
| ( ( function @ SV566 )
= $false )
| ( ( relation @ ( function_inverse @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(4667,plain,
! [SV484: $i,SV611: $i,SV631: $i] :
( ( ( ~ ( function @ SV631 ) )
= $true )
| ( ( ~ ( relation @ SV631 ) )
= $true )
| ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(4668,plain,
! [SV684: $i,SV484: $i] :
( ( ! [SY7360: $i] :
( ~ ( function @ SY7360 )
| ~ ( relation @ SY7360 )
| ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SY7360 )
| ( SV684
= ( apply @ SY7360 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4530]) ).
thf(4669,plain,
! [SV685: $i,SV484: $i] :
( ( ! [SY7361: $i] :
( ~ ( function @ SY7361 )
| ~ ( relation @ SY7361 )
| ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SY7361 )
| ( in @ SV484 @ ( relation_dom @ SY7361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(4670,plain,
! [SV612: $i,SV485: $i,SV632: $i] :
( ( ( relation @ SV632 )
= $false )
| ( ( ~ ( in @ SV485 @ SV612 )
| ~ ( in @ SV485 @ ( relation_dom @ SV632 ) )
| ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4671,plain,
! [SV686: $i,SV485: $i] :
( ( ! [SY7362: $i] :
( ~ ( relation @ SY7362 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7362 @ SV686 ) ) )
| ( in @ SV485 @ SV686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4533]) ).
thf(4672,plain,
! [SV687: $i,SV485: $i] :
( ( ! [SY7363: $i] :
( ~ ( relation @ SY7363 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SY7363 @ SV687 ) ) )
| ( in @ SV485 @ ( relation_dom @ SY7363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4534]) ).
thf(4673,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_C @ SV659 @ SV486 ) @ SV659 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 ) ) )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(4674,plain,
! [SV660: $i,SV486: $i] :
( ( ( ~ ( is_reflexive_in @ SV486 @ SV660 ) )
= $true )
| ( ( ! [SY7322: $i] :
( ~ ( in @ SY7322 @ SV660 )
| ( in @ ( ordered_pair @ SY7322 @ SY7322 ) @ SV486 ) ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(4675,plain,
! [SV567: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(4676,plain,
! [SV568: $i] :
( ( ( transitive @ SV568 )
= $false )
| ( ( ! [SY7237: $i,SY7238: $i,SY7239: $i] :
( ~ ( in @ ( ordered_pair @ SY7237 @ SY7238 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7238 @ SY7239 ) @ SV568 )
| ( in @ ( ordered_pair @ SY7237 @ SY7239 ) @ SV568 ) ) )
= $true )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(4677,plain,
! [SV613: $i,SV487: $i,SV633: $i] :
( ( ( relation @ SV633 )
= $false )
| ( ( ! [SY7290: $i] :
( ~ ( in @ SY7290 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SY7290 @ SV487 ) @ SV633 )
| ~ ( in @ SY7290 @ SV613 ) )
| ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4678,plain,
! [SV614: $i,SV487: $i,SV634: $i] :
( ( ( relation @ SV634 )
= $false )
| ( ( ~ ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4679,plain,
! [SV661: $i,SV488: $i] :
( ( ( ~ ( ~ ! [SY7323: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7323 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SY7323 @ ( sK35_C @ SV661 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(4680,plain,
! [SV662: $i,SV488: $i] :
( ( ( ~ ( is_well_founded_in @ SV488 @ SV662 ) )
= $true )
| ( ( ! [SY7324: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) ) @ SY7324 )
| ~ ( in @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) @ SY7324 ) )
| ( SY7324 = empty_set )
| ~ ( subset @ SY7324 @ SV662 ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4681,plain,
! [SV489: $i,SV663: $i] :
( ( ( ~ ( relation @ SV663 ) )
= $true )
| ( ( ~ ( subset @ SV489 @ SV663 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SV663 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(4682,plain,
! [SV489: $i,SV664: $i] :
( ( ( ~ ( relation @ SV664 ) )
= $true )
| ( ( ~ ( subset @ SV489 @ SV664 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SV664 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4683,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4545]) ).
thf(4684,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4545]) ).
thf(4685,plain,
! [SV569: $i] :
( ( ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
= $false )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4686,plain,
! [SV570: $i] :
( ( ( reflexive @ SV570 )
= $false )
| ( ( ! [SY7240: $i] :
( ~ ( in @ SY7240 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SY7240 @ SY7240 ) @ SV570 ) ) )
= $true )
| ( ( relation @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4687,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4548]) ).
thf(4688,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4548]) ).
thf(4689,plain,
! [SV571: $i] :
( ( ( is_well_founded_in @ SV571 @ ( relation_field @ SV571 ) )
= $false )
| ( ( well_founded_relation @ SV571 )
= $true )
| ( ( relation @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4549]) ).
thf(4690,plain,
! [SV572: $i] :
( ( ( well_founded_relation @ SV572 )
= $false )
| ( ( is_well_founded_in @ SV572 @ ( relation_field @ SV572 ) )
= $true )
| ( ( relation @ SV572 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4691,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(4692,plain,
! [SV666: $i,SV491: $i] :
( ( ( ~ ( is_connected_in @ SV491 @ SV666 ) )
= $true )
| ( ( ! [SY7325: $i,SY7326: $i] :
( ( SY7325 = SY7326 )
| ~ ( in @ SY7325 @ SV666 )
| ~ ( in @ SY7326 @ SV666 )
| ( in @ ( ordered_pair @ SY7325 @ SY7326 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7326 @ SY7325 ) @ SV491 ) ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(4693,plain,
! [SV573: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
| ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(4694,plain,
! [SV574: $i] :
( ( ( antisymmetric @ SV574 )
= $false )
| ( ( ! [SY7241: $i,SY7242: $i] :
( ~ ( in @ ( ordered_pair @ SY7241 @ SY7242 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7242 @ SY7241 ) @ SV574 )
| ( SY7241 = SY7242 ) ) )
= $true )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4695,plain,
! [SV492: $i,SV615: $i,SV635: $i] :
( ( ( ~ ( function @ SV635 ) )
= $true )
| ( ( ~ ( relation @ SV635 ) )
= $true )
| ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4555]) ).
thf(4696,plain,
! [SV492: $i,SV688: $i] :
( ( ! [SY7364: $i] :
( ~ ( function @ SY7364 )
| ~ ( relation @ SY7364 )
| ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SY7364 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SY7364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4556]) ).
thf(4697,plain,
! [SV492: $i,SV689: $i] :
( ( ! [SY7365: $i] :
( ~ ( function @ SY7365 )
| ~ ( relation @ SY7365 )
| ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SY7365 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4557]) ).
thf(4698,plain,
! [SV575: $i] :
( ( ( ( relation_dom @ SV575 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV575 )
= empty_set )
= $true )
| ( ( relation @ SV575 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4558]) ).
thf(4699,plain,
! [SV576: $i] :
( ( ( ( relation_rng @ SV576 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV576 )
= empty_set )
= $true )
| ( ( relation @ SV576 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4559]) ).
thf(4700,plain,
! [SV493: $i] :
( ( ( ! [SY7152: $i] :
( ~ ( ~ ( ! [SY7153: $i] :
( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ SY7153 ) )
| ~ ( in @ SY7153 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) )
| ~ ( ~ ( ( ( sK27_C @ SY7152 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SY7152 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SY7152 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SY7152 @ SV493 ) @ SY7152 ) ) )
| ( SY7152
= ( relation_rng @ SV493 ) ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4560]) ).
thf(4701,plain,
! [SV493: $i] :
( ( ( ! [SY7154: $i] :
( ( SY7154
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7155: $i] :
( ! [SY7156: $i] :
( ( SY7155
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7155 @ SY7154 ) )
| ~ ! [SY7157: $i] :
( ~ ( in @ SY7157 @ SY7154 )
| ~ ( ( SY7157
!= ( apply @ SV493 @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7157 @ SY7154 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4561]) ).
thf(4702,plain,
! [SV494: $i,SV577: $i] :
( ( ( ~ ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) ) )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4703,plain,
! [SV577: $i,SV494: $i] :
( ( ( ~ ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4704,plain,
! [SV616: $i,SV495: $i,SV636: $i] :
( ( ( relation @ SV636 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SV636 )
| ( in @ SV495 @ ( relation_dom @ SV636 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4563]) ).
thf(4705,plain,
! [SV617: $i,SV495: $i,SV637: $i] :
( ( ( relation @ SV637 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SV637 )
| ( in @ SV617 @ ( relation_rng @ SV637 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(4706,plain,
! [SV618: $i,SV578: $i] :
( ( ( empty @ SV578 )
= $false )
| ( ( ~ ( relation @ SV618 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV618 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4707,plain,
! [SV619: $i,SV579: $i] :
( ( ( empty @ SV579 )
= $false )
| ( ( ~ ( relation @ SV619 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV619 @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4708,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( relation @ SV667 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
| ( SV667
= ( relation_inverse @ SV496 ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(4709,plain,
! [SV496: $i,SV668: $i] :
( ( ( ~ ( relation @ SV668 ) )
= $true )
| ( ( ( SV668
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(4710,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4711,plain,
! [SV581: $i,SV621: $i] :
( ( ( ( SV621
!= ( identity_relation @ SV581 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) ) )
= $true )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(4712,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( relation @ SV669 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
| ( subset @ SV497 @ SV669 ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(4713,plain,
! [SV497: $i,SV670: $i] :
( ( ( ~ ( relation @ SV670 ) )
= $true )
| ( ( ~ ( subset @ SV497 @ SV670 )
| ! [SY7331: $i,SY7332: $i] :
( ~ ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV670 ) ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(4714,plain,
! [SV582: $i] :
( ( ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) )
| ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4715,plain,
! [SV583: $i] :
( ( ( well_founded_relation @ SV583 )
= $false )
| ( ( ! [SY7262: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SY7262 @ SV583 ) ) @ SY7262 )
| ~ ( in @ ( sK38_C @ SY7262 @ SV583 ) @ SY7262 ) )
| ( SY7262 = empty_set )
| ~ ( subset @ SY7262 @ ( relation_field @ SV583 ) ) ) )
= $true )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4716,plain,
! [SV498: $i] :
( ( ( ~ ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4575]) ).
thf(4717,plain,
! [SV498: $i] :
( ( ( ~ ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4576]) ).
thf(4718,plain,
! [SV584: $i] :
( ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 )
| ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(4719,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4578]) ).
thf(4720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4578]) ).
thf(4721,plain,
! [SV671: $i] :
( ( ( ~ ( relation @ SV671 ) )
= $true )
| ( ( ~ ( well_ordering @ SV671 )
| ( well_founded_relation @ SV671 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(4722,plain,
! [SV585: $i] :
( ( ( relation @ SV585 )
= $false )
| ( ( function @ SV585 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
| ( one_to_one @ SV585 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4723,plain,
! [SV586: $i] :
( ( ( relation @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( ~ ( one_to_one @ SV586 )
| ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4724,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ~ ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) ) )
| ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4582]) ).
thf(4725,plain,
! [SV673: $i,SV499: $i,SV691: $i] :
( ( ( ( SV691
!= ( relation_inverse_image @ SV499 @ SV673 ) )
| ~ ( ~ ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) )
| ~ ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4583]) ).
thf(4726,plain,
! [SV589: $i] :
( ( ( antisymmetric @ SV589 )
= $false )
| ( ( is_antisymmetric_in @ SV589 @ ( relation_field @ SV589 ) )
= $true )
| ( ( relation @ SV589 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4727,plain,
! [SV590: $i] :
( ( ( is_antisymmetric_in @ SV590 @ ( relation_field @ SV590 ) )
= $false )
| ( ( antisymmetric @ SV590 )
= $true )
| ( ( relation @ SV590 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4728,plain,
! [SV591: $i,SV622: $i] :
( ( ( function @ SV622 )
= $false )
| ( ( ~ ( relation @ SV622 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 )
| ( SV622
= ( identity_relation @ SV591 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4729,plain,
! [SV674: $i,SV692: $i] :
( ( ~ ( function @ SV692 )
| ~ ( relation @ SV692 )
| ( SV692
!= ( identity_relation @ SV674 ) )
| ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4587]) ).
thf(4730,plain,
! [SV675: $i,SV693: $i] :
( ( ~ ( function @ SV693 )
| ~ ( relation @ SV693 )
| ( SV693
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SV693 )
= SV675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4588]) ).
thf(4731,plain,
! [SV623: $i,SV592: $i] :
( ( ( empty @ SV592 )
= $false )
| ( ( ~ ( relation @ SV623 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV592 @ SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4732,plain,
! [SV624: $i,SV593: $i] :
( ( ( empty @ SV593 )
= $false )
| ( ( ~ ( relation @ SV624 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV593 @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(4733,plain,
! [SV594: $i] :
( ( ( connected @ SV594 )
= $false )
| ( ( is_connected_in @ SV594 @ ( relation_field @ SV594 ) )
= $true )
| ( ( relation @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4734,plain,
! [SV595: $i] :
( ( ( is_connected_in @ SV595 @ ( relation_field @ SV595 ) )
= $false )
| ( ( connected @ SV595 )
= $true )
| ( ( relation @ SV595 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4592]) ).
thf(4735,plain,
! [SV596: $i] :
( ( ( function @ SV596 )
= $false )
| ( ( ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( one_to_one @ SV596 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4593]) ).
thf(4736,plain,
! [SV597: $i] :
( ( ( function @ SV597 )
= $false )
| ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( one_to_one @ SV597 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(4737,plain,
! [SV513: $i,SV439: $i,SV638: $i] :
( ( ( ~ ( function @ SV638 ) )
= $true )
| ( ( ~ ( relation @ SV638 ) )
= $true )
| ( ( ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) ) )
= $true )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4597]) ).
thf(4738,plain,
! [SV514: $i,SV440: $i,SV639: $i] :
( ( ( ~ ( function @ SV639 ) )
= $true )
| ( ( ~ ( relation @ SV639 ) )
= $true )
| ( ( ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) ) )
= $true )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(4739,plain,
! [SV447: $i,SV532: $i,SV515: $i] :
( ( ( in @ SV515 @ ( relation_dom @ ( relation_dom_restriction @ SV532 @ SV447 ) ) )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV532 @ SV447 ) @ SV515 )
= ( apply @ SV532 @ SV515 ) )
= $true )
| ( ( function @ SV532 )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(4740,plain,
! [SV533: $i,SV448: $i,SV516: $i] :
( ( ( in @ SV516 @ SV448 )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV533 @ SV448 ) @ SV516 )
= ( apply @ SV533 @ SV516 ) )
= $true )
| ( ( function @ SV533 )
= $false )
| ( ( relation @ SV533 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4602]) ).
thf(4741,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ~ ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) ) ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(4742,plain,
! [SV641: $i,SV467: $i,SV677: $i] :
( ( ( ( SV677
!= ( relation_image @ SV467 @ SV641 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) )
| ~ ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4606]) ).
thf(4743,plain,
! [SV694: $i,SV542: $i] :
( ( ( function @ ( relation_dom_restriction @ SV542 @ SV694 ) )
= $true )
| ( ( function @ SV542 )
= $false )
| ( ( relation @ SV542 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4607]) ).
thf(4744,plain,
! [SV695: $i,SV543: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV543 @ SV695 ) )
= $true )
| ( ( function @ SV543 )
= $false )
| ( ( relation @ SV543 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4608]) ).
thf(4745,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(4746,plain,
! [SV643: $i,SV468: $i] :
( ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( ! [SY7297: $i,SY7298: $i,SY7299: $i] :
( ~ ( in @ SY7297 @ SV643 )
| ~ ( in @ SY7298 @ SV643 )
| ~ ( in @ SY7299 @ SV643 )
| ~ ( in @ ( ordered_pair @ SY7297 @ SY7298 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7298 @ SY7299 ) @ SV468 )
| ( in @ ( ordered_pair @ SY7297 @ SY7299 ) @ SV468 ) ) )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(4747,plain,
! [SV696: $i,SV469: $i] :
( ( ( ! [SY7371: $i] :
( ~ ( ~ ( ! [SY7372: $i] :
( ~ ( in @ SY7372 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7372 @ SV696 )
| ( ( sK56_D @ SY7371 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7372 ) ) )
| ~ ( in @ ( sK56_D @ SY7371 @ SV696 @ SV469 ) @ SY7371 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SY7371 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SY7371 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SY7371 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SY7371 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SY7371 @ SV696 @ SV469 ) @ SY7371 ) ) )
| ( SY7371
= ( relation_image @ SV469 @ SV696 ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4611]) ).
thf(4748,plain,
! [SV697: $i,SV469: $i] :
( ( ( ! [SY7373: $i] :
( ( SY7373
!= ( relation_image @ SV469 @ SV697 ) )
| ~ ( ~ ! [SY7374: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7374
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7374 @ SY7373 ) )
| ~ ! [SY7376: $i] :
( ~ ( in @ SY7376 @ SY7373 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7376 @ SY7373 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7376 @ SY7373 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7376
!= ( apply @ SV469 @ ( sK55_E @ SY7376 @ SY7373 @ SV697 @ SV469 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(4749,plain,
! [SV470: $i,SV698: $i] :
( ( ( ! [SY7377: $i] :
( ~ ( ~ ( ~ ( in @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) @ SY7377 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) @ SY7377 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SY7377 @ SV698 @ SV470 ) @ SY7377 ) ) ) )
| ( SY7377
= ( relation_inverse_image @ SV470 @ SV698 ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4613]) ).
thf(4750,plain,
! [SV699: $i,SV470: $i] :
( ( ( ! [SY7378: $i] :
( ( SY7378
!= ( relation_inverse_image @ SV470 @ SV699 ) )
| ~ ( ~ ! [SY7379: $i] :
( ~ ( in @ SY7379 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7379 ) @ SV699 )
| ( in @ SY7379 @ SY7378 ) )
| ~ ~ ( ~ ! [SY7025: $i] :
( ~ ( in @ SY7025 @ SY7378 )
| ( in @ SY7025 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7381: $i] :
( ~ ( in @ SY7381 @ SY7378 )
| ( in @ ( apply @ SV470 @ SY7381 ) @ SV699 ) ) ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(4751,plain,
! [SV700: $i,SV544: $i] :
( ( ( ! [SY7382: $i] :
( ( sK45_B @ SV544 )
!= ( ordered_pair @ SV700 @ SY7382 ) ) )
= $true )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4615]) ).
thf(4752,plain,
! [SV545: $i,SV644: $i] :
( ( ( in @ SV644 @ SV545 )
= $false )
| ( ( SV644
= ( ordered_pair @ ( sK43_C @ SV644 @ SV545 ) @ ( sK44_SY6449 @ SV644 @ SV545 ) ) )
= $true )
| ( ( relation @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(4753,plain,
! [SV701: $i,SV546: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV546 @ SV701 ) )
= $true )
| ( ( relation @ SV546 )
= $false )
| ( ( relation_empty_yielding @ SV546 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(4754,plain,
! [SV702: $i,SV547: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV547 @ SV702 ) )
= $true )
| ( ( relation @ SV547 )
= $false )
| ( ( relation_empty_yielding @ SV547 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(4755,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 )
| ~ ( is_transitive_in @ SV471 @ SV645 )
| ~ ( is_antisymmetric_in @ SV471 @ SV645 )
| ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4620]) ).
thf(4756,plain,
! [SV471: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4621]) ).
thf(4757,plain,
! [SV471: $i] :
( ( ( ! [SY7032: $i] :
( ~ ( well_orders @ SV471 @ SY7032 )
| ( is_well_founded_in @ SV471 @ SY7032 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4622]) ).
thf(4758,plain,
! [SV472: $i,SV526: $i] :
( ( ( ! [SY7203: $i] :
( ~ ( function @ SY7203 )
| ~ ( relation @ SY7203 )
| ~ ( ~ ( in @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) )
!= ( apply @ SY7203 @ ( sK62_D @ SY7203 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SY7203 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SY7203 @ SV472 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4623]) ).
thf(4759,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4624]) ).
thf(4760,plain,
! [SV473: $i,SV646: $i] :
( ( ( ~ ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) ) )
= $false )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(4761,plain,
! [SV473: $i,SV647: $i] :
( ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( ~ ( ~ ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) )
| ~ ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4762,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( ( ( sK29_C @ SV648 @ SV474 )
!= ( sK30_SY6442 @ SV648 @ SV474 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4763,plain,
! [SV649: $i,SV474: $i] :
( ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( ! [SY7304: $i,SY7305: $i] :
( ~ ( in @ SY7304 @ SV649 )
| ~ ( in @ SY7305 @ SV649 )
| ~ ( in @ ( ordered_pair @ SY7304 @ SY7305 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7305 @ SY7304 ) @ SV474 )
| ( SY7304 = SY7305 ) ) )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4764,plain,
! [SV552: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4631]) ).
thf(4765,plain,
! [SV552: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4631]) ).
thf(4766,plain,
! [SV553: $i,SV703: $i] :
( ( ( ! [SY7383: $i] :
( ( SV703 = SY7383 )
| ~ ( in @ SV703 @ ( relation_field @ SV553 ) )
| ~ ( in @ SY7383 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SV703 @ SY7383 ) @ SV553 )
| ( in @ ( ordered_pair @ SY7383 @ SV703 ) @ SV553 ) ) )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4632]) ).
thf(4767,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4633]) ).
thf(4768,plain,
( ( epsilon_transitive @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4634]) ).
thf(4769,plain,
! [SV602: $i,SV475: $i,SV625: $i] :
( ( ( ! [SY7288: $i] :
( ~ ( in @ SY7288 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SY7288 ) @ SV625 )
| ~ ( in @ SY7288 @ SV602 ) ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(4770,plain,
! [SV603: $i,SV626: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) ) )
= $true )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(4771,plain,
! [SV627: $i,SV604: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SV627 ) )
= $true )
| ( ( in @ SV476 @ ( relation_field @ SV627 ) )
= $true )
| ( ( relation @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4637]) ).
thf(4772,plain,
! [SV628: $i,SV605: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SV628 ) )
= $true )
| ( ( in @ SV605 @ ( relation_field @ SV628 ) )
= $true )
| ( ( relation @ SV628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(4773,plain,
! [SV650: $i] :
( ( ( ~ ( empty @ SV650 )
| ~ ( relation @ SV650 ) )
= $true )
| ( ( ~ ( function @ SV650 ) )
= $true )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(4774,plain,
! [SV651: $i] :
( ( ( ~ ( empty @ SV651 )
| ~ ( relation @ SV651 ) )
= $true )
| ( ( ~ ( function @ SV651 ) )
= $true )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(4775,plain,
! [SV554: $i] :
( ( ( relation @ SV554 )
= $false )
| ( ( empty @ SV554 )
= $false )
| ( ( ~ ( function @ SV554 ) )
= $true )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4641]) ).
thf(4776,plain,
! [SV606: $i,SV555: $i] :
( ( ( ~ ( function @ SV555 ) )
= $true )
| ( ( ~ ( relation @ SV555 ) )
= $true )
| ( ( ~ ( relation @ SV606 ) )
= $true )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4777,plain,
! [SV607: $i,SV556: $i] :
( ( ( ~ ( function @ SV556 ) )
= $true )
| ( ( ~ ( relation @ SV556 ) )
= $true )
| ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(4778,plain,
! [SV629: $i,SV608: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV608 )
| ~ ( in @ SV477 @ ( relation_rng @ SV629 ) ) )
= $true )
| ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) )
= $true )
| ( ( relation @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(4779,plain,
! [SV678: $i,SV477: $i,SV704: $i] :
( ( ~ ( relation @ SV704 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SV704 ) ) )
| ( in @ SV477 @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(4780,plain,
! [SV679: $i,SV477: $i,SV705: $i] :
( ( ~ ( relation @ SV705 )
| ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SV705 ) ) )
| ( in @ SV477 @ ( relation_rng @ SV705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(4781,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( relation @ SV680 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
| ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(4782,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( ~ ( relation @ SV681 ) )
= $true )
| ( ( ( SV681
!= ( relation_dom_restriction @ SV478 @ SV653 ) )
| ~ ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(4783,plain,
! [SV557: $i,SV609: $i] :
( ( ( relation @ SV609 )
= $false )
| ( ( function @ SV609 )
= $false )
| ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 )
| ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4649]) ).
thf(4784,plain,
! [SV558: $i,SV610: $i] :
( ( ( relation @ SV610 )
= $false )
| ( ( function @ SV610 )
= $false )
| ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 )
| ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4650]) ).
thf(4785,plain,
! [SV479: $i,SV654: $i] :
( ( ( ~ ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) ) )
= $false )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(4786,plain,
! [SV479: $i,SV655: $i] :
( ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( ~ ( ~ ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) )
| ~ ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(4787,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( relation @ SV682 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
| ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4653]) ).
thf(4788,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ( relation @ SV683 ) )
= $true )
| ( ( ( SV683
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4654]) ).
thf(4789,plain,
! [SV481: $i,SV656: $i] :
( ( ( relation @ SV656 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
| ( SV481 = SV656 ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4790,plain,
! [SV481: $i,SV657: $i] :
( ( ( relation @ SV657 )
= $false )
| ( ( ( SV481 != SV657 )
| ~ ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4658]) ).
thf(4791,plain,
! [SV482: $i] :
( ( ( ~ ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4659]) ).
thf(4792,plain,
! [SV482: $i] :
( ( ( ~ ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4659]) ).
thf(4793,plain,
! [SV563: $i] :
( ( ( ~ ( one_to_one @ SV563 ) )
= $true )
| ( ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) )
= $true )
| ( ( function @ SV563 )
= $false )
| ( ( relation @ SV563 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(4794,plain,
! [SV564: $i] :
( ( ( ~ ( one_to_one @ SV564 ) )
= $true )
| ( ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) )
= $true )
| ( ( function @ SV564 )
= $false )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(4795,plain,
! [SV528: $i,SV630: $i,SV483: $i,SV658: $i] :
( ( ( relation @ SV658 )
= $false )
| ( ( ~ ( in @ SV483 @ SV630 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(4796,plain,
! [SV706: $i,SV528: $i,SV483: $i] :
( ( ! [SY7384: $i] :
( ~ ( relation @ SY7384 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SY7384 ) )
| ( in @ SV483 @ SV706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4663]) ).
thf(4797,plain,
! [SV707: $i,SV528: $i,SV483: $i] :
( ( ! [SY7385: $i] :
( ~ ( relation @ SY7385 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SY7385 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SY7385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(4798,plain,
! [SV484: $i,SV611: $i,SV631: $i] :
( ( ( function @ SV631 )
= $false )
| ( ( ~ ( relation @ SV631 ) )
= $true )
| ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4667]) ).
thf(4799,plain,
! [SV684: $i,SV484: $i,SV708: $i] :
( ( ~ ( function @ SV708 )
| ~ ( relation @ SV708 )
| ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
| ( SV684
= ( apply @ SV708 @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4668]) ).
thf(4800,plain,
! [SV685: $i,SV484: $i,SV709: $i] :
( ( ~ ( function @ SV709 )
| ~ ( relation @ SV709 )
| ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
| ( in @ SV484 @ ( relation_dom @ SV709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4669]) ).
thf(4801,plain,
! [SV632: $i,SV612: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV612 )
| ~ ( in @ SV485 @ ( relation_dom @ SV632 ) ) )
= $true )
| ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) )
= $true )
| ( ( relation @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(4802,plain,
! [SV686: $i,SV485: $i,SV710: $i] :
( ( ~ ( relation @ SV710 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV710 @ SV686 ) ) )
| ( in @ SV485 @ SV686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4671]) ).
thf(4803,plain,
! [SV687: $i,SV485: $i,SV711: $i] :
( ( ~ ( relation @ SV711 )
| ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV711 @ SV687 ) ) )
| ( in @ SV485 @ ( relation_dom @ SV711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4672]) ).
thf(4804,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV659 @ SV486 ) @ SV659 )
| ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 ) )
= $false )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4805,plain,
! [SV660: $i,SV486: $i] :
( ( ( is_reflexive_in @ SV486 @ SV660 )
= $false )
| ( ( ! [SY7322: $i] :
( ~ ( in @ SY7322 @ SV660 )
| ( in @ ( ordered_pair @ SY7322 @ SY7322 ) @ SV486 ) ) )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4674]) ).
thf(4806,plain,
! [SV567: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4675]) ).
thf(4807,plain,
! [SV567: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4675]) ).
thf(4808,plain,
! [SV568: $i,SV712: $i] :
( ( ( ! [SY7386: $i,SY7387: $i] :
( ~ ( in @ ( ordered_pair @ SV712 @ SY7386 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SY7386 @ SY7387 ) @ SV568 )
| ( in @ ( ordered_pair @ SV712 @ SY7387 ) @ SV568 ) ) )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4676]) ).
thf(4809,plain,
! [SV613: $i,SV487: $i,SV633: $i] :
( ( ( ! [SY7290: $i] :
( ~ ( in @ SY7290 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SY7290 @ SV487 ) @ SV633 )
| ~ ( in @ SY7290 @ SV613 ) ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(4810,plain,
! [SV614: $i,SV634: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) ) )
= $true )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(4811,plain,
! [SV661: $i,SV488: $i] :
( ( ( ~ ! [SY7323: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7323 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SY7323 @ ( sK35_C @ SV661 @ SV488 ) ) )
| ~ ~ ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(4812,plain,
! [SV662: $i,SV488: $i] :
( ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( ! [SY7324: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) ) @ SY7324 )
| ~ ( in @ ( sK34_D @ SY7324 @ SV662 @ SV488 ) @ SY7324 ) )
| ( SY7324 = empty_set )
| ~ ( subset @ SY7324 @ SV662 ) ) )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4813,plain,
! [SV489: $i,SV663: $i] :
( ( ( relation @ SV663 )
= $false )
| ( ( ~ ( subset @ SV489 @ SV663 )
| ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SV663 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4814,plain,
! [SV489: $i,SV664: $i] :
( ( ( relation @ SV664 )
= $false )
| ( ( ~ ( subset @ SV489 @ SV664 )
| ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SV664 ) ) )
= $true )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(4815,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4683]) ).
thf(4816,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4684]) ).
thf(4817,plain,
! [SV569: $i] :
( ( ( ~ ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) ) )
= $false )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4685]) ).
thf(4818,plain,
! [SV569: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
= $false )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4685]) ).
thf(4819,plain,
! [SV570: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ ( relation_field @ SV570 ) )
| ( in @ ( ordered_pair @ SV713 @ SV713 ) @ SV570 ) )
= $true )
| ( ( reflexive @ SV570 )
= $false )
| ( ( relation @ SV570 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(4820,plain,
! [SV529: $i,SV490: $i] :
( ( ( ! [SY7221: $i] :
( ~ ( function @ SY7221 )
| ~ ( relation @ SY7221 )
| ~ ( in @ SV490 @ ( relation_dom @ SY7221 ) )
| ~ ( in @ ( apply @ SY7221 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7221 @ SV529 ) ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4687]) ).
thf(4821,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4688]) ).
thf(4822,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(4823,plain,
! [SV666: $i,SV491: $i] :
( ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( ! [SY7325: $i,SY7326: $i] :
( ( SY7325 = SY7326 )
| ~ ( in @ SY7325 @ SV666 )
| ~ ( in @ SY7326 @ SV666 )
| ( in @ ( ordered_pair @ SY7325 @ SY7326 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7326 @ SY7325 ) @ SV491 ) ) )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4824,plain,
! [SV573: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4693]) ).
thf(4825,plain,
! [SV573: $i] :
( ( ( ~ ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4693]) ).
thf(4826,plain,
! [SV574: $i,SV714: $i] :
( ( ( ! [SY7388: $i] :
( ~ ( in @ ( ordered_pair @ SV714 @ SY7388 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SY7388 @ SV714 ) @ SV574 )
| ( SV714 = SY7388 ) ) )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4694]) ).
thf(4827,plain,
! [SV492: $i,SV615: $i,SV635: $i] :
( ( ( function @ SV635 )
= $false )
| ( ( ~ ( relation @ SV635 ) )
= $true )
| ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(4828,plain,
! [SV492: $i,SV688: $i,SV715: $i] :
( ( ~ ( function @ SV715 )
| ~ ( relation @ SV715 )
| ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SV715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4696]) ).
thf(4829,plain,
! [SV492: $i,SV689: $i,SV716: $i] :
( ( ~ ( function @ SV716 )
| ~ ( relation @ SV716 )
| ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4697]) ).
thf(4830,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ~ ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
| ~ ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) ) )
| ( SV717
= ( relation_rng @ SV493 ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(4831,plain,
! [SV493: $i,SV718: $i] :
( ( ( ( SV718
!= ( relation_rng @ SV493 ) )
| ~ ( ~ ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) )
| ~ ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(4832,plain,
! [SV494: $i,SV577: $i] :
( ( ( ! [SY7243: $i] :
( ~ ( relation @ SY7243 )
| ~ ( ~ ( ! [SY7244: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ SY7244 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7244 @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SY7243 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SY7243 @ SV577 @ SV494 ) ) @ SY7243 ) ) )
| ( SY7243
= ( relation_composition @ SV494 @ SV577 ) ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4702]) ).
thf(4833,plain,
! [SV577: $i,SV494: $i] :
( ( ( ! [SY7245: $i] :
( ~ ( relation @ SY7245 )
| ( SY7245
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7246: $i,SY7247: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7246 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7247 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7246 @ SY7247 ) @ SY7245 ) )
| ~ ! [SY7249: $i,SY7250: $i] :
( ~ ( in @ ( ordered_pair @ SY7249 @ SY7250 ) @ SY7245 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7249 @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7250 @ SY7249 @ SY7245 @ SV577 @ SV494 ) @ SY7250 ) @ SV577 ) ) ) ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4703]) ).
thf(4834,plain,
! [SV636: $i,SV616: $i,SV495: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SV636 ) )
= $true )
| ( ( in @ SV495 @ ( relation_dom @ SV636 ) )
= $true )
| ( ( relation @ SV636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4704]) ).
thf(4835,plain,
! [SV637: $i,SV617: $i,SV495: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SV637 ) )
= $true )
| ( ( in @ SV617 @ ( relation_rng @ SV637 ) )
= $true )
| ( ( relation @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(4836,plain,
! [SV578: $i,SV618: $i] :
( ( ( relation @ SV618 )
= $false )
| ( ( empty @ SV578 )
= $false )
| ( ( empty @ ( relation_composition @ SV618 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(4837,plain,
! [SV579: $i,SV619: $i] :
( ( ( relation @ SV619 )
= $false )
| ( ( empty @ SV579 )
= $false )
| ( ( relation @ ( relation_composition @ SV619 @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(4838,plain,
! [SV496: $i,SV667: $i] :
( ( ( relation @ SV667 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
| ( SV667
= ( relation_inverse @ SV496 ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4708]) ).
thf(4839,plain,
! [SV496: $i,SV668: $i] :
( ( ( relation @ SV668 )
= $false )
| ( ( ( SV668
!= ( relation_inverse @ SV496 ) )
| ~ ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) ) )
= $true )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(4840,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(4841,plain,
! [SV581: $i,SV621: $i] :
( ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( ~ ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) ) )
= $true )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4842,plain,
! [SV497: $i,SV669: $i] :
( ( ( relation @ SV669 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
| ( subset @ SV497 @ SV669 ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4712]) ).
thf(4843,plain,
! [SV497: $i,SV670: $i] :
( ( ( relation @ SV670 )
= $false )
| ( ( ~ ( subset @ SV497 @ SV670 )
| ! [SY7331: $i,SY7332: $i] :
( ~ ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV670 ) ) )
= $true )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4844,plain,
! [SV582: $i] :
( ( ( ~ ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4714]) ).
thf(4845,plain,
! [SV582: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4714]) ).
thf(4846,plain,
! [SV719: $i,SV583: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
| ~ ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 ) )
| ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4715]) ).
thf(4847,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) )
| ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4716]) ).
thf(4848,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) )
| ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4717]) ).
thf(4849,plain,
! [SV584: $i] :
( ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 )
| ~ ( antisymmetric @ SV584 ) )
= $true )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(4850,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4719]) ).
thf(4851,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4720]) ).
thf(4852,plain,
! [SV671: $i] :
( ( ( relation @ SV671 )
= $false )
| ( ( ~ ( well_ordering @ SV671 )
| ( well_founded_relation @ SV671 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(4853,plain,
! [SV585: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4722]) ).
thf(4854,plain,
! [SV586: $i] :
( ( ( ~ ( one_to_one @ SV586 ) )
= $true )
| ( ( ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(4855,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ~ ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) ) ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(4856,plain,
! [SV673: $i,SV499: $i,SV691: $i] :
( ( ( ( SV691
!= ( relation_inverse_image @ SV499 @ SV673 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) )
| ~ ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4725]) ).
thf(4857,plain,
! [SV591: $i,SV622: $i] :
( ( ( relation @ SV622 )
= $false )
| ( ( function @ SV622 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 )
| ( SV622
= ( identity_relation @ SV591 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(4858,plain,
! [SV674: $i,SV692: $i] :
( ( ( ~ ( function @ SV692 )
| ~ ( relation @ SV692 ) )
= $true )
| ( ( ( SV692
!= ( identity_relation @ SV674 ) )
| ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4729]) ).
thf(4859,plain,
! [SV675: $i,SV693: $i] :
( ( ( ~ ( function @ SV693 )
| ~ ( relation @ SV693 ) )
= $true )
| ( ( ( SV693
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SV693 )
= SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(4860,plain,
! [SV592: $i,SV623: $i] :
( ( ( relation @ SV623 )
= $false )
| ( ( empty @ SV592 )
= $false )
| ( ( empty @ ( relation_composition @ SV592 @ SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4861,plain,
! [SV593: $i,SV624: $i] :
( ( ( relation @ SV624 )
= $false )
| ( ( empty @ SV593 )
= $false )
| ( ( relation @ ( relation_composition @ SV593 @ SV624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4732]) ).
thf(4862,plain,
! [SV596: $i] :
( ( ( relation @ SV596 )
= $false )
| ( ( function @ SV596 )
= $false )
| ( ( ~ ( one_to_one @ SV596 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4735]) ).
thf(4863,plain,
! [SV597: $i] :
( ( ( relation @ SV597 )
= $false )
| ( ( function @ SV597 )
= $false )
| ( ( ~ ( one_to_one @ SV597 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4736]) ).
thf(4864,plain,
! [SV513: $i,SV439: $i,SV638: $i] :
( ( ( function @ SV638 )
= $false )
| ( ( ~ ( relation @ SV638 ) )
= $true )
| ( ( ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) ) )
= $true )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4737]) ).
thf(4865,plain,
! [SV514: $i,SV440: $i,SV639: $i] :
( ( ( function @ SV639 )
= $false )
| ( ( ~ ( relation @ SV639 ) )
= $true )
| ( ( ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) ) )
= $true )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4738]) ).
thf(4866,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) ) )
= $false )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(4867,plain,
! [SV641: $i,SV467: $i,SV677: $i] :
( ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( ~ ( ~ ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) )
| ~ ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4742]) ).
thf(4868,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4745]) ).
thf(4869,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4745]) ).
thf(4870,plain,
! [SV468: $i,SV643: $i,SV720: $i] :
( ( ( ! [SY7393: $i,SY7394: $i] :
( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SY7393 @ SV643 )
| ~ ( in @ SY7394 @ SV643 )
| ~ ( in @ ( ordered_pair @ SV720 @ SY7393 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SY7393 @ SY7394 ) @ SV468 )
| ( in @ ( ordered_pair @ SV720 @ SY7394 ) @ SV468 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(4871,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ~ ( ~ ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) )
| ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) ) )
| ( SV721
= ( relation_image @ SV469 @ SV696 ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(4872,plain,
! [SV697: $i,SV469: $i,SV722: $i] :
( ( ( ( SV722
!= ( relation_image @ SV469 @ SV697 ) )
| ~ ( ~ ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) )
| ~ ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4748]) ).
thf(4873,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) ) )
| ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(4874,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ( SV724
!= ( relation_inverse_image @ SV470 @ SV699 ) )
| ~ ( ~ ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) )
| ~ ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4750]) ).
thf(4875,plain,
! [SV725: $i,SV700: $i,SV544: $i] :
( ( ( ( ( sK45_B @ SV544 )
!= ( ordered_pair @ SV700 @ SV725 ) ) )
= $true )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4751]) ).
thf(4876,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 )
| ~ ( is_transitive_in @ SV471 @ SV645 )
| ~ ( is_antisymmetric_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(4877,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
| ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4756]) ).
thf(4878,plain,
! [SV726: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV726 )
| ( is_well_founded_in @ SV471 @ SV726 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4757]) ).
thf(4879,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( function @ SV727 )
| ~ ( relation @ SV727 )
| ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4758]) ).
thf(4880,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) )
| ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(4881,plain,
! [SV473: $i,SV646: $i] :
( ( ( ~ ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) ) )
= $false )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4760]) ).
thf(4882,plain,
! [SV473: $i,SV646: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) ) )
= $false )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4760]) ).
thf(4883,plain,
! [SV647: $i,SV473: $i] :
( ( ( ~ ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) )
| ~ ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) )
= $false )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4761]) ).
thf(4884,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4762]) ).
thf(4885,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ( ( sK29_C @ SV648 @ SV474 )
!= ( sK30_SY6442 @ SV648 @ SV474 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4762]) ).
thf(4886,plain,
! [SV474: $i,SV649: $i,SV728: $i] :
( ( ( ! [SY7402: $i] :
( ~ ( in @ SV728 @ SV649 )
| ~ ( in @ SY7402 @ SV649 )
| ~ ( in @ ( ordered_pair @ SV728 @ SY7402 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SY7402 @ SV728 ) @ SV474 )
| ( SV728 = SY7402 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4763]) ).
thf(4887,plain,
! [SV552: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4764]) ).
thf(4888,plain,
! [SV552: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4765]) ).
thf(4889,plain,
! [SV553: $i,SV729: $i,SV703: $i] :
( ( ( ( SV703 = SV729 )
| ~ ( in @ SV703 @ ( relation_field @ SV553 ) )
| ~ ( in @ SV729 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
| ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 ) )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4766]) ).
thf(4890,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
| ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(4891,plain,
! [SV602: $i,SV475: $i,SV625: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 )
| ~ ( in @ SV730 @ SV602 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4769]) ).
thf(4892,plain,
! [SV603: $i,SV626: $i,SV475: $i] :
( ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) ) )
= $true )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(4893,plain,
! [SV627: $i,SV604: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ SV604 ) @ SV627 )
= $false )
| ( ( in @ SV476 @ ( relation_field @ SV627 ) )
= $true )
| ( ( relation @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(4894,plain,
! [SV628: $i,SV605: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ SV605 ) @ SV628 )
= $false )
| ( ( in @ SV605 @ ( relation_field @ SV628 ) )
= $true )
| ( ( relation @ SV628 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4895,plain,
! [SV650: $i] :
( ( ( ~ ( empty @ SV650 ) )
= $true )
| ( ( ~ ( relation @ SV650 ) )
= $true )
| ( ( ~ ( function @ SV650 ) )
= $true )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4773]) ).
thf(4896,plain,
! [SV651: $i] :
( ( ( ~ ( empty @ SV651 ) )
= $true )
| ( ( ~ ( relation @ SV651 ) )
= $true )
| ( ( ~ ( function @ SV651 ) )
= $true )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(4897,plain,
! [SV554: $i] :
( ( ( function @ SV554 )
= $false )
| ( ( empty @ SV554 )
= $false )
| ( ( relation @ SV554 )
= $false )
| ( ( one_to_one @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4898,plain,
! [SV606: $i,SV555: $i] :
( ( ( function @ SV555 )
= $false )
| ( ( ~ ( relation @ SV555 ) )
= $true )
| ( ( ~ ( relation @ SV606 ) )
= $true )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(4899,plain,
! [SV607: $i,SV556: $i] :
( ( ( function @ SV556 )
= $false )
| ( ( ~ ( relation @ SV556 ) )
= $true )
| ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4900,plain,
! [SV629: $i,SV608: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV608 ) )
= $true )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ SV629 ) ) )
= $true )
| ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) )
= $true )
| ( ( relation @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(4901,plain,
! [SV678: $i,SV477: $i,SV704: $i] :
( ( ( ~ ( relation @ SV704 ) )
= $true )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SV704 ) ) )
| ( in @ SV477 @ SV678 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(4902,plain,
! [SV679: $i,SV477: $i,SV705: $i] :
( ( ( ~ ( relation @ SV705 ) )
= $true )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SV705 ) ) )
| ( in @ SV477 @ ( relation_rng @ SV705 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(4903,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( relation @ SV680 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
| ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(4904,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( relation @ SV681 )
= $false )
| ( ( ( SV681
!= ( relation_dom_restriction @ SV478 @ SV653 ) )
| ~ ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) ) )
= $true )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(4905,plain,
! [SV609: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) )
| ~ ( one_to_one @ SV609 ) )
= $true )
| ( ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) )
= $true )
| ( ( function @ SV609 )
= $false )
| ( ( relation @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(4906,plain,
! [SV610: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) )
| ~ ( one_to_one @ SV610 ) )
= $true )
| ( ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) )
= $true )
| ( ( function @ SV610 )
= $false )
| ( ( relation @ SV610 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(4907,plain,
! [SV479: $i,SV654: $i] :
( ( ( ~ ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) ) )
= $false )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4785]) ).
thf(4908,plain,
! [SV479: $i,SV654: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) ) )
= $false )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4785]) ).
thf(4909,plain,
! [SV655: $i,SV479: $i] :
( ( ( ~ ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) )
| ~ ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) )
= $false )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(4910,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( relation @ SV682 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
| ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(4911,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( relation @ SV683 )
= $false )
| ( ( ( SV683
!= ( relation_rng_restriction @ SV480 @ SV527 ) )
| ~ ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) ) )
= $true )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4788]) ).
thf(4912,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) ) )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(4913,plain,
! [SV657: $i,SV481: $i] :
( ( ( ( SV481 != SV657 ) )
= $true )
| ( ( ~ ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4790]) ).
thf(4914,plain,
! [SV482: $i] :
( ( ( ! [SY7094: $i] :
( ~ ( function @ SY7094 )
| ~ ( relation @ SY7094 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SY7094 @ SV482 )
= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SY7094 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SY7094 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SY7094 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SY7094 @ SV482 )
!= ( apply @ SY7094 @ ( sK65_C @ SY7094 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SY7094 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SY7094 )
!= ( relation_rng @ SV482 ) )
| ( SY7094
= ( function_inverse @ SV482 ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4791]) ).
thf(4915,plain,
! [SV482: $i] :
( ( ( ~ ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4792]) ).
thf(4916,plain,
! [SV563: $i] :
( ( ( one_to_one @ SV563 )
= $false )
| ( ( ( relation_rng @ SV563 )
= ( relation_dom @ ( function_inverse @ SV563 ) ) )
= $true )
| ( ( function @ SV563 )
= $false )
| ( ( relation @ SV563 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4917,plain,
! [SV564: $i] :
( ( ( one_to_one @ SV564 )
= $false )
| ( ( ( relation_dom @ SV564 )
= ( relation_rng @ ( function_inverse @ SV564 ) ) )
= $true )
| ( ( function @ SV564 )
= $false )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4794]) ).
thf(4918,plain,
! [SV658: $i,SV528: $i,SV630: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV630 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4795]) ).
thf(4919,plain,
! [SV706: $i,SV528: $i,SV483: $i,SV731: $i] :
( ( ~ ( relation @ SV731 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SV731 ) )
| ( in @ SV483 @ SV706 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4796]) ).
thf(4920,plain,
! [SV707: $i,SV528: $i,SV483: $i,SV732: $i] :
( ( ~ ( relation @ SV732 )
| ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SV732 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV732 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4797]) ).
thf(4921,plain,
! [SV484: $i,SV611: $i,SV631: $i] :
( ( ( relation @ SV631 )
= $false )
| ( ( function @ SV631 )
= $false )
| ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) )
| ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(4922,plain,
! [SV684: $i,SV484: $i,SV708: $i] :
( ( ( ~ ( function @ SV708 )
| ~ ( relation @ SV708 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
| ( SV684
= ( apply @ SV708 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(4923,plain,
! [SV685: $i,SV484: $i,SV709: $i] :
( ( ( ~ ( function @ SV709 )
| ~ ( relation @ SV709 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
| ( in @ SV484 @ ( relation_dom @ SV709 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4800]) ).
thf(4924,plain,
! [SV632: $i,SV612: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV612 ) )
= $true )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ SV632 ) ) )
= $true )
| ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) )
= $true )
| ( ( relation @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4801]) ).
thf(4925,plain,
! [SV686: $i,SV485: $i,SV710: $i] :
( ( ( ~ ( relation @ SV710 ) )
= $true )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV710 @ SV686 ) ) )
| ( in @ SV485 @ SV686 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4802]) ).
thf(4926,plain,
! [SV687: $i,SV485: $i,SV711: $i] :
( ( ( ~ ( relation @ SV711 ) )
= $true )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV711 @ SV687 ) ) )
| ( in @ SV485 @ ( relation_dom @ SV711 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4803]) ).
thf(4927,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV659 @ SV486 ) @ SV659 ) )
= $false )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4804]) ).
thf(4928,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 ) )
= $false )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4804]) ).
thf(4929,plain,
! [SV486: $i,SV660: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV660 )
| ( in @ ( ordered_pair @ SV733 @ SV733 ) @ SV486 ) )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV660 )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4805]) ).
thf(4930,plain,
! [SV567: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) ) )
= $true )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4806]) ).
thf(4931,plain,
! [SV567: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
= $true )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4807]) ).
thf(4932,plain,
! [SV568: $i,SV734: $i,SV712: $i] :
( ( ( ! [SY7403: $i] :
( ~ ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SV734 @ SY7403 ) @ SV568 )
| ( in @ ( ordered_pair @ SV712 @ SY7403 ) @ SV568 ) ) )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4808]) ).
thf(4933,plain,
! [SV613: $i,SV487: $i,SV633: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 )
| ~ ( in @ SV735 @ SV613 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4809]) ).
thf(4934,plain,
! [SV614: $i,SV634: $i,SV487: $i] :
( ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) ) )
= $true )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4810]) ).
thf(4935,plain,
! [SV661: $i,SV488: $i] :
( ( ( ~ ! [SY7323: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7323 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SY7323 @ ( sK35_C @ SV661 @ SV488 ) ) ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4811]) ).
thf(4936,plain,
! [SV488: $i,SV661: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4811]) ).
thf(4937,plain,
! [SV662: $i,SV736: $i,SV488: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
| ~ ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 ) )
| ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4812]) ).
thf(4938,plain,
! [SV663: $i,SV489: $i] :
( ( ( ~ ( subset @ SV489 @ SV663 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SV663 ) )
= $true )
| ( ( relation @ SV663 )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(4939,plain,
! [SV664: $i,SV489: $i] :
( ( ( ~ ( subset @ SV489 @ SV664 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SV664 ) )
= $true )
| ( ( relation @ SV664 )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(4940,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
| ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4815]) ).
thf(4941,plain,
! [SV569: $i] :
( ( ( in @ ( sK77_B @ SV569 ) @ ( relation_field @ SV569 ) )
= $true )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4817]) ).
thf(4942,plain,
! [SV569: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 ) )
= $true )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4818]) ).
thf(4943,plain,
! [SV570: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ ( relation_field @ SV570 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV713 @ SV713 ) @ SV570 )
= $true )
| ( ( reflexive @ SV570 )
= $false )
| ( ( relation @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(4944,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( ~ ( function @ SV737 )
| ~ ( relation @ SV737 )
| ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4820]) ).
thf(4945,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) )
| ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(4946,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4822]) ).
thf(4947,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4822]) ).
thf(4948,plain,
! [SV491: $i,SV666: $i,SV738: $i] :
( ( ( ! [SY7404: $i] :
( ( SV738 = SY7404 )
| ~ ( in @ SV738 @ SV666 )
| ~ ( in @ SY7404 @ SV666 )
| ( in @ ( ordered_pair @ SV738 @ SY7404 ) @ SV491 )
| ( in @ ( ordered_pair @ SY7404 @ SV738 ) @ SV491 ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(4949,plain,
! [SV573: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) ) )
= $true )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4824]) ).
thf(4950,plain,
! [SV573: $i] :
( ( ( ( ( sK72_B @ SV573 )
!= ( sK73_SY6464 @ SV573 ) ) )
= $true )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4825]) ).
thf(4951,plain,
! [SV574: $i,SV739: $i,SV714: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV714 @ SV739 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SV739 @ SV714 ) @ SV574 )
| ( SV714 = SV739 ) )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4826]) ).
thf(4952,plain,
! [SV492: $i,SV615: $i,SV635: $i] :
( ( ( relation @ SV635 )
= $false )
| ( ( function @ SV635 )
= $false )
| ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 )
| ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(4953,plain,
! [SV492: $i,SV688: $i,SV715: $i] :
( ( ( ~ ( function @ SV715 )
| ~ ( relation @ SV715 ) )
= $true )
| ( ( ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SV715 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4828]) ).
thf(4954,plain,
! [SV492: $i,SV689: $i,SV716: $i] :
( ( ( ~ ( function @ SV716 )
| ~ ( relation @ SV716 ) )
= $true )
| ( ( ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4829]) ).
thf(4955,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ~ ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
| ~ ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) ) ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4830]) ).
thf(4956,plain,
! [SV493: $i,SV718: $i] :
( ( ( ( SV718
!= ( relation_rng @ SV493 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) )
| ~ ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4831]) ).
thf(4957,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( relation @ SV740 )
| ~ ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
| ( SV740
= ( relation_composition @ SV494 @ SV577 ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4832]) ).
thf(4958,plain,
! [SV577: $i,SV494: $i,SV741: $i] :
( ( ( ~ ( relation @ SV741 )
| ( SV741
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4833]) ).
thf(4959,plain,
! [SV636: $i,SV616: $i,SV495: $i] :
( ( ( in @ ( ordered_pair @ SV495 @ SV616 ) @ SV636 )
= $false )
| ( ( in @ SV495 @ ( relation_dom @ SV636 ) )
= $true )
| ( ( relation @ SV636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(4960,plain,
! [SV637: $i,SV617: $i,SV495: $i] :
( ( ( in @ ( ordered_pair @ SV495 @ SV617 ) @ SV637 )
= $false )
| ( ( in @ SV617 @ ( relation_rng @ SV637 ) )
= $true )
| ( ( relation @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4835]) ).
thf(4961,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) ) )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4838]) ).
thf(4962,plain,
! [SV496: $i,SV668: $i] :
( ( ( ( SV668
!= ( relation_inverse @ SV496 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) ) )
= $true )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(4963,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4964,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4965,plain,
! [SV621: $i,SV581: $i] :
( ( ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) )
| ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4966,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) ) )
= $true )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(4967,plain,
! [SV670: $i,SV497: $i] :
( ( ( ~ ( subset @ SV497 @ SV670 ) )
= $true )
| ( ( ! [SY7331: $i,SY7332: $i] :
( ~ ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV670 ) ) )
= $true )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(4968,plain,
! [SV582: $i] :
( ( ( ! [SY7261: $i] :
( ~ ( disjoint @ ( fiber @ SV582 @ SY7261 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SY7261 @ ( sK39_B @ SV582 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4844]) ).
thf(4969,plain,
! [SV582: $i] :
( ( ( ~ ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4845]) ).
thf(4970,plain,
! [SV719: $i,SV583: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
| ~ ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 ) ) )
= $true )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(4971,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4847]) ).
thf(4972,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4847]) ).
thf(4973,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4848]) ).
thf(4974,plain,
! [SV498: $i] :
( ( ( ~ ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4848]) ).
thf(4975,plain,
! [SV584: $i] :
( ( ( ~ ( reflexive @ SV584 )
| ~ ( transitive @ SV584 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV584 ) )
= $true )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(4976,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(4977,plain,
! [SV742: $i] :
( ( ~ ( relation @ SV742 )
| ~ ( well_ordering @ SV742 )
| ( connected @ SV742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(4978,plain,
! [SV671: $i] :
( ( ( ~ ( well_ordering @ SV671 ) )
= $true )
| ( ( well_founded_relation @ SV671 )
= $true )
| ( ( relation @ SV671 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(4979,plain,
! [SV585: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
| ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4980,plain,
! [SV586: $i] :
( ( ( one_to_one @ SV586 )
= $false )
| ( ( ! [SY7263: $i,SY7264: $i] :
( ~ ( in @ SY7263 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7264 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SY7263 )
!= ( apply @ SV586 @ SY7264 ) )
| ( SY7263 = SY7264 ) ) )
= $true )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4854]) ).
thf(4981,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) ) )
= $false )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(4982,plain,
! [SV673: $i,SV499: $i,SV691: $i] :
( ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( ~ ( ~ ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) )
| ~ ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(4983,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
| ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(4984,plain,
! [SV674: $i,SV692: $i] :
( ( ( ~ ( function @ SV692 ) )
= $true )
| ( ( ~ ( relation @ SV692 ) )
= $true )
| ( ( ( SV692
!= ( identity_relation @ SV674 ) )
| ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(4985,plain,
! [SV675: $i,SV693: $i] :
( ( ( ~ ( function @ SV693 ) )
= $true )
| ( ( ~ ( relation @ SV693 ) )
= $true )
| ( ( ( SV693
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SV693 )
= SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4859]) ).
thf(4986,plain,
! [SV596: $i] :
( ( ( one_to_one @ SV596 )
= $false )
| ( ( function @ SV596 )
= $false )
| ( ( relation @ SV596 )
= $false )
| ( ( function @ ( relation_inverse @ SV596 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(4987,plain,
! [SV597: $i] :
( ( ( one_to_one @ SV597 )
= $false )
| ( ( function @ SV597 )
= $false )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ ( relation_inverse @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(4988,plain,
! [SV513: $i,SV439: $i,SV638: $i] :
( ( ( relation @ SV638 )
= $false )
| ( ( function @ SV638 )
= $false )
| ( ( ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
| ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) ) )
= $true )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(4989,plain,
! [SV514: $i,SV440: $i,SV639: $i] :
( ( ( relation @ SV639 )
= $false )
| ( ( function @ SV639 )
= $false )
| ( ( ~ ( in @ SV440 @ ( relation_dom @ SV514 ) )
| ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) ) )
= $true )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(4990,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) ) )
= $false )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4866]) ).
thf(4991,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) ) )
= $false )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4866]) ).
thf(4992,plain,
! [SV677: $i,SV641: $i,SV467: $i] :
( ( ( ~ ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) )
| ~ ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4867]) ).
thf(4993,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4868]) ).
thf(4994,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4869]) ).
thf(4995,plain,
! [SV468: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ! [SY7411: $i] :
( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 )
| ~ ( in @ SY7411 @ SV643 )
| ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SV743 @ SY7411 ) @ SV468 )
| ( in @ ( ordered_pair @ SV720 @ SY7411 ) @ SV468 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4870]) ).
thf(4996,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ~ ( ~ ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) )
| ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) ) ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(4997,plain,
! [SV697: $i,SV469: $i,SV722: $i] :
( ( ( ( SV722
!= ( relation_image @ SV469 @ SV697 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) )
| ~ ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(4998,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) ) ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(4999,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ( SV724
!= ( relation_inverse_image @ SV470 @ SV699 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) )
| ~ ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5000,plain,
! [SV725: $i,SV700: $i,SV544: $i] :
( ( ( ( sK45_B @ SV544 )
= ( ordered_pair @ SV700 @ SV725 ) )
= $false )
| ( ( relation @ SV544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4875]) ).
thf(5001,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 )
| ~ ( is_transitive_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5002,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4877]) ).
thf(5003,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4877]) ).
thf(5004,plain,
! [SV726: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV726 ) )
= $true )
| ( ( is_well_founded_in @ SV471 @ SV726 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(5005,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( function @ SV727 )
| ~ ( relation @ SV727 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4879]) ).
thf(5006,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4880]) ).
thf(5007,plain,
! [SV472: $i,SV526: $i] :
( ( ( ~ ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4880]) ).
thf(5008,plain,
! [SV473: $i,SV646: $i] :
( ( ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 )
| ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4881]) ).
thf(5009,plain,
! [SV473: $i,SV646: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
| ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4882]) ).
thf(5010,plain,
! [SV647: $i,SV473: $i] :
( ( ( ~ ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) ) )
= $false )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4883]) ).
thf(5011,plain,
! [SV473: $i,SV647: $i] :
( ( ( ~ ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) )
= $false )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4883]) ).
thf(5012,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4884]) ).
thf(5013,plain,
! [SV474: $i,SV648: $i] :
( ( ( ( ( sK29_C @ SV648 @ SV474 )
!= ( sK30_SY6442 @ SV648 @ SV474 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4885]) ).
thf(5014,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV649 )
| ~ ( in @ SV744 @ SV649 )
| ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 )
| ( SV728 = SV744 ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4886]) ).
thf(5015,plain,
! [SV552: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(5016,plain,
! [SV552: $i] :
( ( ( in @ ( ordered_pair @ ( sK71_SY6463 @ SV552 ) @ ( sK70_B @ SV552 ) ) @ SV552 )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5017,plain,
! [SV553: $i,SV729: $i,SV703: $i] :
( ( ( ( SV703 = SV729 )
| ~ ( in @ SV703 @ ( relation_field @ SV553 ) )
| ~ ( in @ SV729 @ ( relation_field @ SV553 ) )
| ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(5018,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(5019,plain,
( ( ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4890]) ).
thf(5020,plain,
! [SV602: $i,SV475: $i,SV625: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( relation_rng @ SV625 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 ) )
= $true )
| ( ( ~ ( in @ SV730 @ SV602 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4891]) ).
thf(5021,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
| ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5022,plain,
! [SV650: $i] :
( ( ( empty @ SV650 )
= $false )
| ( ( ~ ( relation @ SV650 ) )
= $true )
| ( ( ~ ( function @ SV650 ) )
= $true )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4895]) ).
thf(5023,plain,
! [SV651: $i] :
( ( ( empty @ SV651 )
= $false )
| ( ( ~ ( relation @ SV651 ) )
= $true )
| ( ( ~ ( function @ SV651 ) )
= $true )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4896]) ).
thf(5024,plain,
! [SV606: $i,SV555: $i] :
( ( ( relation @ SV555 )
= $false )
| ( ( function @ SV555 )
= $false )
| ( ( ~ ( relation @ SV606 ) )
= $true )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5025,plain,
! [SV607: $i,SV556: $i] :
( ( ( relation @ SV556 )
= $false )
| ( ( function @ SV556 )
= $false )
| ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(5026,plain,
! [SV629: $i,SV608: $i,SV477: $i] :
( ( ( in @ SV477 @ SV608 )
= $false )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ SV629 ) ) )
= $true )
| ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) )
= $true )
| ( ( relation @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5027,plain,
! [SV678: $i,SV477: $i,SV704: $i] :
( ( ( relation @ SV704 )
= $false )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SV704 ) ) )
| ( in @ SV477 @ SV678 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4901]) ).
thf(5028,plain,
! [SV679: $i,SV477: $i,SV705: $i] :
( ( ( relation @ SV705 )
= $false )
| ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SV705 ) ) )
| ( in @ SV477 @ ( relation_rng @ SV705 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4902]) ).
thf(5029,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5030,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( ( SV681
!= ( relation_dom_restriction @ SV478 @ SV653 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5031,plain,
! [SV609: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( relation_rng @ SV609 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV609 ) )
= $true )
| ( ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) )
= $true )
| ( ( function @ SV609 )
= $false )
| ( ( relation @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5032,plain,
! [SV610: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ ( relation_rng @ SV610 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV610 ) )
= $true )
| ( ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) )
= $true )
| ( ( function @ SV610 )
= $false )
| ( ( relation @ SV610 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5033,plain,
! [SV479: $i,SV654: $i] :
( ( ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4907]) ).
thf(5034,plain,
! [SV479: $i,SV654: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
| ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4908]) ).
thf(5035,plain,
! [SV655: $i,SV479: $i] :
( ( ( ~ ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) ) )
= $false )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4909]) ).
thf(5036,plain,
! [SV479: $i,SV655: $i] :
( ( ( ~ ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) )
= $false )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4909]) ).
thf(5037,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4910]) ).
thf(5038,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ( SV683
!= ( relation_rng_restriction @ SV480 @ SV527 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) ) )
= $true )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4911]) ).
thf(5039,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
= $false )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5040,plain,
! [SV657: $i,SV481: $i] :
( ( ( SV481 = SV657 )
= $false )
| ( ( ~ ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) ) )
= $true )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5041,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( function @ SV745 )
| ~ ( relation @ SV745 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) )
| ( SV745
= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4914]) ).
thf(5042,plain,
! [SV482: $i] :
( ( ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
| ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4915]) ).
thf(5043,plain,
! [SV658: $i,SV528: $i,SV630: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV630 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(5044,plain,
! [SV706: $i,SV528: $i,SV483: $i,SV731: $i] :
( ( ( ~ ( relation @ SV731 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SV731 ) )
| ( in @ SV483 @ SV706 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4919]) ).
thf(5045,plain,
! [SV707: $i,SV528: $i,SV483: $i,SV732: $i] :
( ( ( ~ ( relation @ SV732 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SV732 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV732 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5046,plain,
! [SV484: $i,SV631: $i,SV611: $i] :
( ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) )
| ~ ( in @ SV484 @ ( relation_dom @ SV631 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 )
= $true )
| ( ( function @ SV631 )
= $false )
| ( ( relation @ SV631 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5047,plain,
! [SV684: $i,SV484: $i,SV708: $i] :
( ( ( ~ ( function @ SV708 ) )
= $true )
| ( ( ~ ( relation @ SV708 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
| ( SV684
= ( apply @ SV708 @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5048,plain,
! [SV685: $i,SV484: $i,SV709: $i] :
( ( ( ~ ( function @ SV709 ) )
= $true )
| ( ( ~ ( relation @ SV709 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
| ( in @ SV484 @ ( relation_dom @ SV709 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5049,plain,
! [SV632: $i,SV612: $i,SV485: $i] :
( ( ( in @ SV485 @ SV612 )
= $false )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ SV632 ) ) )
= $true )
| ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) )
= $true )
| ( ( relation @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4924]) ).
thf(5050,plain,
! [SV686: $i,SV485: $i,SV710: $i] :
( ( ( relation @ SV710 )
= $false )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV710 @ SV686 ) ) )
| ( in @ SV485 @ SV686 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5051,plain,
! [SV687: $i,SV485: $i,SV711: $i] :
( ( ( relation @ SV711 )
= $false )
| ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV711 @ SV687 ) ) )
| ( in @ SV485 @ ( relation_dom @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4926]) ).
thf(5052,plain,
! [SV486: $i,SV659: $i] :
( ( ( in @ ( sK42_C @ SV659 @ SV486 ) @ SV659 )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4927]) ).
thf(5053,plain,
! [SV486: $i,SV659: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 ) )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4928]) ).
thf(5054,plain,
! [SV486: $i,SV660: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV660 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV733 @ SV733 ) @ SV486 )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV660 )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4929]) ).
thf(5055,plain,
! [SV567: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
| ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(5056,plain,
! [SV567: $i] :
( ( ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(5057,plain,
! [SV746: $i,SV568: $i,SV734: $i,SV712: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SV734 @ SV746 ) @ SV568 )
| ( in @ ( ordered_pair @ SV712 @ SV746 ) @ SV568 ) )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4932]) ).
thf(5058,plain,
! [SV613: $i,SV487: $i,SV633: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( relation_dom @ SV633 ) )
| ~ ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 ) )
= $true )
| ( ( ~ ( in @ SV735 @ SV613 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(5059,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
| ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5060,plain,
! [SV661: $i,SV488: $i] :
( ( ( ! [SY7323: $i] :
( ~ ( disjoint @ ( fiber @ SV488 @ SY7323 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SY7323 @ ( sK35_C @ SV661 @ SV488 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4935]) ).
thf(5061,plain,
! [SV488: $i,SV661: $i] :
( ( ( ~ ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4936]) ).
thf(5062,plain,
! [SV662: $i,SV736: $i,SV488: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
| ~ ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 ) ) )
= $true )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4937]) ).
thf(5063,plain,
! [SV663: $i,SV489: $i] :
( ( ( subset @ SV489 @ SV663 )
= $false )
| ( ( subset @ ( relation_dom @ SV489 ) @ ( relation_dom @ SV663 ) )
= $true )
| ( ( relation @ SV663 )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(5064,plain,
! [SV664: $i,SV489: $i] :
( ( ( subset @ SV489 @ SV664 )
= $false )
| ( ( subset @ ( relation_rng @ SV489 ) @ ( relation_rng @ SV664 ) )
= $true )
| ( ( relation @ SV664 )
= $false )
| ( ( relation @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4939]) ).
thf(5065,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4940]) ).
thf(5066,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4940]) ).
thf(5067,plain,
! [SV569: $i] :
( ( ( in @ ( ordered_pair @ ( sK77_B @ SV569 ) @ ( sK77_B @ SV569 ) ) @ SV569 )
= $false )
| ( ( reflexive @ SV569 )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5068,plain,
! [SV570: $i,SV713: $i] :
( ( ( in @ SV713 @ ( relation_field @ SV570 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV713 @ SV713 ) @ SV570 )
= $true )
| ( ( reflexive @ SV570 )
= $false )
| ( ( relation @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5069,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( ~ ( function @ SV737 )
| ~ ( relation @ SV737 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4944]) ).
thf(5070,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5071,plain,
! [SV529: $i,SV490: $i] :
( ( ( ~ ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5072,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4946]) ).
thf(5073,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4947]) ).
thf(5074,plain,
! [SV491: $i,SV666: $i,SV747: $i,SV738: $i] :
( ( ( ( SV738 = SV747 )
| ~ ( in @ SV738 @ SV666 )
| ~ ( in @ SV747 @ SV666 )
| ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
| ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5075,plain,
! [SV573: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
| ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5076,plain,
! [SV573: $i] :
( ( ( ( sK72_B @ SV573 )
= ( sK73_SY6464 @ SV573 ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5077,plain,
! [SV574: $i,SV739: $i,SV714: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV714 @ SV739 ) @ SV574 )
| ~ ( in @ ( ordered_pair @ SV739 @ SV714 ) @ SV574 ) )
= $true )
| ( ( SV714 = SV739 )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4951]) ).
thf(5078,plain,
! [SV492: $i,SV635: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) )
| ~ ( in @ SV615 @ SV492 ) )
= $true )
| ( ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) )
= $true )
| ( ( function @ SV635 )
= $false )
| ( ( relation @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(5079,plain,
! [SV492: $i,SV688: $i,SV715: $i] :
( ( ( ~ ( function @ SV715 ) )
= $true )
| ( ( ~ ( relation @ SV715 ) )
= $true )
| ( ( ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SV715 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(5080,plain,
! [SV492: $i,SV689: $i,SV716: $i] :
( ( ( ~ ( function @ SV716 ) )
= $true )
| ( ( ~ ( relation @ SV716 ) )
= $true )
| ( ( ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5081,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
| ~ ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) ) )
= $false )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(5082,plain,
! [SV493: $i,SV718: $i] :
( ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( ~ ( ~ ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) )
| ~ ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5083,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( relation @ SV740 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
| ( SV740
= ( relation_composition @ SV494 @ SV577 ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4957]) ).
thf(5084,plain,
! [SV577: $i,SV494: $i,SV741: $i] :
( ( ( ~ ( relation @ SV741 ) )
= $true )
| ( ( ( SV741
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(5085,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
= $false )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4961]) ).
thf(5086,plain,
! [SV496: $i,SV668: $i] :
( ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( ~ ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) ) )
= $true )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(5087,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4963]) ).
thf(5088,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4964]) ).
thf(5089,plain,
! [SV621: $i,SV581: $i] :
( ( ( ~ ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4965]) ).
thf(5090,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4965]) ).
thf(5091,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
= $false )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4966]) ).
thf(5092,plain,
! [SV670: $i,SV497: $i] :
( ( ( subset @ SV497 @ SV670 )
= $false )
| ( ( ! [SY7331: $i,SY7332: $i] :
( ~ ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV497 )
| ( in @ ( ordered_pair @ SY7331 @ SY7332 ) @ SV670 ) ) )
= $true )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5093,plain,
! [SV748: $i,SV582: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV582 @ SV748 ) @ ( sK39_B @ SV582 ) )
| ~ ( in @ SV748 @ ( sK39_B @ SV582 ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4968]) ).
thf(5094,plain,
! [SV582: $i] :
( ( ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) )
| ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5095,plain,
! [SV719: $i,SV583: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
| ~ ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 ) )
= $false )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4970]) ).
thf(5096,plain,
! [SV498: $i] :
( ( ( ! [SY7181: $i] :
( ~ ( in @ SY7181 @ ( relation_dom @ SV498 ) )
| ! [SY7182: $i] :
( ( SY7182
!= ( apply @ SV498 @ SY7181 ) )
| ( in @ ( ordered_pair @ SY7181 @ SY7182 ) @ SV498 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4971]) ).
thf(5097,plain,
! [SV498: $i] :
( ( ( ! [SY7183: $i] :
( ~ ( in @ SY7183 @ ( relation_dom @ SV498 ) )
| ! [SY7184: $i] :
( ~ ( in @ ( ordered_pair @ SY7183 @ SY7184 ) @ SV498 )
| ( SY7184
= ( apply @ SV498 @ SY7183 ) ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4972]) ).
thf(5098,plain,
! [SV498: $i] :
( ( ( ! [SY7185: $i] :
( ( in @ SY7185 @ ( relation_dom @ SV498 ) )
| ! [SY7186: $i] :
( ( SY7186
!= ( apply @ SV498 @ SY7185 ) )
| ( SY7186 = empty_set ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4973]) ).
thf(5099,plain,
! [SV498: $i] :
( ( ( ! [SY7187: $i] :
( ( in @ SY7187 @ ( relation_dom @ SV498 ) )
| ! [SY7188: $i] :
( ( SY7188 != empty_set )
| ( SY7188
= ( apply @ SV498 @ SY7187 ) ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4974]) ).
thf(5100,plain,
! [SV584: $i] :
( ( ( ~ ( reflexive @ SV584 ) )
= $true )
| ( ( ~ ( transitive @ SV584 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV584 ) )
= $true )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5101,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4976]) ).
thf(5102,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4976]) ).
thf(5103,plain,
! [SV742: $i] :
( ( ( ~ ( relation @ SV742 ) )
= $true )
| ( ( ~ ( well_ordering @ SV742 )
| ( connected @ SV742 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5104,plain,
! [SV671: $i] :
( ( ( well_ordering @ SV671 )
= $false )
| ( ( well_founded_relation @ SV671 )
= $true )
| ( ( relation @ SV671 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5105,plain,
! [SV585: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4979]) ).
thf(5106,plain,
! [SV585: $i] :
( ( ( ~ ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4979]) ).
thf(5107,plain,
! [SV586: $i,SV749: $i] :
( ( ( ! [SY7412: $i] :
( ~ ( in @ SV749 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SY7412 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SY7412 ) )
| ( SV749 = SY7412 ) ) )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4980]) ).
thf(5108,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) ) )
= $false )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4981]) ).
thf(5109,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) ) )
= $false )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4981]) ).
thf(5110,plain,
! [SV691: $i,SV673: $i,SV499: $i] :
( ( ( ~ ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) )
| ~ ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4982]) ).
thf(5111,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(5112,plain,
! [SV674: $i,SV692: $i] :
( ( ( function @ SV692 )
= $false )
| ( ( ~ ( relation @ SV692 ) )
= $true )
| ( ( ( SV692
!= ( identity_relation @ SV674 ) )
| ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5113,plain,
! [SV675: $i,SV693: $i] :
( ( ( function @ SV693 )
= $false )
| ( ( ~ ( relation @ SV693 ) )
= $true )
| ( ( ( SV693
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SV693 )
= SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4985]) ).
thf(5114,plain,
! [SV513: $i,SV638: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) )
= $true )
| ( ( function @ SV638 )
= $false )
| ( ( relation @ SV638 )
= $false )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(5115,plain,
! [SV639: $i,SV514: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ ( relation_dom @ SV514 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) )
= $true )
| ( ( function @ SV639 )
= $false )
| ( ( relation @ SV639 )
= $false )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4989]) ).
thf(5116,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) )
| ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4990]) ).
thf(5117,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
| ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4991]) ).
thf(5118,plain,
! [SV677: $i,SV641: $i,SV467: $i] :
( ( ( ~ ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) ) )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4992]) ).
thf(5119,plain,
! [SV467: $i,SV641: $i,SV677: $i] :
( ( ( ~ ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4992]) ).
thf(5120,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
| ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5121,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4994]) ).
thf(5122,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 )
| ~ ( in @ SV750 @ SV643 )
| ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 )
| ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4995]) ).
thf(5123,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ~ ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) )
| ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) ) )
= $false )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4996]) ).
thf(5124,plain,
! [SV697: $i,SV469: $i,SV722: $i] :
( ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( ~ ( ~ ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) )
| ~ ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4997]) ).
thf(5125,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ~ ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5126,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( ~ ( ~ ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) )
| ~ ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4999]) ).
thf(5127,plain,
! [SV645: $i,SV471: $i] :
( ( ( ~ ( is_reflexive_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(5128,plain,
! [SV471: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5002]) ).
thf(5129,plain,
! [SV471: $i] :
( ( ( ! [SY7031: $i] :
( ~ ( well_orders @ SV471 @ SY7031 )
| ( is_connected_in @ SV471 @ SY7031 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5003]) ).
thf(5130,plain,
! [SV726: $i,SV471: $i] :
( ( ( well_orders @ SV471 @ SV726 )
= $false )
| ( ( is_well_founded_in @ SV471 @ SV726 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5004]) ).
thf(5131,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( function @ SV727 ) )
= $true )
| ( ( ~ ( relation @ SV727 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(5132,plain,
! [SV472: $i,SV526: $i] :
( ( ( ! [SY7204: $i] :
( ~ ( function @ SY7204 )
| ~ ( relation @ SY7204 )
| ( SV526
!= ( relation_dom_restriction @ SY7204 @ SV472 ) )
| ! [SY7205: $i] :
( ~ ( in @ SY7205 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7205 )
= ( apply @ SY7204 @ SY7205 ) ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5006]) ).
thf(5133,plain,
! [SV472: $i,SV526: $i] :
( ( ( ! [SY7206: $i] :
( ~ ( function @ SY7206 )
| ~ ( relation @ SY7206 )
| ( SV526
!= ( relation_dom_restriction @ SY7206 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SY7206 ) @ SV472 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5007]) ).
thf(5134,plain,
! [SV473: $i,SV646: $i] :
( ( ( ! [SY7300: $i] :
~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SY7300 ) @ SV473 ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5135,plain,
! [SV473: $i,SV646: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ ( sK33_SY6444 @ SV646 @ SV473 ) ) @ SV473 )
= $true )
| ( ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5009]) ).
thf(5136,plain,
! [SV647: $i,SV473: $i] :
( ( ( ! [SY7301: $i] :
( ! [SY7042: $i] :
~ ( in @ ( ordered_pair @ SY7301 @ SY7042 ) @ SV473 )
| ( in @ SY7301 @ SV647 ) ) )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5010]) ).
thf(5137,plain,
! [SV473: $i,SV647: $i] :
( ( ( ! [SY7303: $i] :
( ~ ( in @ SY7303 @ SV647 )
| ( in @ ( ordered_pair @ SY7303 @ ( sK31_D @ SY7303 @ SV647 @ SV473 ) ) @ SV473 ) ) )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5011]) ).
thf(5138,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
| ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5139,plain,
! [SV474: $i,SV648: $i] :
( ( ( ( sK29_C @ SV648 @ SV474 )
= ( sK30_SY6442 @ SV648 @ SV474 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5140,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV649 )
| ~ ( in @ SV744 @ SV649 )
| ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 )
| ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5141,plain,
! [SV552: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5015]) ).
thf(5142,plain,
! [SV552: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5015]) ).
thf(5143,plain,
! [SV553: $i,SV729: $i,SV703: $i] :
( ( ( ( SV703 = SV729 )
| ~ ( in @ SV703 @ ( relation_field @ SV553 ) )
| ~ ( in @ SV729 @ ( relation_field @ SV553 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5144,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5018]) ).
thf(5145,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5019]) ).
thf(5146,plain,
! [SV602: $i,SV475: $i,SV625: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( relation_rng @ SV625 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 ) )
= $true )
| ( ( ~ ( in @ SV730 @ SV602 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(5147,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5021]) ).
thf(5148,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5021]) ).
thf(5149,plain,
! [SV650: $i] :
( ( ( relation @ SV650 )
= $false )
| ( ( empty @ SV650 )
= $false )
| ( ( ~ ( function @ SV650 ) )
= $true )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5150,plain,
! [SV651: $i] :
( ( ( relation @ SV651 )
= $false )
| ( ( empty @ SV651 )
= $false )
| ( ( ~ ( function @ SV651 ) )
= $true )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5023]) ).
thf(5151,plain,
! [SV555: $i,SV606: $i] :
( ( ( relation @ SV606 )
= $false )
| ( ( function @ SV555 )
= $false )
| ( ( relation @ SV555 )
= $false )
| ( ( ~ ( function @ SV606 ) )
= $true )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5152,plain,
! [SV556: $i,SV607: $i] :
( ( ( relation @ SV607 )
= $false )
| ( ( function @ SV556 )
= $false )
| ( ( relation @ SV556 )
= $false )
| ( ( ~ ( function @ SV607 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5025]) ).
thf(5153,plain,
! [SV608: $i,SV629: $i,SV477: $i] :
( ( ( in @ SV477 @ ( relation_rng @ SV629 ) )
= $false )
| ( ( in @ SV477 @ SV608 )
= $false )
| ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV608 @ SV629 ) ) )
= $true )
| ( ( relation @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5154,plain,
! [SV704: $i,SV678: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SV704 ) ) ) )
= $true )
| ( ( in @ SV477 @ SV678 )
= $true )
| ( ( relation @ SV704 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(5155,plain,
! [SV705: $i,SV679: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SV705 ) ) ) )
= $true )
| ( ( in @ SV477 @ ( relation_rng @ SV705 ) )
= $true )
| ( ( relation @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(5156,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5157,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( ~ ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) ) )
= $true )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5158,plain,
! [SV609: $i,SV557: $i] :
( ( ( in @ SV557 @ ( relation_rng @ SV609 ) )
= $false )
| ( ( ~ ( one_to_one @ SV609 ) )
= $true )
| ( ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) )
= $true )
| ( ( function @ SV609 )
= $false )
| ( ( relation @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5159,plain,
! [SV610: $i,SV558: $i] :
( ( ( in @ SV558 @ ( relation_rng @ SV610 ) )
= $false )
| ( ( ~ ( one_to_one @ SV610 ) )
= $true )
| ( ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) )
= $true )
| ( ( function @ SV610 )
= $false )
| ( ( relation @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5160,plain,
! [SV479: $i,SV654: $i] :
( ( ( ! [SY7314: $i] :
~ ( in @ ( ordered_pair @ SY7314 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5033]) ).
thf(5161,plain,
! [SV479: $i,SV654: $i] :
( ( ( in @ ( ordered_pair @ ( sK25_SY6439 @ SV654 @ SV479 ) @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
= $true )
| ( ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5034]) ).
thf(5162,plain,
! [SV655: $i,SV479: $i] :
( ( ( ! [SY7315: $i] :
( ! [SY7077: $i] :
~ ( in @ ( ordered_pair @ SY7077 @ SY7315 ) @ SV479 )
| ( in @ SY7315 @ SV655 ) ) )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5035]) ).
thf(5163,plain,
! [SV479: $i,SV655: $i] :
( ( ( ! [SY7317: $i] :
( ~ ( in @ SY7317 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SY7317 @ SV655 @ SV479 ) @ SY7317 ) @ SV479 ) ) )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5036]) ).
thf(5164,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5165,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( ~ ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) ) )
= $true )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5166,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
= $false )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5039]) ).
thf(5167,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) ) )
= $false )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5039]) ).
thf(5168,plain,
! [SV657: $i,SV481: $i] :
( ( ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) )
| ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) )
= $false )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5169,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( function @ SV745 )
| ~ ( relation @ SV745 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) )
| ( SV745
= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5041]) ).
thf(5170,plain,
! [SV482: $i] :
( ( ( ~ ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5042]) ).
thf(5171,plain,
! [SV482: $i] :
( ( ( ~ ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5042]) ).
thf(5172,plain,
! [SV658: $i,SV528: $i,SV630: $i,SV483: $i] :
( ( ( in @ SV483 @ SV630 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5173,plain,
! [SV706: $i,SV528: $i,SV483: $i,SV731: $i] :
( ( ( relation @ SV731 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SV731 ) )
| ( in @ SV483 @ SV706 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5174,plain,
! [SV707: $i,SV528: $i,SV483: $i,SV732: $i] :
( ( ( relation @ SV732 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SV732 ) )
| ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV732 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5045]) ).
thf(5175,plain,
! [SV484: $i,SV631: $i,SV611: $i] :
( ( ( ( SV611
!= ( apply @ SV631 @ SV484 ) ) )
= $true )
| ( ( ~ ( in @ SV484 @ ( relation_dom @ SV631 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 )
= $true )
| ( ( function @ SV631 )
= $false )
| ( ( relation @ SV631 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5176,plain,
! [SV684: $i,SV484: $i,SV708: $i] :
( ( ( function @ SV708 )
= $false )
| ( ( ~ ( relation @ SV708 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
| ( SV684
= ( apply @ SV708 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5047]) ).
thf(5177,plain,
! [SV685: $i,SV484: $i,SV709: $i] :
( ( ( function @ SV709 )
= $false )
| ( ( ~ ( relation @ SV709 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
| ( in @ SV484 @ ( relation_dom @ SV709 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5048]) ).
thf(5178,plain,
! [SV612: $i,SV632: $i,SV485: $i] :
( ( ( in @ SV485 @ ( relation_dom @ SV632 ) )
= $false )
| ( ( in @ SV485 @ SV612 )
= $false )
| ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV632 @ SV612 ) ) )
= $true )
| ( ( relation @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5179,plain,
! [SV686: $i,SV710: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV710 @ SV686 ) ) ) )
= $true )
| ( ( in @ SV485 @ SV686 )
= $true )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(5180,plain,
! [SV687: $i,SV711: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV711 @ SV687 ) ) ) )
= $true )
| ( ( in @ SV485 @ ( relation_dom @ SV711 ) )
= $true )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(5181,plain,
! [SV486: $i,SV659: $i] :
( ( ( in @ ( ordered_pair @ ( sK42_C @ SV659 @ SV486 ) @ ( sK42_C @ SV659 @ SV486 ) ) @ SV486 )
= $false )
| ( ( is_reflexive_in @ SV486 @ SV659 )
= $true )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5182,plain,
! [SV486: $i,SV660: $i,SV733: $i] :
( ( ( in @ SV733 @ SV660 )
= $false )
| ( ( in @ ( ordered_pair @ SV733 @ SV733 ) @ SV486 )
= $true )
| ( ( is_reflexive_in @ SV486 @ SV660 )
= $false )
| ( ( relation @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5183,plain,
! [SV567: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5055]) ).
thf(5184,plain,
! [SV567: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 ) )
= $false )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5055]) ).
thf(5185,plain,
! [SV746: $i,SV568: $i,SV734: $i,SV712: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 )
| ~ ( in @ ( ordered_pair @ SV734 @ SV746 ) @ SV568 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV712 @ SV746 ) @ SV568 )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(5186,plain,
! [SV613: $i,SV487: $i,SV633: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( relation_dom @ SV633 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 ) )
= $true )
| ( ( ~ ( in @ SV735 @ SV613 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5187,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5059]) ).
thf(5188,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5059]) ).
thf(5189,plain,
! [SV661: $i,SV751: $i,SV488: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV488 @ SV751 ) @ ( sK35_C @ SV661 @ SV488 ) )
| ~ ( in @ SV751 @ ( sK35_C @ SV661 @ SV488 ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5060]) ).
thf(5190,plain,
! [SV488: $i,SV661: $i] :
( ( ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
| ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5191,plain,
! [SV662: $i,SV736: $i,SV488: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
| ~ ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 ) )
= $false )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5192,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5065]) ).
thf(5193,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5066]) ).
thf(5194,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( ~ ( function @ SV737 ) )
= $true )
| ( ( ~ ( relation @ SV737 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5195,plain,
! [SV529: $i,SV490: $i] :
( ( ( ! [SY7222: $i] :
( ~ ( function @ SY7222 )
| ~ ( relation @ SY7222 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7222 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SY7222 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5070]) ).
thf(5196,plain,
! [SV529: $i,SV490: $i] :
( ( ( ! [SY7223: $i] :
( ~ ( function @ SY7223 )
| ~ ( relation @ SY7223 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SY7223 @ SV529 ) ) )
| ( in @ ( apply @ SY7223 @ SV490 ) @ ( relation_dom @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5071]) ).
thf(5197,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5072]) ).
thf(5198,plain,
! [SV491: $i,SV665: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_SY6437 @ SV665 @ SV491 ) @ ( sK21_C @ SV665 @ SV491 ) ) @ SV491 )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5073]) ).
thf(5199,plain,
! [SV491: $i,SV666: $i,SV747: $i,SV738: $i] :
( ( ( ( SV738 = SV747 )
| ~ ( in @ SV738 @ SV666 )
| ~ ( in @ SV747 @ SV666 )
| ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5074]) ).
thf(5200,plain,
! [SV573: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5075]) ).
thf(5201,plain,
! [SV573: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 ) )
= $false )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5075]) ).
thf(5202,plain,
! [SV574: $i,SV739: $i,SV714: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV714 @ SV739 ) @ SV574 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV739 @ SV714 ) @ SV574 ) )
= $true )
| ( ( SV714 = SV739 )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5203,plain,
! [SV492: $i,SV635: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ ( relation_dom @ SV635 ) ) )
= $true )
| ( ( ~ ( in @ SV615 @ SV492 ) )
= $true )
| ( ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) )
= $true )
| ( ( function @ SV635 )
= $false )
| ( ( relation @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5204,plain,
! [SV492: $i,SV688: $i,SV715: $i] :
( ( ( function @ SV715 )
= $false )
| ( ( ~ ( relation @ SV715 ) )
= $true )
| ( ( ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SV715 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5079]) ).
thf(5205,plain,
! [SV492: $i,SV689: $i,SV716: $i] :
( ( ( function @ SV716 )
= $false )
| ( ( ~ ( relation @ SV716 ) )
= $true )
| ( ( ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5080]) ).
thf(5206,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) ) )
= $false )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5081]) ).
thf(5207,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) ) )
= $false )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5081]) ).
thf(5208,plain,
! [SV718: $i,SV493: $i] :
( ( ( ~ ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) )
| ~ ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5209,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( relation @ SV740 )
= $false )
| ( ( ~ ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
| ( SV740
= ( relation_composition @ SV494 @ SV577 ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5210,plain,
! [SV577: $i,SV494: $i,SV741: $i] :
( ( ( relation @ SV741 )
= $false )
| ( ( ( SV741
!= ( relation_composition @ SV494 @ SV577 ) )
| ~ ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) ) )
= $true )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5211,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
= $false )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5085]) ).
thf(5212,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) ) )
= $false )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5085]) ).
thf(5213,plain,
! [SV496: $i,SV668: $i] :
( ( ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) )
| ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) )
= $false )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5086]) ).
thf(5214,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5215,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
| ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5088]) ).
thf(5216,plain,
! [SV621: $i,SV581: $i] :
( ( ( ! [SY7282: $i,SY7283: $i] :
( ( SY7282 != SY7283 )
| ~ ( in @ SY7282 @ SV581 )
| ( in @ ( ordered_pair @ SY7282 @ SY7283 ) @ SV621 ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5089]) ).
thf(5217,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5090]) ).
thf(5218,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 ) )
= $false )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5091]) ).
thf(5219,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
= $false )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5091]) ).
thf(5220,plain,
! [SV670: $i,SV497: $i,SV752: $i] :
( ( ( ! [SY7413: $i] :
( ~ ( in @ ( ordered_pair @ SV752 @ SY7413 ) @ SV497 )
| ( in @ ( ordered_pair @ SV752 @ SY7413 ) @ SV670 ) ) )
= $true )
| ( ( subset @ SV497 @ SV670 )
= $false )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5092]) ).
thf(5221,plain,
! [SV748: $i,SV582: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV582 @ SV748 ) @ ( sK39_B @ SV582 ) ) )
= $true )
| ( ( ~ ( in @ SV748 @ ( sK39_B @ SV582 ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5222,plain,
! [SV582: $i] :
( ( ( ~ ( ( ( sK39_B @ SV582 )
!= empty_set ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5223,plain,
! [SV582: $i] :
( ( ( ~ ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5224,plain,
! [SV719: $i,SV583: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 ) )
= $false )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5095]) ).
thf(5225,plain,
! [SV583: $i,SV719: $i] :
( ( ( ~ ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 ) )
= $false )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5095]) ).
thf(5226,plain,
! [SV498: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ ( relation_dom @ SV498 ) )
| ! [SY7414: $i] :
( ( SY7414
!= ( apply @ SV498 @ SV753 ) )
| ( in @ ( ordered_pair @ SV753 @ SY7414 ) @ SV498 ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5096]) ).
thf(5227,plain,
! [SV498: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( relation_dom @ SV498 ) )
| ! [SY7415: $i] :
( ~ ( in @ ( ordered_pair @ SV754 @ SY7415 ) @ SV498 )
| ( SY7415
= ( apply @ SV498 @ SV754 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5097]) ).
thf(5228,plain,
! [SV498: $i,SV755: $i] :
( ( ( ( in @ SV755 @ ( relation_dom @ SV498 ) )
| ! [SY7416: $i] :
( ( SY7416
!= ( apply @ SV498 @ SV755 ) )
| ( SY7416 = empty_set ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5098]) ).
thf(5229,plain,
! [SV498: $i,SV756: $i] :
( ( ( ( in @ SV756 @ ( relation_dom @ SV498 ) )
| ! [SY7417: $i] :
( ( SY7417 != empty_set )
| ( SY7417
= ( apply @ SV498 @ SV756 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5099]) ).
thf(5230,plain,
! [SV584: $i] :
( ( ( reflexive @ SV584 )
= $false )
| ( ( ~ ( transitive @ SV584 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV584 ) )
= $true )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5231,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5101]) ).
thf(5232,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5102]) ).
thf(5233,plain,
! [SV742: $i] :
( ( ( relation @ SV742 )
= $false )
| ( ( ~ ( well_ordering @ SV742 )
| ( connected @ SV742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5234,plain,
! [SV585: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5105]) ).
thf(5235,plain,
! [SV585: $i] :
( ( ( ( ( sK17_B @ SV585 )
!= ( sK18_SY6435 @ SV585 ) ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5106]) ).
thf(5236,plain,
! [SV757: $i,SV586: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SV757 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) )
| ( SV749 = SV757 ) )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5107]) ).
thf(5237,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) )
| ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5108]) ).
thf(5238,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
| ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5109]) ).
thf(5239,plain,
! [SV691: $i,SV673: $i,SV499: $i] :
( ( ( ~ ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) ) )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5110]) ).
thf(5240,plain,
! [SV499: $i,SV673: $i,SV691: $i] :
( ( ( ~ ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5110]) ).
thf(5241,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
| ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5242,plain,
! [SV674: $i,SV692: $i] :
( ( ( relation @ SV692 )
= $false )
| ( ( function @ SV692 )
= $false )
| ( ( ( SV692
!= ( identity_relation @ SV674 ) )
| ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5243,plain,
! [SV675: $i,SV693: $i] :
( ( ( relation @ SV693 )
= $false )
| ( ( function @ SV693 )
= $false )
| ( ( ( SV693
!= ( identity_relation @ SV675 ) )
| ( ( relation_dom @ SV693 )
= SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5244,plain,
! [SV513: $i,SV638: $i,SV439: $i] :
( ( ( in @ SV439 @ ( relation_dom @ ( relation_composition @ SV638 @ SV513 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV638 @ SV513 ) @ SV439 )
= ( apply @ SV513 @ ( apply @ SV638 @ SV439 ) ) )
= $true )
| ( ( function @ SV638 )
= $false )
| ( ( relation @ SV638 )
= $false )
| ( ( function @ SV513 )
= $false )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5245,plain,
! [SV639: $i,SV514: $i,SV440: $i] :
( ( ( in @ SV440 @ ( relation_dom @ SV514 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV514 @ SV639 ) @ SV440 )
= ( apply @ SV639 @ ( apply @ SV514 @ SV440 ) ) )
= $true )
| ( ( function @ SV639 )
= $false )
| ( ( relation @ SV639 )
= $false )
| ( ( function @ SV514 )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5246,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ! [SY7342: $i] :
( ~ ( in @ ( ordered_pair @ SY7342 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SY7342 @ SV640 ) ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5247,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) ) )
= $true )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5248,plain,
! [SV677: $i,SV641: $i,SV467: $i] :
( ( ( ! [SY7343: $i] :
( ! [SY7295: $i] :
( ~ ( in @ ( ordered_pair @ SY7295 @ SY7343 ) @ SV467 )
| ~ ( in @ SY7295 @ SV641 ) )
| ( in @ SY7343 @ SV677 ) ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5118]) ).
thf(5249,plain,
! [SV467: $i,SV641: $i,SV677: $i] :
( ( ( ! [SY7345: $i] :
( ~ ( in @ SY7345 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SY7345 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SY7345 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5119]) ).
thf(5250,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5120]) ).
thf(5251,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5120]) ).
thf(5252,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 )
| ~ ( in @ SV750 @ SV643 )
| ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 )
| ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5253,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ~ ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) )
| ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) ) )
= $false )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5123]) ).
thf(5254,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) ) )
= $false )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5123]) ).
thf(5255,plain,
! [SV722: $i,SV697: $i,SV469: $i] :
( ( ( ~ ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) )
| ~ ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5124]) ).
thf(5256,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5125]) ).
thf(5257,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5125]) ).
thf(5258,plain,
! [SV724: $i,SV699: $i,SV470: $i] :
( ( ( ~ ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) )
| ~ ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5126]) ).
thf(5259,plain,
! [SV645: $i,SV471: $i] :
( ( ( is_reflexive_in @ SV471 @ SV645 )
= $false )
| ( ( ~ ( is_transitive_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5127]) ).
thf(5260,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
| ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5261,plain,
! [SV758: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV758 )
| ( is_connected_in @ SV471 @ SV758 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5129]) ).
thf(5262,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( function @ SV727 )
= $false )
| ( ( ~ ( relation @ SV727 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5131]) ).
thf(5263,plain,
! [SV472: $i,SV526: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 )
| ~ ( relation @ SV759 )
| ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) )
| ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5132]) ).
thf(5264,plain,
! [SV472: $i,SV526: $i,SV760: $i] :
( ( ( ~ ( function @ SV760 )
| ~ ( relation @ SV760 )
| ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5133]) ).
thf(5265,plain,
! [SV761: $i,SV473: $i,SV646: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SV761 ) @ SV473 ) )
= $true )
| ( ( ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5134]) ).
thf(5266,plain,
! [SV647: $i,SV473: $i,SV762: $i] :
( ( ( ! [SY7419: $i] :
~ ( in @ ( ordered_pair @ SV762 @ SY7419 ) @ SV473 )
| ( in @ SV762 @ SV647 ) )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5136]) ).
thf(5267,plain,
! [SV473: $i,SV647: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV647 )
| ( in @ ( ordered_pair @ SV763 @ ( sK31_D @ SV763 @ SV647 @ SV473 ) ) @ SV473 ) )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5137]) ).
thf(5268,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5138]) ).
thf(5269,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5138]) ).
thf(5270,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV649 )
| ~ ( in @ SV744 @ SV649 )
| ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5271,plain,
! [SV552: $i] :
( ( ( ~ ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5141]) ).
thf(5272,plain,
! [SV552: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5142]) ).
thf(5273,plain,
! [SV553: $i,SV729: $i,SV703: $i] :
( ( ( SV703 = SV729 )
= $true )
| ( ( ~ ( in @ SV703 @ ( relation_field @ SV553 ) )
| ~ ( in @ SV729 @ ( relation_field @ SV553 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5274,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5275,plain,
! [SV602: $i,SV475: $i,SV625: $i,SV730: $i] :
( ( ( in @ SV730 @ ( relation_rng @ SV625 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 ) )
= $true )
| ( ( ~ ( in @ SV730 @ SV602 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5276,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5147]) ).
thf(5277,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ SV603 )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5148]) ).
thf(5278,plain,
! [SV650: $i] :
( ( ( function @ SV650 )
= $false )
| ( ( empty @ SV650 )
= $false )
| ( ( relation @ SV650 )
= $false )
| ( ( function @ SV650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5149]) ).
thf(5279,plain,
! [SV651: $i] :
( ( ( function @ SV651 )
= $false )
| ( ( empty @ SV651 )
= $false )
| ( ( relation @ SV651 )
= $false )
| ( ( relation @ SV651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5280,plain,
! [SV555: $i,SV606: $i] :
( ( ( function @ SV606 )
= $false )
| ( ( relation @ SV555 )
= $false )
| ( ( function @ SV555 )
= $false )
| ( ( relation @ SV606 )
= $false )
| ( ( function @ ( relation_composition @ SV555 @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5281,plain,
! [SV556: $i,SV607: $i] :
( ( ( function @ SV607 )
= $false )
| ( ( relation @ SV556 )
= $false )
| ( ( function @ SV556 )
= $false )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ ( relation_composition @ SV556 @ SV607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5152]) ).
thf(5282,plain,
! [SV704: $i,SV678: $i,SV477: $i] :
( ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV678 @ SV704 ) ) )
= $false )
| ( ( in @ SV477 @ SV678 )
= $true )
| ( ( relation @ SV704 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5154]) ).
thf(5283,plain,
! [SV705: $i,SV679: $i,SV477: $i] :
( ( ( in @ SV477 @ ( relation_rng @ ( relation_rng_restriction @ SV679 @ SV705 ) ) )
= $false )
| ( ( in @ SV477 @ ( relation_rng @ SV705 ) )
= $true )
| ( ( relation @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5284,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5156]) ).
thf(5285,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5156]) ).
thf(5286,plain,
! [SV681: $i,SV478: $i,SV653: $i] :
( ( ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) )
| ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5157]) ).
thf(5287,plain,
! [SV557: $i,SV609: $i] :
( ( ( one_to_one @ SV609 )
= $false )
| ( ( in @ SV557 @ ( relation_rng @ SV609 ) )
= $false )
| ( ( SV557
= ( apply @ SV609 @ ( apply @ ( function_inverse @ SV609 ) @ SV557 ) ) )
= $true )
| ( ( function @ SV609 )
= $false )
| ( ( relation @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5158]) ).
thf(5288,plain,
! [SV558: $i,SV610: $i] :
( ( ( one_to_one @ SV610 )
= $false )
| ( ( in @ SV558 @ ( relation_rng @ SV610 ) )
= $false )
| ( ( SV558
= ( apply @ ( relation_composition @ ( function_inverse @ SV610 ) @ SV610 ) @ SV558 ) )
= $true )
| ( ( function @ SV610 )
= $false )
| ( ( relation @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5159]) ).
thf(5289,plain,
! [SV479: $i,SV654: $i,SV764: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 ) )
= $true )
| ( ( ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5160]) ).
thf(5290,plain,
! [SV655: $i,SV479: $i,SV765: $i] :
( ( ( ! [SY7420: $i] :
~ ( in @ ( ordered_pair @ SY7420 @ SV765 ) @ SV479 )
| ( in @ SV765 @ SV655 ) )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5162]) ).
thf(5291,plain,
! [SV479: $i,SV655: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV655 )
| ( in @ ( ordered_pair @ ( sK23_D @ SV766 @ SV655 @ SV479 ) @ SV766 ) @ SV479 ) )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5163]) ).
thf(5292,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5164]) ).
thf(5293,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5164]) ).
thf(5294,plain,
! [SV683: $i,SV527: $i,SV480: $i] :
( ( ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) )
| ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5295,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5166]) ).
thf(5296,plain,
! [SV481: $i,SV656: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
| ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5167]) ).
thf(5297,plain,
! [SV657: $i,SV481: $i] :
( ( ( ~ ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) ) )
= $false )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5168]) ).
thf(5298,plain,
! [SV481: $i,SV657: $i] :
( ( ( ~ ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) )
= $false )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5168]) ).
thf(5299,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( function @ SV745 ) )
= $true )
| ( ( ~ ( relation @ SV745 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) )
| ( SV745
= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(5300,plain,
! [SV482: $i] :
( ( ( ! [SY7095: $i] :
( ~ ( function @ SY7095 )
| ~ ( relation @ SY7095 )
| ( SY7095
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7096: $i,SY7097: $i] :
( ( SY7097
!= ( apply @ SY7095 @ SY7096 ) )
| ~ ( in @ SY7096 @ ( relation_rng @ SV482 ) )
| ( SY7096
= ( apply @ SV482 @ SY7097 ) ) )
| ~ ! [SY7098: $i,SY7099: $i] :
( ( SY7099
!= ( apply @ SY7095 @ SY7098 ) )
| ~ ( in @ SY7098 @ ( relation_rng @ SV482 ) )
| ( in @ SY7099 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7100: $i,SY7101: $i] :
( ( SY7100
!= ( apply @ SV482 @ SY7101 ) )
| ~ ( in @ SY7101 @ ( relation_dom @ SV482 ) )
| ( SY7101
= ( apply @ SY7095 @ SY7100 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5170]) ).
thf(5301,plain,
! [SV482: $i] :
( ( ( ! [SY7104: $i] :
( ~ ( function @ SY7104 )
| ~ ( relation @ SY7104 )
| ( SY7104
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SY7104 )
= ( relation_rng @ SV482 ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5171]) ).
thf(5302,plain,
! [SV630: $i,SV658: $i,SV528: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV658 )
= $false )
| ( ( in @ SV483 @ SV630 )
= $false )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV630 ) @ SV658 ) )
= $true )
| ( ( relation @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5303,plain,
! [SV731: $i,SV706: $i,SV528: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SV731 ) ) )
= $true )
| ( ( in @ SV483 @ SV706 )
= $true )
| ( ( relation @ SV731 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5304,plain,
! [SV732: $i,SV707: $i,SV528: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SV732 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV732 )
= $true )
| ( ( relation @ SV732 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(5305,plain,
! [SV484: $i,SV631: $i,SV611: $i] :
( ( ( SV611
= ( apply @ SV631 @ SV484 ) )
= $false )
| ( ( ~ ( in @ SV484 @ ( relation_dom @ SV631 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 )
= $true )
| ( ( function @ SV631 )
= $false )
| ( ( relation @ SV631 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5175]) ).
thf(5306,plain,
! [SV684: $i,SV484: $i,SV708: $i] :
( ( ( relation @ SV708 )
= $false )
| ( ( function @ SV708 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
| ( SV684
= ( apply @ SV708 @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5307,plain,
! [SV685: $i,SV484: $i,SV709: $i] :
( ( ( relation @ SV709 )
= $false )
| ( ( function @ SV709 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
| ( in @ SV484 @ ( relation_dom @ SV709 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5308,plain,
! [SV686: $i,SV710: $i,SV485: $i] :
( ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV710 @ SV686 ) ) )
= $false )
| ( ( in @ SV485 @ SV686 )
= $true )
| ( ( relation @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5309,plain,
! [SV687: $i,SV711: $i,SV485: $i] :
( ( ( in @ SV485 @ ( relation_dom @ ( relation_dom_restriction @ SV711 @ SV687 ) ) )
= $false )
| ( ( in @ SV485 @ ( relation_dom @ SV711 ) )
= $true )
| ( ( relation @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5310,plain,
! [SV567: $i] :
( ( ( in @ ( ordered_pair @ ( sK74_B @ SV567 ) @ ( sK75_SY6465 @ SV567 ) ) @ SV567 )
= $true )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5183]) ).
thf(5311,plain,
! [SV567: $i] :
( ( ( in @ ( ordered_pair @ ( sK75_SY6465 @ SV567 ) @ ( sK76_SY6467 @ SV567 ) ) @ SV567 )
= $true )
| ( ( transitive @ SV567 )
= $true )
| ( ( relation @ SV567 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5184]) ).
thf(5312,plain,
! [SV746: $i,SV568: $i,SV734: $i,SV712: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV734 @ SV746 ) @ SV568 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV712 @ SV746 ) @ SV568 )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5185]) ).
thf(5313,plain,
! [SV613: $i,SV487: $i,SV633: $i,SV735: $i] :
( ( ( in @ SV735 @ ( relation_dom @ SV633 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 ) )
= $true )
| ( ( ~ ( in @ SV735 @ SV613 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5186]) ).
thf(5314,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5187]) ).
thf(5315,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV614 )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5188]) ).
thf(5316,plain,
! [SV661: $i,SV751: $i,SV488: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV488 @ SV751 ) @ ( sK35_C @ SV661 @ SV488 ) ) )
= $true )
| ( ( ~ ( in @ SV751 @ ( sK35_C @ SV661 @ SV488 ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5317,plain,
! [SV488: $i,SV661: $i] :
( ( ( ~ ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5190]) ).
thf(5318,plain,
! [SV488: $i,SV661: $i] :
( ( ( ~ ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5190]) ).
thf(5319,plain,
! [SV662: $i,SV736: $i,SV488: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 ) )
= $false )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5320,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( ~ ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 ) )
= $false )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5321,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5322,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( function @ SV737 )
= $false )
| ( ( ~ ( relation @ SV737 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5323,plain,
! [SV529: $i,SV490: $i,SV767: $i] :
( ( ( ~ ( function @ SV767 )
| ~ ( relation @ SV767 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SV767 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5195]) ).
thf(5324,plain,
! [SV529: $i,SV490: $i,SV768: $i] :
( ( ( ~ ( function @ SV768 )
| ~ ( relation @ SV768 )
| ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
| ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5196]) ).
thf(5325,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5197]) ).
thf(5326,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5197]) ).
thf(5327,plain,
! [SV491: $i,SV666: $i,SV747: $i,SV738: $i] :
( ( ( ( SV738 = SV747 )
| ~ ( in @ SV738 @ SV666 )
| ~ ( in @ SV747 @ SV666 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(5328,plain,
! [SV573: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_B @ SV573 ) @ ( sK73_SY6464 @ SV573 ) ) @ SV573 )
= $true )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5200]) ).
thf(5329,plain,
! [SV573: $i] :
( ( ( in @ ( ordered_pair @ ( sK73_SY6464 @ SV573 ) @ ( sK72_B @ SV573 ) ) @ SV573 )
= $true )
| ( ( antisymmetric @ SV573 )
= $true )
| ( ( relation @ SV573 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5201]) ).
thf(5330,plain,
! [SV574: $i,SV739: $i,SV714: $i] :
( ( ( in @ ( ordered_pair @ SV714 @ SV739 ) @ SV574 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV739 @ SV714 ) @ SV574 ) )
= $true )
| ( ( SV714 = SV739 )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5331,plain,
! [SV492: $i,SV635: $i,SV615: $i] :
( ( ( in @ SV615 @ ( relation_dom @ SV635 ) )
= $false )
| ( ( ~ ( in @ SV615 @ SV492 ) )
= $true )
| ( ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) )
= $true )
| ( ( function @ SV635 )
= $false )
| ( ( relation @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5332,plain,
! [SV492: $i,SV688: $i,SV715: $i] :
( ( ( relation @ SV715 )
= $false )
| ( ( function @ SV715 )
= $false )
| ( ( ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
| ( in @ SV688 @ ( relation_dom @ SV715 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5204]) ).
thf(5333,plain,
! [SV492: $i,SV689: $i,SV716: $i] :
( ( ( relation @ SV716 )
= $false )
| ( ( function @ SV716 )
= $false )
| ( ( ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
| ( in @ SV689 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5334,plain,
! [SV493: $i,SV717: $i] :
( ( ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) )
| ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5206]) ).
thf(5335,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
| ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5207]) ).
thf(5336,plain,
! [SV718: $i,SV493: $i] :
( ( ( ~ ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) ) )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5208]) ).
thf(5337,plain,
! [SV493: $i,SV718: $i] :
( ( ( ~ ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5208]) ).
thf(5338,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5339,plain,
! [SV577: $i,SV494: $i,SV741: $i] :
( ( ( ( SV741
!= ( relation_composition @ SV494 @ SV577 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) ) )
= $true )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5340,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5211]) ).
thf(5341,plain,
! [SV496: $i,SV667: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
| ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5212]) ).
thf(5342,plain,
! [SV496: $i,SV668: $i] :
( ( ( ~ ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) ) )
= $false )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5213]) ).
thf(5343,plain,
! [SV668: $i,SV496: $i] :
( ( ( ~ ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) )
= $false )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5213]) ).
thf(5344,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( ( sK60_C @ SV620 @ SV580 )
!= ( sK61_SY6460 @ SV620 @ SV580 ) ) )
= $true )
| ( ( ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5214]) ).
thf(5345,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5215]) ).
thf(5346,plain,
! [SV580: $i,SV620: $i] :
( ( ( ~ ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) ) )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5215]) ).
thf(5347,plain,
! [SV621: $i,SV581: $i,SV769: $i] :
( ( ( ! [SY7421: $i] :
( ( SV769 != SY7421 )
| ~ ( in @ SV769 @ SV581 )
| ( in @ ( ordered_pair @ SV769 @ SY7421 ) @ SV621 ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5216]) ).
thf(5348,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) )
| ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5349,plain,
! [SV497: $i,SV669: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV497 )
= $true )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5218]) ).
thf(5350,plain,
! [SV497: $i,SV669: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 ) )
= $true )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5219]) ).
thf(5351,plain,
! [SV670: $i,SV497: $i,SV770: $i,SV752: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV497 )
| ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV670 ) )
= $true )
| ( ( subset @ SV497 @ SV670 )
= $false )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5220]) ).
thf(5352,plain,
! [SV748: $i,SV582: $i] :
( ( ( disjoint @ ( fiber @ SV582 @ SV748 ) @ ( sK39_B @ SV582 ) )
= $false )
| ( ( ~ ( in @ SV748 @ ( sK39_B @ SV582 ) ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5353,plain,
! [SV582: $i] :
( ( ( ( ( sK39_B @ SV582 )
!= empty_set ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5222]) ).
thf(5354,plain,
! [SV582: $i] :
( ( ( subset @ ( sK39_B @ SV582 ) @ ( relation_field @ SV582 ) )
= $true )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5223]) ).
thf(5355,plain,
! [SV719: $i,SV583: $i] :
( ( ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
= $true )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5224]) ).
thf(5356,plain,
! [SV583: $i,SV719: $i] :
( ( ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 )
= $true )
| ( ( ( SV719 = empty_set )
| ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5225]) ).
thf(5357,plain,
! [SV498: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ ( relation_dom @ SV498 ) ) )
= $true )
| ( ( ! [SY7414: $i] :
( ( SY7414
!= ( apply @ SV498 @ SV753 ) )
| ( in @ ( ordered_pair @ SV753 @ SY7414 ) @ SV498 ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5226]) ).
thf(5358,plain,
! [SV498: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( relation_dom @ SV498 ) ) )
= $true )
| ( ( ! [SY7415: $i] :
( ~ ( in @ ( ordered_pair @ SV754 @ SY7415 ) @ SV498 )
| ( SY7415
= ( apply @ SV498 @ SV754 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5227]) ).
thf(5359,plain,
! [SV498: $i,SV755: $i] :
( ( ( in @ SV755 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( ! [SY7416: $i] :
( ( SY7416
!= ( apply @ SV498 @ SV755 ) )
| ( SY7416 = empty_set ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(5360,plain,
! [SV498: $i,SV756: $i] :
( ( ( in @ SV756 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( ! [SY7417: $i] :
( ( SY7417 != empty_set )
| ( SY7417
= ( apply @ SV498 @ SV756 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(5361,plain,
! [SV584: $i] :
( ( ( transitive @ SV584 )
= $false )
| ( ( reflexive @ SV584 )
= $false )
| ( ( ~ ( antisymmetric @ SV584 ) )
= $true )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5230]) ).
thf(5362,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5231]) ).
thf(5363,plain,
! [SV771: $i] :
( ( ~ ( relation @ SV771 )
| ~ ( well_ordering @ SV771 )
| ( antisymmetric @ SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5232]) ).
thf(5364,plain,
! [SV742: $i] :
( ( ( ~ ( well_ordering @ SV742 ) )
= $true )
| ( ( connected @ SV742 )
= $true )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(5365,plain,
! [SV585: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
| ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5234]) ).
thf(5366,plain,
! [SV585: $i] :
( ( ( ( sK17_B @ SV585 )
= ( sK18_SY6435 @ SV585 ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5235]) ).
thf(5367,plain,
! [SV757: $i,SV586: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SV757 @ ( relation_dom @ SV586 ) )
| ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) ) )
= $true )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5236]) ).
thf(5368,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ! [SY7366: $i] :
( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SY7366 ) @ SV499 )
| ~ ( in @ SY7366 @ SV672 ) ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5369,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) ) )
= $true )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5238]) ).
thf(5370,plain,
! [SV691: $i,SV673: $i,SV499: $i] :
( ( ( ! [SY7367: $i] :
( ! [SY7337: $i] :
( ~ ( in @ ( ordered_pair @ SY7367 @ SY7337 ) @ SV499 )
| ~ ( in @ SY7337 @ SV673 ) )
| ( in @ SY7367 @ SV691 ) ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5239]) ).
thf(5371,plain,
! [SV499: $i,SV673: $i,SV691: $i] :
( ( ( ! [SY7369: $i] :
( ~ ( in @ SY7369 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7369 @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SY7369 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5240]) ).
thf(5372,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 ) )
= $false )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5241]) ).
thf(5373,plain,
! [SV591: $i,SV622: $i] :
( ( ( ~ ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5241]) ).
thf(5374,plain,
! [SV674: $i,SV692: $i] :
( ( ( ( SV692
!= ( identity_relation @ SV674 ) ) )
= $true )
| ( ( ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true )
| ( ( function @ SV692 )
= $false )
| ( ( relation @ SV692 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5242]) ).
thf(5375,plain,
! [SV675: $i,SV693: $i] :
( ( ( ( SV693
!= ( identity_relation @ SV675 ) ) )
= $true )
| ( ( ( relation_dom @ SV693 )
= SV675 )
= $true )
| ( ( function @ SV693 )
= $false )
| ( ( relation @ SV693 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5243]) ).
thf(5376,plain,
! [SV467: $i,SV640: $i,SV676: $i,SV772: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV772 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ SV772 @ SV640 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5246]) ).
thf(5377,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
| ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
= $false )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5378,plain,
! [SV677: $i,SV641: $i,SV467: $i,SV773: $i] :
( ( ( ! [SY7422: $i] :
( ~ ( in @ ( ordered_pair @ SY7422 @ SV773 ) @ SV467 )
| ~ ( in @ SY7422 @ SV641 ) )
| ( in @ SV773 @ SV677 ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5248]) ).
thf(5379,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV677 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5249]) ).
thf(5380,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5250]) ).
thf(5381,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( ordered_pair @ ( sK11_SY6427 @ SV642 @ SV468 ) @ ( sK12_SY6429 @ SV642 @ SV468 ) ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5251]) ).
thf(5382,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 )
| ~ ( in @ SV750 @ SV643 )
| ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5252]) ).
thf(5383,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) )
| ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5253]) ).
thf(5384,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
| ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5254]) ).
thf(5385,plain,
! [SV722: $i,SV697: $i,SV469: $i] :
( ( ( ~ ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) ) )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5255]) ).
thf(5386,plain,
! [SV469: $i,SV697: $i,SV722: $i] :
( ( ( ~ ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5255]) ).
thf(5387,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5256]) ).
thf(5388,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5257]) ).
thf(5389,plain,
! [SV724: $i,SV699: $i,SV470: $i] :
( ( ( ~ ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5258]) ).
thf(5390,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ~ ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5258]) ).
thf(5391,plain,
! [SV645: $i,SV471: $i] :
( ( ( is_transitive_in @ SV471 @ SV645 )
= $false )
| ( ( is_reflexive_in @ SV471 @ SV645 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5259]) ).
thf(5392,plain,
! [SV471: $i] :
( ( ( ~ ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5260]) ).
thf(5393,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5260]) ).
thf(5394,plain,
! [SV758: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV758 ) )
= $true )
| ( ( is_connected_in @ SV471 @ SV758 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(5395,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( relation @ SV727 )
= $false )
| ( ( function @ SV727 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
| ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5396,plain,
! [SV472: $i,SV526: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 )
| ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) )
| ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(5397,plain,
! [SV472: $i,SV526: $i,SV760: $i] :
( ( ( ~ ( function @ SV760 )
| ~ ( relation @ SV760 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5264]) ).
thf(5398,plain,
! [SV761: $i,SV473: $i,SV646: $i] :
( ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SV761 ) @ SV473 )
= $false )
| ( ( ~ ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 ) )
= $true )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5265]) ).
thf(5399,plain,
! [SV647: $i,SV473: $i,SV762: $i] :
( ( ( ! [SY7419: $i] :
~ ( in @ ( ordered_pair @ SV762 @ SY7419 ) @ SV473 ) )
= $true )
| ( ( in @ SV762 @ SV647 )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5266]) ).
thf(5400,plain,
! [SV473: $i,SV647: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV647 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV763 @ ( sK31_D @ SV763 @ SV647 @ SV473 ) ) @ SV473 )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5401,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5268]) ).
thf(5402,plain,
! [SV474: $i,SV648: $i] :
( ( ( in @ ( ordered_pair @ ( sK30_SY6442 @ SV648 @ SV474 ) @ ( sK29_C @ SV648 @ SV474 ) ) @ SV474 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5269]) ).
thf(5403,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV649 )
| ~ ( in @ SV744 @ SV649 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5270]) ).
thf(5404,plain,
! [SV552: $i] :
( ( ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
| ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5405,plain,
! [SV552: $i] :
( ( ( in @ ( ordered_pair @ ( sK70_B @ SV552 ) @ ( sK71_SY6463 @ SV552 ) ) @ SV552 )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5406,plain,
! [SV729: $i,SV553: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ ( relation_field @ SV553 ) ) )
= $true )
| ( ( ~ ( in @ SV729 @ ( relation_field @ SV553 ) ) )
= $true )
| ( ( SV703 = SV729 )
= $true )
| ( ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5273]) ).
thf(5407,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5274]) ).
thf(5408,plain,
( ( ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5274]) ).
thf(5409,plain,
! [SV602: $i,SV625: $i,SV730: $i,SV475: $i] :
( ( ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 )
= $false )
| ( ( in @ SV730 @ ( relation_rng @ SV625 ) )
= $false )
| ( ( ~ ( in @ SV730 @ SV602 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5410,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
| ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5411,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5284]) ).
thf(5412,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5285]) ).
thf(5413,plain,
! [SV681: $i,SV478: $i,SV653: $i] :
( ( ( ~ ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5286]) ).
thf(5414,plain,
! [SV478: $i,SV653: $i,SV681: $i] :
( ( ( ~ ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5286]) ).
thf(5415,plain,
! [SV479: $i,SV654: $i,SV764: $i] :
( ( ( in @ ( ordered_pair @ SV764 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
= $false )
| ( ( ~ ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 ) )
= $true )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5416,plain,
! [SV655: $i,SV479: $i,SV765: $i] :
( ( ( ! [SY7420: $i] :
~ ( in @ ( ordered_pair @ SY7420 @ SV765 ) @ SV479 ) )
= $true )
| ( ( in @ SV765 @ SV655 )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5417,plain,
! [SV479: $i,SV655: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV655 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_D @ SV766 @ SV655 @ SV479 ) @ SV766 ) @ SV479 )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(5418,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5292]) ).
thf(5419,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5293]) ).
thf(5420,plain,
! [SV683: $i,SV527: $i,SV480: $i] :
( ( ( ~ ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5294]) ).
thf(5421,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5294]) ).
thf(5422,plain,
! [SV481: $i,SV656: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(5423,plain,
! [SV481: $i,SV656: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5424,plain,
! [SV657: $i,SV481: $i] :
( ( ( ! [SY7318: $i,SY7319: $i] :
( ~ ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV481 )
| ( in @ ( ordered_pair @ SY7318 @ SY7319 ) @ SV657 ) ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5297]) ).
thf(5425,plain,
! [SV481: $i,SV657: $i] :
( ( ( ! [SY7320: $i,SY7321: $i] :
( ~ ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV657 )
| ( in @ ( ordered_pair @ SY7320 @ SY7321 ) @ SV481 ) ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5298]) ).
thf(5426,plain,
! [SV482: $i,SV745: $i] :
( ( ( function @ SV745 )
= $false )
| ( ( ~ ( relation @ SV745 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) )
| ( SV745
= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5427,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ( function @ SV775 )
| ~ ( relation @ SV775 )
| ( SV775
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5300]) ).
thf(5428,plain,
! [SV482: $i,SV776: $i] :
( ( ( ~ ( function @ SV776 )
| ~ ( relation @ SV776 )
| ( SV776
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5301]) ).
thf(5429,plain,
! [SV731: $i,SV706: $i,SV528: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV706 ) @ SV731 ) )
= $false )
| ( ( in @ SV483 @ SV706 )
= $true )
| ( ( relation @ SV731 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5430,plain,
! [SV732: $i,SV707: $i,SV528: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ ( relation_composition @ ( identity_relation @ SV707 ) @ SV732 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV483 @ SV528 ) @ SV732 )
= $true )
| ( ( relation @ SV732 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5304]) ).
thf(5431,plain,
! [SV611: $i,SV631: $i,SV484: $i] :
( ( ( in @ SV484 @ ( relation_dom @ SV631 ) )
= $false )
| ( ( SV611
= ( apply @ SV631 @ SV484 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV484 @ SV611 ) @ SV631 )
= $true )
| ( ( function @ SV631 )
= $false )
| ( ( relation @ SV631 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5432,plain,
! [SV708: $i,SV684: $i,SV484: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 ) )
= $true )
| ( ( SV684
= ( apply @ SV708 @ SV484 ) )
= $true )
| ( ( function @ SV708 )
= $false )
| ( ( relation @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5306]) ).
thf(5433,plain,
! [SV709: $i,SV685: $i,SV484: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 ) )
= $true )
| ( ( in @ SV484 @ ( relation_dom @ SV709 ) )
= $true )
| ( ( function @ SV709 )
= $false )
| ( ( relation @ SV709 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5307]) ).
thf(5434,plain,
! [SV746: $i,SV568: $i,SV734: $i,SV712: $i] :
( ( ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV734 @ SV746 ) @ SV568 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV712 @ SV746 ) @ SV568 )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5435,plain,
! [SV613: $i,SV633: $i,SV487: $i,SV735: $i] :
( ( ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 )
= $false )
| ( ( in @ SV735 @ ( relation_dom @ SV633 ) )
= $false )
| ( ( ~ ( in @ SV735 @ SV613 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5313]) ).
thf(5436,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
| ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5437,plain,
! [SV661: $i,SV751: $i,SV488: $i] :
( ( ( disjoint @ ( fiber @ SV488 @ SV751 ) @ ( sK35_C @ SV661 @ SV488 ) )
= $false )
| ( ( ~ ( in @ SV751 @ ( sK35_C @ SV661 @ SV488 ) ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5438,plain,
! [SV488: $i,SV661: $i] :
( ( ( ( ( sK35_C @ SV661 @ SV488 )
!= empty_set ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5317]) ).
thf(5439,plain,
! [SV488: $i,SV661: $i] :
( ( ( subset @ ( sK35_C @ SV661 @ SV488 ) @ SV661 )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5318]) ).
thf(5440,plain,
! [SV662: $i,SV736: $i,SV488: $i] :
( ( ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
= $true )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5319]) ).
thf(5441,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 )
= $true )
| ( ( ( SV736 = empty_set )
| ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5320]) ).
thf(5442,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5321]) ).
thf(5443,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5321]) ).
thf(5444,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( relation @ SV737 )
= $false )
| ( ( function @ SV737 )
= $false )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
| ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5322]) ).
thf(5445,plain,
! [SV529: $i,SV490: $i,SV767: $i] :
( ( ( ~ ( function @ SV767 )
| ~ ( relation @ SV767 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SV767 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5323]) ).
thf(5446,plain,
! [SV529: $i,SV490: $i,SV768: $i] :
( ( ( ~ ( function @ SV768 )
| ~ ( relation @ SV768 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
| ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5324]) ).
thf(5447,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5325]) ).
thf(5448,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5326]) ).
thf(5449,plain,
! [SV491: $i,SV666: $i,SV747: $i,SV738: $i] :
( ( ( SV738 = SV747 )
= $true )
| ( ( ~ ( in @ SV738 @ SV666 )
| ~ ( in @ SV747 @ SV666 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5450,plain,
! [SV574: $i,SV714: $i,SV739: $i] :
( ( ( in @ ( ordered_pair @ SV739 @ SV714 ) @ SV574 )
= $false )
| ( ( in @ ( ordered_pair @ SV714 @ SV739 ) @ SV574 )
= $false )
| ( ( SV714 = SV739 )
= $true )
| ( ( antisymmetric @ SV574 )
= $false )
| ( ( relation @ SV574 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(5451,plain,
! [SV635: $i,SV492: $i,SV615: $i] :
( ( ( in @ SV615 @ SV492 )
= $false )
| ( ( in @ SV615 @ ( relation_dom @ SV635 ) )
= $false )
| ( ( in @ SV615 @ ( relation_dom @ ( relation_dom_restriction @ SV635 @ SV492 ) ) )
= $true )
| ( ( function @ SV635 )
= $false )
| ( ( relation @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5452,plain,
! [SV492: $i,SV715: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) ) )
= $true )
| ( ( in @ SV688 @ ( relation_dom @ SV715 ) )
= $true )
| ( ( function @ SV715 )
= $false )
| ( ( relation @ SV715 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5332]) ).
thf(5453,plain,
! [SV492: $i,SV716: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) ) )
= $true )
| ( ( in @ SV689 @ SV492 )
= $true )
| ( ( function @ SV716 )
= $false )
| ( ( relation @ SV716 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5454,plain,
! [SV493: $i,SV717: $i] :
( ( ( ! [SY7389: $i] :
( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SY7389 ) )
| ~ ( in @ SY7389 @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(5455,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(5456,plain,
! [SV718: $i,SV493: $i] :
( ( ( ! [SY7390: $i] :
( ! [SY7156: $i] :
( ( SY7390
!= ( apply @ SV493 @ SY7156 ) )
| ~ ( in @ SY7156 @ ( relation_dom @ SV493 ) ) )
| ( in @ SY7390 @ SV718 ) ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5336]) ).
thf(5457,plain,
! [SV493: $i,SV718: $i] :
( ( ( ! [SY7392: $i] :
( ~ ( in @ SY7392 @ SV718 )
| ~ ( ( SY7392
!= ( apply @ SV493 @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SY7392 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5337]) ).
thf(5458,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5338]) ).
thf(5459,plain,
! [SV577: $i,SV494: $i,SV741: $i] :
( ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( ~ ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) ) )
= $true )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5460,plain,
! [SV496: $i,SV667: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5340]) ).
thf(5461,plain,
! [SV496: $i,SV667: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5341]) ).
thf(5462,plain,
! [SV496: $i,SV668: $i] :
( ( ( ! [SY7327: $i,SY7328: $i] :
( ~ ( in @ ( ordered_pair @ SY7327 @ SY7328 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7328 @ SY7327 ) @ SV496 ) ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5342]) ).
thf(5463,plain,
! [SV668: $i,SV496: $i] :
( ( ( ! [SY7329: $i,SY7330: $i] :
( ~ ( in @ ( ordered_pair @ SY7330 @ SY7329 ) @ SV496 )
| ( in @ ( ordered_pair @ SY7329 @ SY7330 ) @ SV668 ) ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5343]) ).
thf(5464,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
= $false )
| ( ( ~ ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(5465,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5345]) ).
thf(5466,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
| ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5346]) ).
thf(5467,plain,
! [SV621: $i,SV581: $i,SV777: $i,SV769: $i] :
( ( ( ( SV769 != SV777 )
| ~ ( in @ SV769 @ SV581 )
| ( in @ ( ordered_pair @ SV769 @ SV777 ) @ SV621 ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5347]) ).
thf(5468,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5348]) ).
thf(5469,plain,
! [SV581: $i,SV621: $i] :
( ( ( ~ ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) )
= $false )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5348]) ).
thf(5470,plain,
! [SV497: $i,SV669: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV669 @ SV497 ) @ ( sK37_SY6446 @ SV669 @ SV497 ) ) @ SV669 )
= $false )
| ( ( subset @ SV497 @ SV669 )
= $true )
| ( ( relation @ SV669 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5471,plain,
! [SV670: $i,SV497: $i,SV770: $i,SV752: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV497 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV670 )
= $true )
| ( ( subset @ SV497 @ SV670 )
= $false )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5472,plain,
! [SV582: $i,SV748: $i] :
( ( ( in @ SV748 @ ( sK39_B @ SV582 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV582 @ SV748 ) @ ( sK39_B @ SV582 ) )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(5473,plain,
! [SV582: $i] :
( ( ( ( sK39_B @ SV582 )
= empty_set )
= $false )
| ( ( well_founded_relation @ SV582 )
= $true )
| ( ( relation @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5474,plain,
! [SV583: $i,SV719: $i] :
( ( ( SV719 = empty_set )
= $true )
| ( ( ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5355]) ).
thf(5475,plain,
! [SV583: $i,SV719: $i] :
( ( ( SV719 = empty_set )
= $true )
| ( ( ~ ( subset @ SV719 @ ( relation_field @ SV583 ) ) )
= $true )
| ( ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5356]) ).
thf(5476,plain,
! [SV498: $i,SV753: $i] :
( ( ( in @ SV753 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( ! [SY7414: $i] :
( ( SY7414
!= ( apply @ SV498 @ SV753 ) )
| ( in @ ( ordered_pair @ SV753 @ SY7414 ) @ SV498 ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5357]) ).
thf(5477,plain,
! [SV498: $i,SV754: $i] :
( ( ( in @ SV754 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( ! [SY7415: $i] :
( ~ ( in @ ( ordered_pair @ SV754 @ SY7415 ) @ SV498 )
| ( SY7415
= ( apply @ SV498 @ SV754 ) ) ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5478,plain,
! [SV755: $i,SV498: $i,SV778: $i] :
( ( ( ( SV778
!= ( apply @ SV498 @ SV755 ) )
| ( SV778 = empty_set ) )
= $true )
| ( ( in @ SV755 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5359]) ).
thf(5479,plain,
! [SV756: $i,SV498: $i,SV779: $i] :
( ( ( ( SV779 != empty_set )
| ( SV779
= ( apply @ SV498 @ SV756 ) ) )
= $true )
| ( ( in @ SV756 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5360]) ).
thf(5480,plain,
! [SV584: $i] :
( ( ( antisymmetric @ SV584 )
= $false )
| ( ( reflexive @ SV584 )
= $false )
| ( ( transitive @ SV584 )
= $false )
| ( ( ~ ( connected @ SV584 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5481,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5362]) ).
thf(5482,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5362]) ).
thf(5483,plain,
! [SV771: $i] :
( ( ( ~ ( relation @ SV771 ) )
= $true )
| ( ( ~ ( well_ordering @ SV771 )
| ( antisymmetric @ SV771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5363]) ).
thf(5484,plain,
! [SV742: $i] :
( ( ( well_ordering @ SV742 )
= $false )
| ( ( connected @ SV742 )
= $true )
| ( ( relation @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5485,plain,
! [SV585: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5365]) ).
thf(5486,plain,
! [SV585: $i] :
( ( ( ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
!= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5365]) ).
thf(5487,plain,
! [SV757: $i,SV586: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( relation_dom @ SV586 ) )
| ~ ( in @ SV757 @ ( relation_dom @ SV586 ) ) )
= $true )
| ( ( ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) ) )
= $true )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(5488,plain,
! [SV780: $i,SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV780 ) @ SV499 )
| ~ ( in @ SV780 @ SV672 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5368]) ).
thf(5489,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
= $false )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(5490,plain,
! [SV691: $i,SV673: $i,SV499: $i,SV781: $i] :
( ( ( ! [SY7431: $i] :
( ~ ( in @ ( ordered_pair @ SV781 @ SY7431 ) @ SV499 )
| ~ ( in @ SY7431 @ SV673 ) )
| ( in @ SV781 @ SV691 ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5370]) ).
thf(5491,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV691 )
| ~ ( ~ ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5371]) ).
thf(5492,plain,
! [SV591: $i,SV622: $i] :
( ( ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
= $true )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5372]) ).
thf(5493,plain,
! [SV591: $i,SV622: $i] :
( ( ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
!= ( sK67_C @ SV622 @ SV591 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5373]) ).
thf(5494,plain,
! [SV674: $i,SV692: $i] :
( ( ( SV692
= ( identity_relation @ SV674 ) )
= $false )
| ( ( ! [SY7370: $i] :
( ~ ( in @ SY7370 @ SV674 )
| ( ( apply @ SV692 @ SY7370 )
= SY7370 ) ) )
= $true )
| ( ( function @ SV692 )
= $false )
| ( ( relation @ SV692 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5495,plain,
! [SV675: $i,SV693: $i] :
( ( ( SV693
= ( identity_relation @ SV675 ) )
= $false )
| ( ( ( relation_dom @ SV693 )
= SV675 )
= $true )
| ( ( function @ SV693 )
= $false )
| ( ( relation @ SV693 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5496,plain,
! [SV467: $i,SV640: $i,SV676: $i,SV772: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV772 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 ) )
= $true )
| ( ( ~ ( in @ SV772 @ SV640 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5376]) ).
thf(5497,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 ) )
= $false )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5377]) ).
thf(5498,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( ~ ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 ) )
= $false )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5377]) ).
thf(5499,plain,
! [SV677: $i,SV641: $i,SV467: $i,SV773: $i] :
( ( ( ! [SY7422: $i] :
( ~ ( in @ ( ordered_pair @ SY7422 @ SV773 ) @ SV467 )
| ~ ( in @ SY7422 @ SV641 ) ) )
= $true )
| ( ( in @ SV773 @ SV677 )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5378]) ).
thf(5500,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV677 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5379]) ).
thf(5501,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5380]) ).
thf(5502,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 )
| ~ ( in @ SV750 @ SV643 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5382]) ).
thf(5503,plain,
! [SV721: $i,SV696: $i,SV469: $i] :
( ( ( ! [SY7395: $i] :
( ~ ( in @ SY7395 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7395 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SY7395 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5383]) ).
thf(5504,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5384]) ).
thf(5505,plain,
! [SV722: $i,SV697: $i,SV469: $i] :
( ( ( ! [SY7396: $i] :
( ! [SY7375: $i] :
( ~ ( in @ SY7375 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7375 @ SV697 )
| ( SY7396
!= ( apply @ SV469 @ SY7375 ) ) )
| ( in @ SY7396 @ SV722 ) ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5385]) ).
thf(5506,plain,
! [SV469: $i,SV697: $i,SV722: $i] :
( ( ( ! [SY7398: $i] :
( ~ ( in @ SY7398 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SY7398
!= ( apply @ SV469 @ ( sK55_E @ SY7398 @ SV722 @ SV697 @ SV469 ) ) ) ) ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5386]) ).
thf(5507,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5387]) ).
thf(5508,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
| ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5509,plain,
! [SV724: $i,SV699: $i,SV470: $i] :
( ( ( ! [SY7399: $i] :
( ~ ( in @ SY7399 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SY7399 ) @ SV699 )
| ( in @ SY7399 @ SV724 ) ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5389]) ).
thf(5510,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ~ ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5390]) ).
thf(5511,plain,
! [SV645: $i,SV471: $i] :
( ( ( is_antisymmetric_in @ SV471 @ SV645 )
= $false )
| ( ( is_reflexive_in @ SV471 @ SV645 )
= $false )
| ( ( is_transitive_in @ SV471 @ SV645 )
= $false )
| ( ( ~ ( is_connected_in @ SV471 @ SV645 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5512,plain,
! [SV471: $i] :
( ( ( ~ ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5392]) ).
thf(5513,plain,
! [SV471: $i] :
( ( ( ! [SY7030: $i] :
( ~ ( well_orders @ SV471 @ SY7030 )
| ( is_antisymmetric_in @ SV471 @ SY7030 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5393]) ).
thf(5514,plain,
! [SV758: $i,SV471: $i] :
( ( ( well_orders @ SV471 @ SV758 )
= $false )
| ( ( is_connected_in @ SV471 @ SV758 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5515,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
| ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5395]) ).
thf(5516,plain,
! [SV472: $i,SV526: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 ) )
= $true )
| ( ( ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) )
| ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5396]) ).
thf(5517,plain,
! [SV472: $i,SV526: $i,SV760: $i] :
( ( ( ~ ( function @ SV760 ) )
= $true )
| ( ( ~ ( relation @ SV760 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5397]) ).
thf(5518,plain,
! [SV761: $i,SV473: $i,SV646: $i] :
( ( ( in @ ( sK32_C @ SV646 @ SV473 ) @ SV646 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK32_C @ SV646 @ SV473 ) @ SV761 ) @ SV473 )
= $false )
| ( ( SV646
= ( relation_dom @ SV473 ) )
= $true )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5398]) ).
thf(5519,plain,
! [SV647: $i,SV473: $i,SV783: $i,SV762: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV762 @ SV783 ) @ SV473 ) )
= $true )
| ( ( in @ SV762 @ SV647 )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(5520,plain,
! [SV473: $i,SV647: $i,SV763: $i] :
( ( ( in @ SV763 @ SV647 )
= $false )
| ( ( in @ ( ordered_pair @ SV763 @ ( sK31_D @ SV763 @ SV647 @ SV473 ) ) @ SV473 )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5400]) ).
thf(5521,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
| ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5401]) ).
thf(5522,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV649 ) )
= $true )
| ( ( ~ ( in @ SV744 @ SV649 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5403]) ).
thf(5523,plain,
! [SV552: $i] :
( ( ( ~ ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5524,plain,
! [SV552: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5404]) ).
thf(5525,plain,
! [SV729: $i,SV553: $i,SV703: $i] :
( ( ( in @ SV703 @ ( relation_field @ SV553 ) )
= $false )
| ( ( ~ ( in @ SV729 @ ( relation_field @ SV553 ) ) )
= $true )
| ( ( SV703 = SV729 )
= $true )
| ( ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5526,plain,
( ( ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5407]) ).
thf(5527,plain,
( ( one_to_one @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5408]) ).
thf(5528,plain,
! [SV475: $i,SV625: $i,SV602: $i,SV730: $i] :
( ( ( in @ SV730 @ SV602 )
= $false )
| ( ( in @ SV730 @ ( relation_rng @ SV625 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV475 @ SV730 ) @ SV625 )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV625 @ SV602 ) )
= $true )
| ( ( relation @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5529,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5530,plain,
! [SV603: $i,SV626: $i,SV475: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 ) )
= $false )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5410]) ).
thf(5531,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5411]) ).
thf(5532,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5412]) ).
thf(5533,plain,
! [SV681: $i,SV478: $i,SV653: $i] :
( ( ( ! [SY7348: $i,SY7349: $i] :
( ~ ( in @ SY7348 @ SV653 )
| ~ ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV478 )
| ( in @ ( ordered_pair @ SY7348 @ SY7349 ) @ SV681 ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5413]) ).
thf(5534,plain,
! [SV478: $i,SV653: $i,SV681: $i] :
( ( ( ~ ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5414]) ).
thf(5535,plain,
! [SV764: $i,SV479: $i,SV654: $i] :
( ( ( in @ ( sK24_C @ SV654 @ SV479 ) @ SV654 )
= $false )
| ( ( in @ ( ordered_pair @ SV764 @ ( sK24_C @ SV654 @ SV479 ) ) @ SV479 )
= $false )
| ( ( SV654
= ( relation_rng @ SV479 ) )
= $true )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5536,plain,
! [SV655: $i,SV479: $i,SV765: $i,SV784: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV784 @ SV765 ) @ SV479 ) )
= $true )
| ( ( in @ SV765 @ SV655 )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5416]) ).
thf(5537,plain,
! [SV479: $i,SV655: $i,SV766: $i] :
( ( ( in @ SV766 @ SV655 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_D @ SV766 @ SV655 @ SV479 ) @ SV766 ) @ SV479 )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5538,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5418]) ).
thf(5539,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5540,plain,
! [SV683: $i,SV527: $i,SV480: $i] :
( ( ( ! [SY7354: $i,SY7355: $i] :
( ~ ( in @ SY7355 @ SV480 )
| ~ ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV527 )
| ( in @ ( ordered_pair @ SY7354 @ SY7355 ) @ SV683 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5420]) ).
thf(5541,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5421]) ).
thf(5542,plain,
! [SV481: $i,SV656: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 ) )
= $true )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5543,plain,
! [SV657: $i,SV481: $i,SV785: $i] :
( ( ( ! [SY7432: $i] :
( ~ ( in @ ( ordered_pair @ SV785 @ SY7432 ) @ SV481 )
| ( in @ ( ordered_pair @ SV785 @ SY7432 ) @ SV657 ) ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5544,plain,
! [SV481: $i,SV657: $i,SV786: $i] :
( ( ( ! [SY7433: $i] :
( ~ ( in @ ( ordered_pair @ SV786 @ SY7433 ) @ SV657 )
| ( in @ ( ordered_pair @ SV786 @ SY7433 ) @ SV481 ) ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5545,plain,
! [SV482: $i,SV745: $i] :
( ( ( relation @ SV745 )
= $false )
| ( ( function @ SV745 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) )
| ( SV745
= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5546,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ( function @ SV775 )
| ~ ( relation @ SV775 ) )
= $true )
| ( ( ( SV775
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5427]) ).
thf(5547,plain,
! [SV482: $i,SV776: $i] :
( ( ( ~ ( function @ SV776 )
| ~ ( relation @ SV776 ) )
= $true )
| ( ( ( SV776
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5548,plain,
! [SV708: $i,SV684: $i,SV484: $i] :
( ( ( in @ ( ordered_pair @ SV484 @ SV684 ) @ SV708 )
= $false )
| ( ( SV684
= ( apply @ SV708 @ SV484 ) )
= $true )
| ( ( function @ SV708 )
= $false )
| ( ( relation @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(5549,plain,
! [SV709: $i,SV685: $i,SV484: $i] :
( ( ( in @ ( ordered_pair @ SV484 @ SV685 ) @ SV709 )
= $false )
| ( ( in @ SV484 @ ( relation_dom @ SV709 ) )
= $true )
| ( ( function @ SV709 )
= $false )
| ( ( relation @ SV709 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(5550,plain,
! [SV712: $i,SV568: $i,SV746: $i,SV734: $i] :
( ( ( in @ ( ordered_pair @ SV734 @ SV746 ) @ SV568 )
= $false )
| ( ( in @ ( ordered_pair @ SV712 @ SV734 ) @ SV568 )
= $false )
| ( ( in @ ( ordered_pair @ SV712 @ SV746 ) @ SV568 )
= $true )
| ( ( transitive @ SV568 )
= $false )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5434]) ).
thf(5551,plain,
! [SV487: $i,SV633: $i,SV613: $i,SV735: $i] :
( ( ( in @ SV735 @ SV613 )
= $false )
| ( ( in @ SV735 @ ( relation_dom @ SV633 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV735 @ SV487 ) @ SV633 )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV633 @ SV613 ) )
= $true )
| ( ( relation @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5552,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5436]) ).
thf(5553,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 ) )
= $false )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5436]) ).
thf(5554,plain,
! [SV488: $i,SV661: $i,SV751: $i] :
( ( ( in @ SV751 @ ( sK35_C @ SV661 @ SV488 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV488 @ SV751 ) @ ( sK35_C @ SV661 @ SV488 ) )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5555,plain,
! [SV488: $i,SV661: $i] :
( ( ( ( sK35_C @ SV661 @ SV488 )
= empty_set )
= $false )
| ( ( is_well_founded_in @ SV488 @ SV661 )
= $true )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5556,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( SV736 = empty_set )
= $true )
| ( ( ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(5557,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( SV736 = empty_set )
= $true )
| ( ( ~ ( subset @ SV736 @ SV662 ) )
= $true )
| ( ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(5558,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5442]) ).
thf(5559,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5443]) ).
thf(5560,plain,
! [SV529: $i,SV737: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) )
| ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) )
= $true )
| ( ( function @ SV737 )
= $false )
| ( ( relation @ SV737 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5444]) ).
thf(5561,plain,
! [SV529: $i,SV490: $i,SV767: $i] :
( ( ( ~ ( function @ SV767 ) )
= $true )
| ( ( ~ ( relation @ SV767 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SV767 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5445]) ).
thf(5562,plain,
! [SV529: $i,SV490: $i,SV768: $i] :
( ( ( ~ ( function @ SV768 ) )
= $true )
| ( ( ~ ( relation @ SV768 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
| ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5446]) ).
thf(5563,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
| ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5564,plain,
! [SV491: $i,SV665: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_C @ SV665 @ SV491 ) @ ( sK22_SY6437 @ SV665 @ SV491 ) ) @ SV491 )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5565,plain,
! [SV491: $i,SV747: $i,SV666: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV666 ) )
= $true )
| ( ( ~ ( in @ SV747 @ SV666 ) )
= $true )
| ( ( SV738 = SV747 )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5449]) ).
thf(5566,plain,
! [SV492: $i,SV715: $i,SV688: $i] :
( ( ( in @ SV688 @ ( relation_dom @ ( relation_dom_restriction @ SV715 @ SV492 ) ) )
= $false )
| ( ( in @ SV688 @ ( relation_dom @ SV715 ) )
= $true )
| ( ( function @ SV715 )
= $false )
| ( ( relation @ SV715 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5452]) ).
thf(5567,plain,
! [SV492: $i,SV716: $i,SV689: $i] :
( ( ( in @ SV689 @ ( relation_dom @ ( relation_dom_restriction @ SV716 @ SV492 ) ) )
= $false )
| ( ( in @ SV689 @ SV492 )
= $true )
| ( ( function @ SV716 )
= $false )
| ( ( relation @ SV716 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5568,plain,
! [SV787: $i,SV493: $i,SV717: $i] :
( ( ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SV787 ) )
| ~ ( in @ SV787 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5454]) ).
thf(5569,plain,
! [SV493: $i,SV717: $i] :
( ( ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
| ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5570,plain,
! [SV718: $i,SV493: $i,SV788: $i] :
( ( ( ! [SY7434: $i] :
( ( SV788
!= ( apply @ SV493 @ SY7434 ) )
| ~ ( in @ SY7434 @ ( relation_dom @ SV493 ) ) )
| ( in @ SV788 @ SV718 ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5456]) ).
thf(5571,plain,
! [SV493: $i,SV718: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV718 )
| ~ ( ( SV789
!= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5457]) ).
thf(5572,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5458]) ).
thf(5573,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) ) )
= $false )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5458]) ).
thf(5574,plain,
! [SV741: $i,SV577: $i,SV494: $i] :
( ( ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) )
| ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5459]) ).
thf(5575,plain,
! [SV496: $i,SV667: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 ) )
= $true )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5576,plain,
! [SV496: $i,SV668: $i,SV790: $i] :
( ( ( ! [SY7435: $i] :
( ~ ( in @ ( ordered_pair @ SV790 @ SY7435 ) @ SV668 )
| ( in @ ( ordered_pair @ SY7435 @ SV790 ) @ SV496 ) ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5462]) ).
thf(5577,plain,
! [SV668: $i,SV496: $i,SV791: $i] :
( ( ( ! [SY7436: $i] :
( ~ ( in @ ( ordered_pair @ SY7436 @ SV791 ) @ SV496 )
| ( in @ ( ordered_pair @ SV791 @ SY7436 ) @ SV668 ) ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5463]) ).
thf(5578,plain,
! [SV580: $i,SV620: $i] :
( ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
= $false )
| ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 ) )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5579,plain,
! [SV580: $i,SV620: $i] :
( ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5465]) ).
thf(5580,plain,
! [SV580: $i,SV620: $i] :
( ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 )
= $true )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5581,plain,
! [SV621: $i,SV581: $i,SV777: $i,SV769: $i] :
( ( ( ( SV769 != SV777 )
| ~ ( in @ SV769 @ SV581 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV769 @ SV777 ) @ SV621 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5467]) ).
thf(5582,plain,
! [SV581: $i,SV621: $i] :
( ( ( ! [SY7284: $i,SY7285: $i] :
( ~ ( in @ ( ordered_pair @ SY7284 @ SY7285 ) @ SV621 )
| ( SY7284 = SY7285 ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5468]) ).
thf(5583,plain,
! [SV581: $i,SV621: $i] :
( ( ( ! [SY7286: $i] :
( ! [SY7287: $i] :
~ ( in @ ( ordered_pair @ SY7286 @ SY7287 ) @ SV621 )
| ( in @ SY7286 @ SV581 ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5469]) ).
thf(5584,plain,
! [SV670: $i,SV497: $i,SV770: $i,SV752: $i] :
( ( ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV497 )
= $false )
| ( ( in @ ( ordered_pair @ SV752 @ SV770 ) @ SV670 )
= $true )
| ( ( subset @ SV497 @ SV670 )
= $false )
| ( ( relation @ SV670 )
= $false )
| ( ( relation @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5471]) ).
thf(5585,plain,
! [SV583: $i,SV719: $i] :
( ( ( subset @ SV719 @ ( relation_field @ SV583 ) )
= $false )
| ( ( SV719 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV583 @ ( sK38_C @ SV719 @ SV583 ) ) @ SV719 )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5586,plain,
! [SV583: $i,SV719: $i] :
( ( ( subset @ SV719 @ ( relation_field @ SV583 ) )
= $false )
| ( ( SV719 = empty_set )
= $true )
| ( ( in @ ( sK38_C @ SV719 @ SV583 ) @ SV719 )
= $true )
| ( ( well_founded_relation @ SV583 )
= $false )
| ( ( relation @ SV583 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5587,plain,
! [SV753: $i,SV498: $i,SV792: $i] :
( ( ( ( SV792
!= ( apply @ SV498 @ SV753 ) )
| ( in @ ( ordered_pair @ SV753 @ SV792 ) @ SV498 ) )
= $true )
| ( ( in @ SV753 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5476]) ).
thf(5588,plain,
! [SV498: $i,SV793: $i,SV754: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV754 @ SV793 ) @ SV498 )
| ( SV793
= ( apply @ SV498 @ SV754 ) ) )
= $true )
| ( ( in @ SV754 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(5589,plain,
! [SV755: $i,SV498: $i,SV778: $i] :
( ( ( ( SV778
!= ( apply @ SV498 @ SV755 ) ) )
= $true )
| ( ( SV778 = empty_set )
= $true )
| ( ( in @ SV755 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5478]) ).
thf(5590,plain,
! [SV756: $i,SV498: $i,SV779: $i] :
( ( ( ( SV779 != empty_set ) )
= $true )
| ( ( SV779
= ( apply @ SV498 @ SV756 ) )
= $true )
| ( ( in @ SV756 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5479]) ).
thf(5591,plain,
! [SV584: $i] :
( ( ( connected @ SV584 )
= $false )
| ( ( transitive @ SV584 )
= $false )
| ( ( reflexive @ SV584 )
= $false )
| ( ( antisymmetric @ SV584 )
= $false )
| ( ( ~ ( well_founded_relation @ SV584 ) )
= $true )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5480]) ).
thf(5592,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5481]) ).
thf(5593,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5482]) ).
thf(5594,plain,
! [SV771: $i] :
( ( ( relation @ SV771 )
= $false )
| ( ( ~ ( well_ordering @ SV771 )
| ( antisymmetric @ SV771 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5595,plain,
! [SV585: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5485]) ).
thf(5596,plain,
! [SV585: $i] :
( ( ( ( apply @ SV585 @ ( sK17_B @ SV585 ) )
= ( apply @ SV585 @ ( sK18_SY6435 @ SV585 ) ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5486]) ).
thf(5597,plain,
! [SV757: $i,SV586: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( relation_dom @ SV586 ) ) )
= $true )
| ( ( ~ ( in @ SV757 @ ( relation_dom @ SV586 ) ) )
= $true )
| ( ( ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) ) )
= $true )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5487]) ).
thf(5598,plain,
! [SV780: $i,SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV780 ) @ SV499 ) )
= $true )
| ( ( ~ ( in @ SV780 @ SV672 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5599,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 ) )
= $false )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5489]) ).
thf(5600,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( ~ ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 ) )
= $false )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5489]) ).
thf(5601,plain,
! [SV691: $i,SV673: $i,SV499: $i,SV781: $i] :
( ( ( ! [SY7431: $i] :
( ~ ( in @ ( ordered_pair @ SV781 @ SY7431 ) @ SV499 )
| ~ ( in @ SY7431 @ SV673 ) ) )
= $true )
| ( ( in @ SV781 @ SV691 )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5490]) ).
thf(5602,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV691 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5491]) ).
thf(5603,plain,
! [SV591: $i,SV622: $i] :
( ( ( ( relation_dom @ SV622 )
= SV591 )
= $false )
| ( ( in @ ( sK67_C @ SV622 @ SV591 ) @ SV591 )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5492]) ).
thf(5604,plain,
! [SV591: $i,SV622: $i] :
( ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
= ( sK67_C @ SV622 @ SV591 ) )
= $false )
| ( ( ( ( relation_dom @ SV622 )
!= SV591 ) )
= $true )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5605,plain,
! [SV692: $i,SV674: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV674 )
| ( ( apply @ SV692 @ SV794 )
= SV794 ) )
= $true )
| ( ( SV692
= ( identity_relation @ SV674 ) )
= $false )
| ( ( function @ SV692 )
= $false )
| ( ( relation @ SV692 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5494]) ).
thf(5606,plain,
! [SV467: $i,SV640: $i,SV676: $i,SV772: $i] :
( ( ( in @ ( ordered_pair @ SV772 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
= $false )
| ( ( ~ ( in @ SV772 @ SV640 ) )
= $true )
| ( ( ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5607,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( in @ ( ordered_pair @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
= $true )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5497]) ).
thf(5608,plain,
! [SV467: $i,SV640: $i,SV676: $i] :
( ( ( in @ ( sK51_SY6455 @ SV676 @ SV640 @ SV467 ) @ SV640 )
= $true )
| ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5498]) ).
thf(5609,plain,
! [SV677: $i,SV641: $i,SV467: $i,SV773: $i,SV795: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV795 @ SV773 ) @ SV467 )
| ~ ( in @ SV795 @ SV641 ) )
= $true )
| ( ( in @ SV773 @ SV677 )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(5610,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( in @ SV774 @ SV677 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 ) ) )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5611,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5612,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5613,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 )
| ~ ( in @ SV743 @ SV643 ) )
= $true )
| ( ( ~ ( in @ SV750 @ SV643 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5502]) ).
thf(5614,plain,
! [SV721: $i,SV696: $i,SV469: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SV796 @ SV696 )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SV796 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5615,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
| ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5504]) ).
thf(5616,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i] :
( ( ( ! [SY7437: $i] :
( ~ ( in @ SY7437 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7437 @ SV697 )
| ( SV797
!= ( apply @ SV469 @ SY7437 ) ) )
| ( in @ SV797 @ SV722 ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5505]) ).
thf(5617,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV722 )
| ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SV798
!= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) ) ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5506]) ).
thf(5618,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5507]) ).
thf(5619,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ~ ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5508]) ).
thf(5620,plain,
! [SV698: $i,SV723: $i,SV470: $i] :
( ( ( ~ ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) ) )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5508]) ).
thf(5621,plain,
! [SV724: $i,SV699: $i,SV470: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SV799 ) @ SV699 )
| ( in @ SV799 @ SV724 ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5509]) ).
thf(5622,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) )
| ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(5623,plain,
! [SV645: $i,SV471: $i] :
( ( ( is_connected_in @ SV471 @ SV645 )
= $false )
| ( ( is_transitive_in @ SV471 @ SV645 )
= $false )
| ( ( is_reflexive_in @ SV471 @ SV645 )
= $false )
| ( ( is_antisymmetric_in @ SV471 @ SV645 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV471 @ SV645 ) )
= $true )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5511]) ).
thf(5624,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) )
| ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5625,plain,
! [SV800: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV800 )
| ( is_antisymmetric_in @ SV471 @ SV800 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5513]) ).
thf(5626,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5515]) ).
thf(5627,plain,
! [SV472: $i,SV526: $i,SV759: $i] :
( ( ( function @ SV759 )
= $false )
| ( ( ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) )
| ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(5628,plain,
! [SV472: $i,SV526: $i,SV760: $i] :
( ( ( function @ SV760 )
= $false )
| ( ( ~ ( relation @ SV760 ) )
= $true )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5517]) ).
thf(5629,plain,
! [SV647: $i,SV473: $i,SV783: $i,SV762: $i] :
( ( ( in @ ( ordered_pair @ SV762 @ SV783 ) @ SV473 )
= $false )
| ( ( in @ SV762 @ SV647 )
= $true )
| ( ( SV647
= ( relation_dom @ SV473 ) )
= $false )
| ( ( relation @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5630,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5521]) ).
thf(5631,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5521]) ).
thf(5632,plain,
! [SV474: $i,SV744: $i,SV649: $i,SV728: $i] :
( ( ( in @ SV728 @ SV649 )
= $false )
| ( ( ~ ( in @ SV744 @ SV649 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5522]) ).
thf(5633,plain,
! [SV552: $i] :
( ( ( ( ( sK70_B @ SV552 )
!= ( sK71_SY6463 @ SV552 ) ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5523]) ).
thf(5634,plain,
! [SV552: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5524]) ).
thf(5635,plain,
! [SV703: $i,SV553: $i,SV729: $i] :
( ( ( in @ SV729 @ ( relation_field @ SV553 ) )
= $false )
| ( ( in @ SV703 @ ( relation_field @ SV553 ) )
= $false )
| ( ( SV703 = SV729 )
= $true )
| ( ( in @ ( ordered_pair @ SV703 @ SV729 ) @ SV553 )
= $true )
| ( ( in @ ( ordered_pair @ SV729 @ SV703 ) @ SV553 )
= $true )
| ( ( connected @ SV553 )
= $false )
| ( ( relation @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5636,plain,
( ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5637,plain,
! [SV475: $i,SV603: $i,SV626: $i] :
( ( ( in @ ( sK68_D @ SV626 @ SV603 @ SV475 ) @ ( relation_rng @ SV626 ) )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5529]) ).
thf(5638,plain,
! [SV603: $i,SV626: $i,SV475: $i] :
( ( ( in @ ( ordered_pair @ SV475 @ ( sK68_D @ SV626 @ SV603 @ SV475 ) ) @ SV626 )
= $true )
| ( ( in @ SV475 @ ( relation_inverse_image @ SV626 @ SV603 ) )
= $false )
| ( ( relation @ SV626 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5530]) ).
thf(5639,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5531]) ).
thf(5640,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5641,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) ) )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5532]) ).
thf(5642,plain,
! [SV681: $i,SV478: $i,SV653: $i,SV801: $i] :
( ( ( ! [SY7438: $i] :
( ~ ( in @ SV801 @ SV653 )
| ~ ( in @ ( ordered_pair @ SV801 @ SY7438 ) @ SV478 )
| ( in @ ( ordered_pair @ SV801 @ SY7438 ) @ SV681 ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5533]) ).
thf(5643,plain,
! [SV478: $i,SV653: $i,SV681: $i] :
( ( ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) )
| ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(5644,plain,
! [SV655: $i,SV479: $i,SV765: $i,SV784: $i] :
( ( ( in @ ( ordered_pair @ SV784 @ SV765 ) @ SV479 )
= $false )
| ( ( in @ SV765 @ SV655 )
= $true )
| ( ( SV655
= ( relation_rng @ SV479 ) )
= $false )
| ( ( relation @ SV479 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5645,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5538]) ).
thf(5646,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5539]) ).
thf(5647,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) ) )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5539]) ).
thf(5648,plain,
! [SV683: $i,SV527: $i,SV802: $i,SV480: $i] :
( ( ( ! [SY7439: $i] :
( ~ ( in @ SY7439 @ SV480 )
| ~ ( in @ ( ordered_pair @ SV802 @ SY7439 ) @ SV527 )
| ( in @ ( ordered_pair @ SV802 @ SY7439 ) @ SV683 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5540]) ).
thf(5649,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) )
| ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(5650,plain,
! [SV481: $i,SV656: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV656 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK40_C @ SV656 @ SV481 ) @ ( sK41_SY6448 @ SV656 @ SV481 ) ) @ SV481 )
= $false )
| ( ( SV481 = SV656 )
= $true )
| ( ( relation @ SV656 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5542]) ).
thf(5651,plain,
! [SV657: $i,SV481: $i,SV803: $i,SV785: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV481 )
| ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV657 ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5543]) ).
thf(5652,plain,
! [SV481: $i,SV657: $i,SV804: $i,SV786: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV657 )
| ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV481 ) )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5544]) ).
thf(5653,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5545]) ).
thf(5654,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ( function @ SV775 ) )
= $true )
| ( ( ~ ( relation @ SV775 ) )
= $true )
| ( ( ( SV775
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5546]) ).
thf(5655,plain,
! [SV482: $i,SV776: $i] :
( ( ( ~ ( function @ SV776 ) )
= $true )
| ( ( ~ ( relation @ SV776 ) )
= $true )
| ( ( ( SV776
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(5656,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( in @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ ( relation_dom @ SV634 ) )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5552]) ).
thf(5657,plain,
! [SV487: $i,SV614: $i,SV634: $i] :
( ( ( in @ ( ordered_pair @ ( sK69_D @ SV634 @ SV614 @ SV487 ) @ SV487 ) @ SV634 )
= $true )
| ( ( in @ SV487 @ ( relation_image @ SV634 @ SV614 ) )
= $false )
| ( ( relation @ SV634 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5553]) ).
thf(5658,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( subset @ SV736 @ SV662 )
= $false )
| ( ( SV736 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV488 @ ( sK34_D @ SV736 @ SV662 @ SV488 ) ) @ SV736 )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5556]) ).
thf(5659,plain,
! [SV488: $i,SV662: $i,SV736: $i] :
( ( ( subset @ SV736 @ SV662 )
= $false )
| ( ( SV736 = empty_set )
= $true )
| ( ( in @ ( sK34_D @ SV736 @ SV662 @ SV488 ) @ SV736 )
= $true )
| ( ( is_well_founded_in @ SV488 @ SV662 )
= $false )
| ( ( relation @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(5660,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(5661,plain,
! [SV529: $i,SV737: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_dom @ SV737 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) )
= $true )
| ( ( function @ SV737 )
= $false )
| ( ( relation @ SV737 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5560]) ).
thf(5662,plain,
! [SV529: $i,SV490: $i,SV767: $i] :
( ( ( function @ SV767 )
= $false )
| ( ( ~ ( relation @ SV767 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SV767 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5663,plain,
! [SV529: $i,SV490: $i,SV768: $i] :
( ( ( function @ SV768 )
= $false )
| ( ( ~ ( relation @ SV768 ) )
= $true )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
| ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(5664,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5563]) ).
thf(5665,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5563]) ).
thf(5666,plain,
! [SV491: $i,SV747: $i,SV666: $i,SV738: $i] :
( ( ( in @ SV738 @ SV666 )
= $false )
| ( ( ~ ( in @ SV747 @ SV666 ) )
= $true )
| ( ( SV738 = SV747 )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5565]) ).
thf(5667,plain,
! [SV787: $i,SV493: $i,SV717: $i] :
( ( ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ SV787 ) ) )
= $true )
| ( ( ~ ( in @ SV787 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5568]) ).
thf(5668,plain,
! [SV493: $i,SV717: $i] :
( ( ( ( ( sK27_C @ SV717 @ SV493 )
!= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5569]) ).
thf(5669,plain,
! [SV493: $i,SV717: $i] :
( ( ( ~ ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
= $false )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5569]) ).
thf(5670,plain,
! [SV718: $i,SV493: $i,SV788: $i] :
( ( ( ! [SY7434: $i] :
( ( SV788
!= ( apply @ SV493 @ SY7434 ) )
| ~ ( in @ SY7434 @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( in @ SV788 @ SV718 )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5570]) ).
thf(5671,plain,
! [SV493: $i,SV718: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV718 ) )
= $true )
| ( ( ~ ( ( SV789
!= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5571]) ).
thf(5672,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5572]) ).
thf(5673,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
| ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5573]) ).
thf(5674,plain,
! [SV741: $i,SV577: $i,SV494: $i] :
( ( ( ~ ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) ) )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5574]) ).
thf(5675,plain,
! [SV494: $i,SV577: $i,SV741: $i] :
( ( ( ~ ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5574]) ).
thf(5676,plain,
! [SV496: $i,SV667: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY6436 @ SV667 @ SV496 ) @ ( sK19_C @ SV667 @ SV496 ) ) @ SV496 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK19_C @ SV667 @ SV496 ) @ ( sK20_SY6436 @ SV667 @ SV496 ) ) @ SV667 )
= $false )
| ( ( SV667
= ( relation_inverse @ SV496 ) )
= $true )
| ( ( relation @ SV667 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(5677,plain,
! [SV496: $i,SV668: $i,SV805: $i,SV790: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV790 @ SV805 ) @ SV668 )
| ( in @ ( ordered_pair @ SV805 @ SV790 ) @ SV496 ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5576]) ).
thf(5678,plain,
! [SV668: $i,SV496: $i,SV791: $i,SV806: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV806 @ SV791 ) @ SV496 )
| ( in @ ( ordered_pair @ SV791 @ SV806 ) @ SV668 ) )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(5679,plain,
! [SV580: $i,SV620: $i] :
( ( ( in @ ( ordered_pair @ ( sK60_C @ SV620 @ SV580 ) @ ( sK61_SY6460 @ SV620 @ SV580 ) ) @ SV620 )
= $false )
| ( ( ( sK60_C @ SV620 @ SV580 )
= ( sK61_SY6460 @ SV620 @ SV580 ) )
= $false )
| ( ( in @ ( sK60_C @ SV620 @ SV580 ) @ SV580 )
= $false )
| ( ( SV620
= ( identity_relation @ SV580 ) )
= $true )
| ( ( relation @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5578]) ).
thf(5680,plain,
! [SV621: $i,SV581: $i,SV777: $i,SV769: $i] :
( ( ( ( SV769 != SV777 ) )
= $true )
| ( ( ~ ( in @ SV769 @ SV581 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV769 @ SV777 ) @ SV621 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5581]) ).
thf(5681,plain,
! [SV581: $i,SV621: $i,SV807: $i] :
( ( ( ! [SY7440: $i] :
( ~ ( in @ ( ordered_pair @ SV807 @ SY7440 ) @ SV621 )
| ( SV807 = SY7440 ) ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5582]) ).
thf(5682,plain,
! [SV581: $i,SV621: $i,SV808: $i] :
( ( ( ! [SY7441: $i] :
~ ( in @ ( ordered_pair @ SV808 @ SY7441 ) @ SV621 )
| ( in @ SV808 @ SV581 ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5583]) ).
thf(5683,plain,
! [SV753: $i,SV498: $i,SV792: $i] :
( ( ( ( SV792
!= ( apply @ SV498 @ SV753 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV753 @ SV792 ) @ SV498 )
= $true )
| ( ( in @ SV753 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5587]) ).
thf(5684,plain,
! [SV498: $i,SV793: $i,SV754: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV754 @ SV793 ) @ SV498 ) )
= $true )
| ( ( SV793
= ( apply @ SV498 @ SV754 ) )
= $true )
| ( ( in @ SV754 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5588]) ).
thf(5685,plain,
! [SV755: $i,SV498: $i,SV778: $i] :
( ( ( SV778
= ( apply @ SV498 @ SV755 ) )
= $false )
| ( ( SV778 = empty_set )
= $true )
| ( ( in @ SV755 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5589]) ).
thf(5686,plain,
! [SV756: $i,SV498: $i,SV779: $i] :
( ( ( SV779 = empty_set )
= $false )
| ( ( SV779
= ( apply @ SV498 @ SV756 ) )
= $true )
| ( ( in @ SV756 @ ( relation_dom @ SV498 ) )
= $true )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(5687,plain,
! [SV584: $i] :
( ( ( well_founded_relation @ SV584 )
= $false )
| ( ( antisymmetric @ SV584 )
= $false )
| ( ( reflexive @ SV584 )
= $false )
| ( ( transitive @ SV584 )
= $false )
| ( ( connected @ SV584 )
= $false )
| ( ( well_ordering @ SV584 )
= $true )
| ( ( relation @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5591]) ).
thf(5688,plain,
! [SV809: $i] :
( ( ~ ( relation @ SV809 )
| ~ ( well_ordering @ SV809 )
| ( reflexive @ SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(5689,plain,
! [SV810: $i] :
( ( ~ ( relation @ SV810 )
| ~ ( well_ordering @ SV810 )
| ( transitive @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5593]) ).
thf(5690,plain,
! [SV771: $i] :
( ( ( ~ ( well_ordering @ SV771 ) )
= $true )
| ( ( antisymmetric @ SV771 )
= $true )
| ( ( relation @ SV771 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5594]) ).
thf(5691,plain,
! [SV585: $i] :
( ( ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
| ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5692,plain,
! [SV757: $i,SV586: $i,SV749: $i] :
( ( ( in @ SV749 @ ( relation_dom @ SV586 ) )
= $false )
| ( ( ~ ( in @ SV757 @ ( relation_dom @ SV586 ) ) )
= $true )
| ( ( ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) ) )
= $true )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5597]) ).
thf(5693,plain,
! [SV780: $i,SV499: $i,SV672: $i,SV690: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV780 ) @ SV499 )
= $false )
| ( ( ~ ( in @ SV780 @ SV672 ) )
= $true )
| ( ( ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5694,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) ) @ SV499 )
= $true )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5599]) ).
thf(5695,plain,
! [SV499: $i,SV672: $i,SV690: $i] :
( ( ( in @ ( sK48_SY6453 @ SV690 @ SV672 @ SV499 ) @ SV672 )
= $true )
| ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5600]) ).
thf(5696,plain,
! [SV691: $i,SV673: $i,SV499: $i,SV811: $i,SV781: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV781 @ SV811 ) @ SV499 )
| ~ ( in @ SV811 @ SV673 ) )
= $true )
| ( ( in @ SV781 @ SV691 )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5697,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( in @ SV782 @ SV691 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 ) ) )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5602]) ).
thf(5698,plain,
! [SV591: $i,SV622: $i] :
( ( ( ( relation_dom @ SV622 )
= SV591 )
= $false )
| ( ( ( apply @ SV622 @ ( sK67_C @ SV622 @ SV591 ) )
= ( sK67_C @ SV622 @ SV591 ) )
= $false )
| ( ( SV622
= ( identity_relation @ SV591 ) )
= $true )
| ( ( function @ SV622 )
= $false )
| ( ( relation @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5604]) ).
thf(5699,plain,
! [SV692: $i,SV674: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV674 ) )
= $true )
| ( ( ( apply @ SV692 @ SV794 )
= SV794 )
= $true )
| ( ( SV692
= ( identity_relation @ SV674 ) )
= $false )
| ( ( function @ SV692 )
= $false )
| ( ( relation @ SV692 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5605]) ).
thf(5700,plain,
! [SV467: $i,SV676: $i,SV640: $i,SV772: $i] :
( ( ( in @ SV772 @ SV640 )
= $false )
| ( ( in @ ( ordered_pair @ SV772 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
= $false )
| ( ( ~ ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 ) )
= $true )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(5701,plain,
! [SV677: $i,SV641: $i,SV467: $i,SV773: $i,SV795: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV795 @ SV773 ) @ SV467 ) )
= $true )
| ( ( ~ ( in @ SV795 @ SV641 ) )
= $true )
| ( ( in @ SV773 @ SV677 )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5609]) ).
thf(5702,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 )
| ~ ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 ) )
= $false )
| ( ( in @ SV774 @ SV677 )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(5703,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5611]) ).
thf(5704,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_C @ SV642 @ SV468 ) @ ( sK11_SY6427 @ SV642 @ SV468 ) ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5612]) ).
thf(5705,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ SV643 ) )
= $true )
| ( ( ~ ( in @ SV743 @ SV643 ) )
= $true )
| ( ( ~ ( in @ SV750 @ SV643 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5613]) ).
thf(5706,plain,
! [SV721: $i,SV696: $i,SV469: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SV796 @ SV696 ) )
= $true )
| ( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SV796 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5614]) ).
thf(5707,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5615]) ).
thf(5708,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5615]) ).
thf(5709,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i] :
( ( ( ! [SY7437: $i] :
( ~ ( in @ SY7437 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SY7437 @ SV697 )
| ( SV797
!= ( apply @ SV469 @ SY7437 ) ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5616]) ).
thf(5710,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV722 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SV798
!= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) ) ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(5711,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5618]) ).
thf(5712,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5619]) ).
thf(5713,plain,
! [SV698: $i,SV723: $i,SV470: $i] :
( ( ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
| ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5620]) ).
thf(5714,plain,
! [SV724: $i,SV699: $i,SV470: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( relation_dom @ SV470 ) )
| ~ ( in @ ( apply @ SV470 @ SV799 ) @ SV699 ) )
= $true )
| ( ( in @ SV799 @ SV724 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(5715,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ~ ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5622]) ).
thf(5716,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ~ ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) )
= $false )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5622]) ).
thf(5717,plain,
! [SV645: $i,SV471: $i] :
( ( ( is_well_founded_in @ SV471 @ SV645 )
= $false )
| ( ( is_antisymmetric_in @ SV471 @ SV645 )
= $false )
| ( ( is_reflexive_in @ SV471 @ SV645 )
= $false )
| ( ( is_transitive_in @ SV471 @ SV645 )
= $false )
| ( ( is_connected_in @ SV471 @ SV645 )
= $false )
| ( ( well_orders @ SV471 @ SV645 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(5718,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5624]) ).
thf(5719,plain,
! [SV471: $i] :
( ( ( ~ ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
= $false )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5624]) ).
thf(5720,plain,
! [SV800: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV800 ) )
= $true )
| ( ( is_antisymmetric_in @ SV471 @ SV800 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5625]) ).
thf(5721,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
| ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5722,plain,
! [SV472: $i,SV526: $i,SV759: $i] :
( ( ( relation @ SV759 )
= $false )
| ( ( function @ SV759 )
= $false )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) )
| ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5627]) ).
thf(5723,plain,
! [SV472: $i,SV526: $i,SV760: $i] :
( ( ( relation @ SV760 )
= $false )
| ( ( function @ SV760 )
= $false )
| ( ( ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) )
| ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) ) )
= $true )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(5724,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5630]) ).
thf(5725,plain,
! [SV474: $i,SV648: $i] :
( ( ( in @ ( ordered_pair @ ( sK29_C @ SV648 @ SV474 ) @ ( sK30_SY6442 @ SV648 @ SV474 ) ) @ SV474 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5631]) ).
thf(5726,plain,
! [SV474: $i,SV728: $i,SV649: $i,SV744: $i] :
( ( ( in @ SV744 @ SV649 )
= $false )
| ( ( in @ SV728 @ SV649 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(5727,plain,
! [SV552: $i] :
( ( ( ( sK70_B @ SV552 )
= ( sK71_SY6463 @ SV552 ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5728,plain,
! [SV552: $i] :
( ( ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
| ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5634]) ).
thf(5729,plain,
( ( ~ ( function @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5636]) ).
thf(5730,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5636]) ).
thf(5731,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(5732,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5640]) ).
thf(5733,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5641]) ).
thf(5734,plain,
! [SV681: $i,SV478: $i,SV812: $i,SV653: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV653 )
| ~ ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV478 )
| ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV681 ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5642]) ).
thf(5735,plain,
! [SV478: $i,SV653: $i,SV681: $i] :
( ( ( ~ ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5643]) ).
thf(5736,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( ~ ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) )
= $false )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5643]) ).
thf(5737,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(5738,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5646]) ).
thf(5739,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
| ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5647]) ).
thf(5740,plain,
! [SV683: $i,SV527: $i,SV802: $i,SV480: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV480 )
| ~ ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV527 )
| ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV683 ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(5741,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ~ ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5742,plain,
! [SV480: $i,SV527: $i,SV683: $i] :
( ( ( ~ ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) )
= $false )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5743,plain,
! [SV657: $i,SV481: $i,SV803: $i,SV785: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV481 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV657 )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5651]) ).
thf(5744,plain,
! [SV481: $i,SV657: $i,SV804: $i,SV786: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV657 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV481 )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5652]) ).
thf(5745,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5653]) ).
thf(5746,plain,
! [SV482: $i,SV775: $i] :
( ( ( function @ SV775 )
= $false )
| ( ( ~ ( relation @ SV775 ) )
= $true )
| ( ( ( SV775
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(5747,plain,
! [SV482: $i,SV776: $i] :
( ( ( function @ SV776 )
= $false )
| ( ( ~ ( relation @ SV776 ) )
= $true )
| ( ( ( SV776
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(5748,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5660]) ).
thf(5749,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5660]) ).
thf(5750,plain,
! [SV529: $i,SV737: $i,SV490: $i] :
( ( ( in @ SV490 @ ( relation_dom @ SV737 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) )
= $true )
| ( ( function @ SV737 )
= $false )
| ( ( relation @ SV737 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5661]) ).
thf(5751,plain,
! [SV529: $i,SV490: $i,SV767: $i] :
( ( ( relation @ SV767 )
= $false )
| ( ( function @ SV767 )
= $false )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
| ( in @ SV490 @ ( relation_dom @ SV767 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(5752,plain,
! [SV529: $i,SV490: $i,SV768: $i] :
( ( ( relation @ SV768 )
= $false )
| ( ( function @ SV768 )
= $false )
| ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
| ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) ) )
= $true )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(5753,plain,
! [SV491: $i,SV665: $i] :
( ( ( ( ( sK21_C @ SV665 @ SV491 )
!= ( sK22_SY6437 @ SV665 @ SV491 ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5664]) ).
thf(5754,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) ) )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5665]) ).
thf(5755,plain,
! [SV491: $i,SV738: $i,SV666: $i,SV747: $i] :
( ( ( in @ SV747 @ SV666 )
= $false )
| ( ( in @ SV738 @ SV666 )
= $false )
| ( ( SV738 = SV747 )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ SV747 ) @ SV491 )
= $true )
| ( ( in @ ( ordered_pair @ SV747 @ SV738 ) @ SV491 )
= $true )
| ( ( is_connected_in @ SV491 @ SV666 )
= $false )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(5756,plain,
! [SV787: $i,SV493: $i,SV717: $i] :
( ( ( ( sK27_C @ SV717 @ SV493 )
= ( apply @ SV493 @ SV787 ) )
= $false )
| ( ( ~ ( in @ SV787 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(5757,plain,
! [SV493: $i,SV717: $i] :
( ( ( ( sK27_C @ SV717 @ SV493 )
= ( apply @ SV493 @ ( sK28_SY6441 @ SV717 @ SV493 ) ) )
= $true )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5668]) ).
thf(5758,plain,
! [SV493: $i,SV717: $i] :
( ( ( in @ ( sK28_SY6441 @ SV717 @ SV493 ) @ ( relation_dom @ SV493 ) )
= $true )
| ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5669]) ).
thf(5759,plain,
! [SV718: $i,SV814: $i,SV493: $i,SV788: $i] :
( ( ( ( SV788
!= ( apply @ SV493 @ SV814 ) )
| ~ ( in @ SV814 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( in @ SV788 @ SV718 )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5760,plain,
! [SV493: $i,SV718: $i,SV789: $i] :
( ( ( in @ SV789 @ SV718 )
= $false )
| ( ( ~ ( ( SV789
!= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) ) )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5671]) ).
thf(5761,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ! [SY7405: $i] :
( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SY7405 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7405 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5672]) ).
thf(5762,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5673]) ).
thf(5763,plain,
! [SV741: $i,SV577: $i,SV494: $i] :
( ( ( ! [SY7406: $i,SY7407: $i] :
( ! [SY7248: $i] :
( ~ ( in @ ( ordered_pair @ SY7406 @ SY7248 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7248 @ SY7407 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SY7406 @ SY7407 ) @ SV741 ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5674]) ).
thf(5764,plain,
! [SV494: $i,SV577: $i,SV741: $i] :
( ( ( ! [SY7409: $i,SY7410: $i] :
( ~ ( in @ ( ordered_pair @ SY7409 @ SY7410 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SY7409 @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7410 @ SY7409 @ SV741 @ SV577 @ SV494 ) @ SY7410 ) @ SV577 ) ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5675]) ).
thf(5765,plain,
! [SV496: $i,SV668: $i,SV805: $i,SV790: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV790 @ SV805 ) @ SV668 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV805 @ SV790 ) @ SV496 )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5677]) ).
thf(5766,plain,
! [SV668: $i,SV496: $i,SV791: $i,SV806: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV806 @ SV791 ) @ SV496 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV791 @ SV806 ) @ SV668 )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5678]) ).
thf(5767,plain,
! [SV621: $i,SV581: $i,SV777: $i,SV769: $i] :
( ( ( SV769 = SV777 )
= $false )
| ( ( ~ ( in @ SV769 @ SV581 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV769 @ SV777 ) @ SV621 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5680]) ).
thf(5768,plain,
! [SV581: $i,SV621: $i,SV815: $i,SV807: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV807 @ SV815 ) @ SV621 )
| ( SV807 = SV815 ) )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5681]) ).
thf(5769,plain,
! [SV581: $i,SV621: $i,SV808: $i] :
( ( ( ! [SY7441: $i] :
~ ( in @ ( ordered_pair @ SV808 @ SY7441 ) @ SV621 ) )
= $true )
| ( ( in @ SV808 @ SV581 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5682]) ).
thf(5770,plain,
! [SV753: $i,SV498: $i,SV792: $i] :
( ( ( SV792
= ( apply @ SV498 @ SV753 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV753 @ SV792 ) @ SV498 )
= $true )
| ( ( in @ SV753 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(5771,plain,
! [SV498: $i,SV793: $i,SV754: $i] :
( ( ( in @ ( ordered_pair @ SV754 @ SV793 ) @ SV498 )
= $false )
| ( ( SV793
= ( apply @ SV498 @ SV754 ) )
= $true )
| ( ( in @ SV754 @ ( relation_dom @ SV498 ) )
= $false )
| ( ( function @ SV498 )
= $false )
| ( ( relation @ SV498 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5684]) ).
thf(5772,plain,
! [SV809: $i] :
( ( ( ~ ( relation @ SV809 ) )
= $true )
| ( ( ~ ( well_ordering @ SV809 )
| ( reflexive @ SV809 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5688]) ).
thf(5773,plain,
! [SV810: $i] :
( ( ( ~ ( relation @ SV810 ) )
= $true )
| ( ( ~ ( well_ordering @ SV810 )
| ( transitive @ SV810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5689]) ).
thf(5774,plain,
! [SV771: $i] :
( ( ( well_ordering @ SV771 )
= $false )
| ( ( antisymmetric @ SV771 )
= $true )
| ( ( relation @ SV771 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(5775,plain,
! [SV585: $i] :
( ( ( ~ ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5691]) ).
thf(5776,plain,
! [SV585: $i] :
( ( ( ~ ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) ) )
= $false )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5691]) ).
thf(5777,plain,
! [SV749: $i,SV586: $i,SV757: $i] :
( ( ( in @ SV757 @ ( relation_dom @ SV586 ) )
= $false )
| ( ( in @ SV749 @ ( relation_dom @ SV586 ) )
= $false )
| ( ( ( ( apply @ SV586 @ SV749 )
!= ( apply @ SV586 @ SV757 ) ) )
= $true )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5692]) ).
thf(5778,plain,
! [SV499: $i,SV690: $i,SV672: $i,SV780: $i] :
( ( ( in @ SV780 @ SV672 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV780 ) @ SV499 )
= $false )
| ( ( ~ ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 ) )
= $true )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5693]) ).
thf(5779,plain,
! [SV691: $i,SV673: $i,SV499: $i,SV811: $i,SV781: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV781 @ SV811 ) @ SV499 ) )
= $true )
| ( ( ~ ( in @ SV811 @ SV673 ) )
= $true )
| ( ( in @ SV781 @ SV691 )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5696]) ).
thf(5780,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
| ~ ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 ) )
= $false )
| ( ( in @ SV782 @ SV691 )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5781,plain,
! [SV692: $i,SV674: $i,SV794: $i] :
( ( ( in @ SV794 @ SV674 )
= $false )
| ( ( ( apply @ SV692 @ SV794 )
= SV794 )
= $true )
| ( ( SV692
= ( identity_relation @ SV674 ) )
= $false )
| ( ( function @ SV692 )
= $false )
| ( ( relation @ SV692 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(5782,plain,
! [SV772: $i,SV467: $i,SV640: $i,SV676: $i] :
( ( ( in @ ( sK50_D @ SV676 @ SV640 @ SV467 ) @ SV676 )
= $false )
| ( ( in @ ( ordered_pair @ SV772 @ ( sK50_D @ SV676 @ SV640 @ SV467 ) ) @ SV467 )
= $false )
| ( ( in @ SV772 @ SV640 )
= $false )
| ( ( SV676
= ( relation_image @ SV467 @ SV640 ) )
= $true )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5700]) ).
thf(5783,plain,
! [SV677: $i,SV641: $i,SV467: $i,SV773: $i,SV795: $i] :
( ( ( in @ ( ordered_pair @ SV795 @ SV773 ) @ SV467 )
= $false )
| ( ( ~ ( in @ SV795 @ SV641 ) )
= $true )
| ( ( in @ SV773 @ SV677 )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5701]) ).
thf(5784,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 ) )
= $false )
| ( ( in @ SV774 @ SV677 )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5702]) ).
thf(5785,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 ) )
= $false )
| ( ( in @ SV774 @ SV677 )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5702]) ).
thf(5786,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
| ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5703]) ).
thf(5787,plain,
! [SV468: $i,SV750: $i,SV743: $i,SV643: $i,SV720: $i] :
( ( ( in @ SV720 @ SV643 )
= $false )
| ( ( ~ ( in @ SV743 @ SV643 ) )
= $true )
| ( ( ~ ( in @ SV750 @ SV643 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5788,plain,
! [SV721: $i,SV696: $i,SV469: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ ( relation_dom @ SV469 ) ) )
= $true )
| ( ( ~ ( in @ SV796 @ SV696 ) )
= $true )
| ( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SV796 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5706]) ).
thf(5789,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5707]) ).
thf(5790,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
= ( apply @ SV469 @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5708]) ).
thf(5791,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SV816 @ SV697 )
| ( SV797
!= ( apply @ SV469 @ SV816 ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(5792,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( in @ SV798 @ SV722 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SV798
!= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) ) ) )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5793,plain,
! [SV698: $i,SV723: $i,SV470: $i] :
( ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
= $false )
| ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
= $false )
| ( ( ~ ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 ) )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(5794,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
= $true )
| ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5712]) ).
thf(5795,plain,
! [SV698: $i,SV723: $i,SV470: $i] :
( ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
= $true )
| ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 )
= $true )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5713]) ).
thf(5796,plain,
! [SV724: $i,SV699: $i,SV470: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( relation_dom @ SV470 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV470 @ SV799 ) @ SV699 ) )
= $true )
| ( ( in @ SV799 @ SV724 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(5797,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ! [SY7400: $i] :
( ~ ( in @ SY7400 @ SV724 )
| ( in @ SY7400 @ ( relation_dom @ SV470 ) ) ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5715]) ).
thf(5798,plain,
! [SV699: $i,SV470: $i,SV724: $i] :
( ( ( ! [SY7401: $i] :
( ~ ( in @ SY7401 @ SV724 )
| ( in @ ( apply @ SV470 @ SY7401 ) @ SV699 ) ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5716]) ).
thf(5799,plain,
! [SV471: $i] :
( ( ( ! [SY7028: $i] :
( ~ ( well_orders @ SV471 @ SY7028 )
| ( is_reflexive_in @ SV471 @ SY7028 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5718]) ).
thf(5800,plain,
! [SV471: $i] :
( ( ( ! [SY7029: $i] :
( ~ ( well_orders @ SV471 @ SY7029 )
| ( is_transitive_in @ SV471 @ SY7029 ) ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5719]) ).
thf(5801,plain,
! [SV800: $i,SV471: $i] :
( ( ( well_orders @ SV471 @ SV800 )
= $false )
| ( ( is_antisymmetric_in @ SV471 @ SV800 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(5802,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( ~ ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5721]) ).
thf(5803,plain,
! [SV472: $i,SV727: $i,SV526: $i] :
( ( ( ~ ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5721]) ).
thf(5804,plain,
! [SV472: $i,SV759: $i,SV526: $i] :
( ( ( ( SV526
!= ( relation_dom_restriction @ SV759 @ SV472 ) ) )
= $true )
| ( ( ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5722]) ).
thf(5805,plain,
! [SV472: $i,SV760: $i,SV526: $i] :
( ( ( ( SV526
!= ( relation_dom_restriction @ SV760 @ SV472 ) ) )
= $true )
| ( ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) )
= $true )
| ( ( function @ SV760 )
= $false )
| ( ( relation @ SV760 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5723]) ).
thf(5806,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
| ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(5807,plain,
! [SV649: $i,SV474: $i,SV744: $i,SV728: $i] :
( ( ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 )
= $false )
| ( ( in @ SV728 @ SV649 )
= $false )
| ( ( in @ SV744 @ SV649 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 ) )
= $true )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(5808,plain,
! [SV552: $i] :
( ( ( ~ ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5728]) ).
thf(5809,plain,
! [SV552: $i] :
( ( ( ~ ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) ) )
= $false )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5728]) ).
thf(5810,plain,
( ( function @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5729]) ).
thf(5811,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5730]) ).
thf(5812,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
= $false )
| ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 ) )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5731]) ).
thf(5813,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5732]) ).
thf(5814,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 )
= $true )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(5815,plain,
! [SV681: $i,SV478: $i,SV812: $i,SV653: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV653 )
| ~ ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV478 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV681 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(5816,plain,
! [SV478: $i,SV653: $i,SV681: $i] :
( ( ( ! [SY7350: $i] :
( ! [SY7351: $i] :
~ ( in @ ( ordered_pair @ SY7350 @ SY7351 ) @ SV681 )
| ( in @ SY7350 @ SV653 ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5735]) ).
thf(5817,plain,
! [SV653: $i,SV478: $i,SV681: $i] :
( ( ( ! [SY7352: $i,SY7353: $i] :
( ~ ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV681 )
| ( in @ ( ordered_pair @ SY7352 @ SY7353 ) @ SV478 ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5736]) ).
thf(5818,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
= $false )
| ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 ) )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5737]) ).
thf(5819,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5820,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 )
= $true )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(5821,plain,
! [SV683: $i,SV527: $i,SV802: $i,SV480: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV480 )
| ~ ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV527 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV683 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5740]) ).
thf(5822,plain,
! [SV527: $i,SV480: $i,SV683: $i] :
( ( ( ! [SY7356: $i,SY7357: $i] :
( ~ ( in @ ( ordered_pair @ SY7356 @ SY7357 ) @ SV683 )
| ( in @ SY7357 @ SV480 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5741]) ).
thf(5823,plain,
! [SV480: $i,SV527: $i,SV683: $i] :
( ( ( ! [SY7358: $i,SY7359: $i] :
( ~ ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV683 )
| ( in @ ( ordered_pair @ SY7358 @ SY7359 ) @ SV527 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5742]) ).
thf(5824,plain,
! [SV657: $i,SV481: $i,SV803: $i,SV785: $i] :
( ( ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV481 )
= $false )
| ( ( in @ ( ordered_pair @ SV785 @ SV803 ) @ SV657 )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(5825,plain,
! [SV481: $i,SV657: $i,SV804: $i,SV786: $i] :
( ( ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV657 )
= $false )
| ( ( in @ ( ordered_pair @ SV786 @ SV804 ) @ SV481 )
= $true )
| ( ( SV481 = SV657 )
= $false )
| ( ( relation @ SV657 )
= $false )
| ( ( relation @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(5826,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(5827,plain,
! [SV482: $i,SV775: $i] :
( ( ( relation @ SV775 )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( ( SV775
!= ( function_inverse @ SV482 ) )
| ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5746]) ).
thf(5828,plain,
! [SV482: $i,SV776: $i] :
( ( ( relation @ SV776 )
= $false )
| ( ( function @ SV776 )
= $false )
| ( ( ( SV776
!= ( function_inverse @ SV482 ) )
| ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(5829,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5748]) ).
thf(5830,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5749]) ).
thf(5831,plain,
! [SV529: $i,SV490: $i,SV737: $i] :
( ( ( in @ ( apply @ SV737 @ SV490 ) @ ( relation_dom @ SV529 ) )
= $false )
| ( ( in @ SV490 @ ( relation_dom @ SV737 ) )
= $false )
| ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV737 @ SV529 ) ) )
= $true )
| ( ( function @ SV737 )
= $false )
| ( ( relation @ SV737 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(5832,plain,
! [SV529: $i,SV767: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) ) )
= $true )
| ( ( in @ SV490 @ ( relation_dom @ SV767 ) )
= $true )
| ( ( function @ SV767 )
= $false )
| ( ( relation @ SV767 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5751]) ).
thf(5833,plain,
! [SV529: $i,SV768: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) )
= $true )
| ( ( function @ SV768 )
= $false )
| ( ( relation @ SV768 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5752]) ).
thf(5834,plain,
! [SV491: $i,SV665: $i] :
( ( ( ( sK21_C @ SV665 @ SV491 )
= ( sK22_SY6437 @ SV665 @ SV491 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5835,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
| ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(5836,plain,
! [SV717: $i,SV493: $i,SV787: $i] :
( ( ( in @ SV787 @ ( relation_dom @ SV493 ) )
= $false )
| ( ( ( sK27_C @ SV717 @ SV493 )
= ( apply @ SV493 @ SV787 ) )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 ) )
= $true )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(5837,plain,
! [SV718: $i,SV814: $i,SV493: $i,SV788: $i] :
( ( ( ( SV788
!= ( apply @ SV493 @ SV814 ) ) )
= $true )
| ( ( ~ ( in @ SV814 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( in @ SV788 @ SV718 )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5759]) ).
thf(5838,plain,
! [SV718: $i,SV493: $i,SV789: $i] :
( ( ( ( SV789
!= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) )
| ~ ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
= $false )
| ( ( in @ SV789 @ SV718 )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(5839,plain,
! [SV817: $i,SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SV817 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SV817 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(5840,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(5841,plain,
! [SV741: $i,SV577: $i,SV494: $i,SV818: $i] :
( ( ( ! [SY7442: $i] :
( ! [SY7443: $i] :
( ~ ( in @ ( ordered_pair @ SV818 @ SY7443 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7443 @ SY7442 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SV818 @ SY7442 ) @ SV741 ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5763]) ).
thf(5842,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV819: $i] :
( ( ( ! [SY7444: $i] :
( ~ ( in @ ( ordered_pair @ SV819 @ SY7444 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SY7444 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SY7444 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SY7444 ) @ SV577 ) ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5764]) ).
thf(5843,plain,
! [SV496: $i,SV668: $i,SV805: $i,SV790: $i] :
( ( ( in @ ( ordered_pair @ SV790 @ SV805 ) @ SV668 )
= $false )
| ( ( in @ ( ordered_pair @ SV805 @ SV790 ) @ SV496 )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(5844,plain,
! [SV668: $i,SV496: $i,SV791: $i,SV806: $i] :
( ( ( in @ ( ordered_pair @ SV806 @ SV791 ) @ SV496 )
= $false )
| ( ( in @ ( ordered_pair @ SV791 @ SV806 ) @ SV668 )
= $true )
| ( ( SV668
= ( relation_inverse @ SV496 ) )
= $false )
| ( ( relation @ SV668 )
= $false )
| ( ( relation @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5845,plain,
! [SV621: $i,SV777: $i,SV581: $i,SV769: $i] :
( ( ( in @ SV769 @ SV581 )
= $false )
| ( ( SV769 = SV777 )
= $false )
| ( ( in @ ( ordered_pair @ SV769 @ SV777 ) @ SV621 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5767]) ).
thf(5846,plain,
! [SV581: $i,SV621: $i,SV815: $i,SV807: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV807 @ SV815 ) @ SV621 ) )
= $true )
| ( ( SV807 = SV815 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5768]) ).
thf(5847,plain,
! [SV581: $i,SV621: $i,SV820: $i,SV808: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV808 @ SV820 ) @ SV621 ) )
= $true )
| ( ( in @ SV808 @ SV581 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(5848,plain,
! [SV809: $i] :
( ( ( relation @ SV809 )
= $false )
| ( ( ~ ( well_ordering @ SV809 )
| ( reflexive @ SV809 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(5849,plain,
! [SV810: $i] :
( ( ( relation @ SV810 )
= $false )
| ( ( ~ ( well_ordering @ SV810 )
| ( transitive @ SV810 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(5850,plain,
! [SV585: $i] :
( ( ( in @ ( sK17_B @ SV585 ) @ ( relation_dom @ SV585 ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5775]) ).
thf(5851,plain,
! [SV585: $i] :
( ( ( in @ ( sK18_SY6435 @ SV585 ) @ ( relation_dom @ SV585 ) )
= $true )
| ( ( one_to_one @ SV585 )
= $true )
| ( ( function @ SV585 )
= $false )
| ( ( relation @ SV585 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5776]) ).
thf(5852,plain,
! [SV757: $i,SV749: $i,SV586: $i] :
( ( ( ( apply @ SV586 @ SV749 )
= ( apply @ SV586 @ SV757 ) )
= $false )
| ( ( in @ SV749 @ ( relation_dom @ SV586 ) )
= $false )
| ( ( in @ SV757 @ ( relation_dom @ SV586 ) )
= $false )
| ( ( SV749 = SV757 )
= $true )
| ( ( one_to_one @ SV586 )
= $false )
| ( ( function @ SV586 )
= $false )
| ( ( relation @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(5853,plain,
! [SV780: $i,SV499: $i,SV672: $i,SV690: $i] :
( ( ( in @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV690 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK47_D @ SV690 @ SV672 @ SV499 ) @ SV780 ) @ SV499 )
= $false )
| ( ( in @ SV780 @ SV672 )
= $false )
| ( ( SV690
= ( relation_inverse_image @ SV499 @ SV672 ) )
= $true )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(5854,plain,
! [SV691: $i,SV673: $i,SV499: $i,SV811: $i,SV781: $i] :
( ( ( in @ ( ordered_pair @ SV781 @ SV811 ) @ SV499 )
= $false )
| ( ( ~ ( in @ SV811 @ SV673 ) )
= $true )
| ( ( in @ SV781 @ SV691 )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5779]) ).
thf(5855,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 ) )
= $false )
| ( ( in @ SV782 @ SV691 )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5780]) ).
thf(5856,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 ) )
= $false )
| ( ( in @ SV782 @ SV691 )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5780]) ).
thf(5857,plain,
! [SV677: $i,SV467: $i,SV773: $i,SV641: $i,SV795: $i] :
( ( ( in @ SV795 @ SV641 )
= $false )
| ( ( in @ ( ordered_pair @ SV795 @ SV773 ) @ SV467 )
= $false )
| ( ( in @ SV773 @ SV677 )
= $true )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(5858,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( in @ ( ordered_pair @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV774 ) @ SV467 )
= $true )
| ( ( in @ SV774 @ SV677 )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5784]) ).
thf(5859,plain,
! [SV467: $i,SV641: $i,SV677: $i,SV774: $i] :
( ( ( in @ ( sK49_E @ SV774 @ SV677 @ SV641 @ SV467 ) @ SV641 )
= $true )
| ( ( in @ SV774 @ SV677 )
= $false )
| ( ( SV677
= ( relation_image @ SV467 @ SV641 ) )
= $false )
| ( ( relation @ SV467 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5785]) ).
thf(5860,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5786]) ).
thf(5861,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5786]) ).
thf(5862,plain,
! [SV468: $i,SV750: $i,SV720: $i,SV643: $i,SV743: $i] :
( ( ( in @ SV743 @ SV643 )
= $false )
| ( ( in @ SV720 @ SV643 )
= $false )
| ( ( ~ ( in @ SV750 @ SV643 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(5863,plain,
! [SV721: $i,SV696: $i,SV469: $i,SV796: $i] :
( ( ( in @ SV796 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( ~ ( in @ SV796 @ SV696 ) )
= $true )
| ( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SV796 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5864,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5865,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ ( relation_dom @ SV469 ) )
| ~ ( in @ SV816 @ SV697 ) )
= $true )
| ( ( ( SV797
!= ( apply @ SV469 @ SV816 ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5791]) ).
thf(5866,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
| ( SV798
!= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(5867,plain,
! [SV470: $i,SV698: $i,SV723: $i] :
( ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ SV723 )
= $false )
| ( ( in @ ( sK52_D @ SV723 @ SV698 @ SV470 ) @ ( relation_dom @ SV470 ) )
= $false )
| ( ( in @ ( apply @ SV470 @ ( sK52_D @ SV723 @ SV698 @ SV470 ) ) @ SV698 )
= $false )
| ( ( SV723
= ( relation_inverse_image @ SV470 @ SV698 ) )
= $true )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(5868,plain,
! [SV724: $i,SV699: $i,SV470: $i,SV799: $i] :
( ( ( in @ SV799 @ ( relation_dom @ SV470 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV470 @ SV799 ) @ SV699 ) )
= $true )
| ( ( in @ SV799 @ SV724 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5796]) ).
thf(5869,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ SV724 )
| ( in @ SV821 @ ( relation_dom @ SV470 ) ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(5870,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV724 )
| ( in @ ( apply @ SV470 @ SV822 ) @ SV699 ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5798]) ).
thf(5871,plain,
! [SV823: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV823 )
| ( is_reflexive_in @ SV471 @ SV823 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5799]) ).
thf(5872,plain,
! [SV824: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV824 )
| ( is_transitive_in @ SV471 @ SV824 ) )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5800]) ).
thf(5873,plain,
! [SV472: $i,SV526: $i,SV727: $i] :
( ( ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
= $true )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5802]) ).
thf(5874,plain,
! [SV472: $i,SV727: $i,SV526: $i] :
( ( ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
!= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5803]) ).
thf(5875,plain,
! [SV472: $i,SV759: $i,SV526: $i] :
( ( ( SV526
= ( relation_dom_restriction @ SV759 @ SV472 ) )
= $false )
| ( ( ! [SY7418: $i] :
( ~ ( in @ SY7418 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SY7418 )
= ( apply @ SV759 @ SY7418 ) ) ) )
= $true )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(5876,plain,
! [SV472: $i,SV760: $i,SV526: $i] :
( ( ( SV526
= ( relation_dom_restriction @ SV760 @ SV472 ) )
= $false )
| ( ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV760 ) @ SV472 ) )
= $true )
| ( ( function @ SV760 )
= $false )
| ( ( relation @ SV760 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(5877,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5806]) ).
thf(5878,plain,
! [SV474: $i,SV648: $i] :
( ( ( ~ ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 ) )
= $false )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5806]) ).
thf(5879,plain,
! [SV649: $i,SV474: $i,SV728: $i,SV744: $i] :
( ( ( in @ ( ordered_pair @ SV744 @ SV728 ) @ SV474 )
= $false )
| ( ( in @ SV744 @ SV649 )
= $false )
| ( ( in @ SV728 @ SV649 )
= $false )
| ( ( in @ ( ordered_pair @ SV728 @ SV744 ) @ SV474 )
= $false )
| ( ( SV728 = SV744 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV649 )
= $false )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5807]) ).
thf(5880,plain,
! [SV552: $i] :
( ( ( in @ ( sK70_B @ SV552 ) @ ( relation_field @ SV552 ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5808]) ).
thf(5881,plain,
! [SV552: $i] :
( ( ( in @ ( sK71_SY6463 @ SV552 ) @ ( relation_field @ SV552 ) )
= $true )
| ( ( connected @ SV552 )
= $true )
| ( ( relation @ SV552 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5809]) ).
thf(5882,plain,
! [SV478: $i,SV652: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV680 )
= $false )
| ( ( in @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ SV652 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV680 @ SV652 @ SV478 ) @ ( sK59_SY6459 @ SV680 @ SV652 @ SV478 ) ) @ SV478 )
= $false )
| ( ( SV680
= ( relation_dom_restriction @ SV478 @ SV652 ) )
= $true )
| ( ( relation @ SV680 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5812]) ).
thf(5883,plain,
! [SV681: $i,SV478: $i,SV812: $i,SV653: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV653 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV478 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV681 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5815]) ).
thf(5884,plain,
! [SV478: $i,SV653: $i,SV681: $i,SV825: $i] :
( ( ( ! [SY7445: $i] :
~ ( in @ ( ordered_pair @ SV825 @ SY7445 ) @ SV681 )
| ( in @ SV825 @ SV653 ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5816]) ).
thf(5885,plain,
! [SV653: $i,SV478: $i,SV681: $i,SV826: $i] :
( ( ( ! [SY7446: $i] :
( ~ ( in @ ( ordered_pair @ SV826 @ SY7446 ) @ SV681 )
| ( in @ ( ordered_pair @ SV826 @ SY7446 ) @ SV478 ) ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5817]) ).
thf(5886,plain,
! [SV480: $i,SV527: $i,SV682: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV682 )
= $false )
| ( ( in @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) @ SV480 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK53_D @ SV682 @ SV527 @ SV480 ) @ ( sK54_SY6456 @ SV682 @ SV527 @ SV480 ) ) @ SV527 )
= $false )
| ( ( SV682
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $true )
| ( ( relation @ SV682 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5818]) ).
thf(5887,plain,
! [SV683: $i,SV527: $i,SV802: $i,SV480: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV480 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV527 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV683 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5821]) ).
thf(5888,plain,
! [SV527: $i,SV480: $i,SV683: $i,SV827: $i] :
( ( ( ! [SY7447: $i] :
( ~ ( in @ ( ordered_pair @ SV827 @ SY7447 ) @ SV683 )
| ( in @ SY7447 @ SV480 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5822]) ).
thf(5889,plain,
! [SV480: $i,SV527: $i,SV683: $i,SV828: $i] :
( ( ( ! [SY7448: $i] :
( ~ ( in @ ( ordered_pair @ SV828 @ SY7448 ) @ SV683 )
| ( in @ ( ordered_pair @ SV828 @ SY7448 ) @ SV527 ) ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5823]) ).
thf(5890,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5826]) ).
thf(5891,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5826]) ).
thf(5892,plain,
! [SV482: $i,SV775: $i] :
( ( ( ( SV775
!= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5827]) ).
thf(5893,plain,
! [SV482: $i,SV776: $i] :
( ( ( ( SV776
!= ( function_inverse @ SV482 ) ) )
= $true )
| ( ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) )
= $true )
| ( ( function @ SV776 )
= $false )
| ( ( relation @ SV776 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(5894,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(5895,plain,
! [SV529: $i,SV767: $i,SV490: $i] :
( ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV767 @ SV529 ) ) )
= $false )
| ( ( in @ SV490 @ ( relation_dom @ SV767 ) )
= $true )
| ( ( function @ SV767 )
= $false )
| ( ( relation @ SV767 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(5896,plain,
! [SV529: $i,SV768: $i,SV490: $i] :
( ( ( in @ SV490 @ ( relation_dom @ ( relation_composition @ SV768 @ SV529 ) ) )
= $false )
| ( ( in @ ( apply @ SV768 @ SV490 ) @ ( relation_dom @ SV529 ) )
= $true )
| ( ( function @ SV768 )
= $false )
| ( ( relation @ SV768 )
= $false )
| ( ( function @ SV529 )
= $false )
| ( ( relation @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5833]) ).
thf(5897,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5835]) ).
thf(5898,plain,
! [SV491: $i,SV665: $i] :
( ( ( ~ ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 ) )
= $false )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5835]) ).
thf(5899,plain,
! [SV787: $i,SV493: $i,SV717: $i] :
( ( ( in @ ( sK27_C @ SV717 @ SV493 ) @ SV717 )
= $false )
| ( ( ( sK27_C @ SV717 @ SV493 )
= ( apply @ SV493 @ SV787 ) )
= $false )
| ( ( in @ SV787 @ ( relation_dom @ SV493 ) )
= $false )
| ( ( SV717
= ( relation_rng @ SV493 ) )
= $true )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(5900,plain,
! [SV718: $i,SV814: $i,SV493: $i,SV788: $i] :
( ( ( SV788
= ( apply @ SV493 @ SV814 ) )
= $false )
| ( ( ~ ( in @ SV814 @ ( relation_dom @ SV493 ) ) )
= $true )
| ( ( in @ SV788 @ SV718 )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(5901,plain,
! [SV718: $i,SV493: $i,SV789: $i] :
( ( ( ( SV789
!= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) ) )
= $false )
| ( ( in @ SV789 @ SV718 )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5838]) ).
thf(5902,plain,
! [SV493: $i,SV718: $i,SV789: $i] :
( ( ( ~ ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) ) )
= $false )
| ( ( in @ SV789 @ SV718 )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5838]) ).
thf(5903,plain,
! [SV817: $i,SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SV817 ) @ SV494 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV817 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5839]) ).
thf(5904,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5840]) ).
thf(5905,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5840]) ).
thf(5906,plain,
! [SV741: $i,SV577: $i,SV829: $i,SV494: $i,SV818: $i] :
( ( ( ! [SY7449: $i] :
( ~ ( in @ ( ordered_pair @ SV818 @ SY7449 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7449 @ SV829 ) @ SV577 ) )
| ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5841]) ).
thf(5907,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
| ~ ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5842]) ).
thf(5908,plain,
! [SV581: $i,SV621: $i,SV815: $i,SV807: $i] :
( ( ( in @ ( ordered_pair @ SV807 @ SV815 ) @ SV621 )
= $false )
| ( ( SV807 = SV815 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5909,plain,
! [SV581: $i,SV621: $i,SV820: $i,SV808: $i] :
( ( ( in @ ( ordered_pair @ SV808 @ SV820 ) @ SV621 )
= $false )
| ( ( in @ SV808 @ SV581 )
= $true )
| ( ( SV621
= ( identity_relation @ SV581 ) )
= $false )
| ( ( relation @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(5910,plain,
! [SV809: $i] :
( ( ( ~ ( well_ordering @ SV809 ) )
= $true )
| ( ( reflexive @ SV809 )
= $true )
| ( ( relation @ SV809 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5848]) ).
thf(5911,plain,
! [SV810: $i] :
( ( ( ~ ( well_ordering @ SV810 ) )
= $true )
| ( ( transitive @ SV810 )
= $true )
| ( ( relation @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5849]) ).
thf(5912,plain,
! [SV691: $i,SV499: $i,SV781: $i,SV673: $i,SV811: $i] :
( ( ( in @ SV811 @ SV673 )
= $false )
| ( ( in @ ( ordered_pair @ SV781 @ SV811 ) @ SV499 )
= $false )
| ( ( in @ SV781 @ SV691 )
= $true )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5913,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( in @ ( ordered_pair @ SV782 @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) ) @ SV499 )
= $true )
| ( ( in @ SV782 @ SV691 )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5855]) ).
thf(5914,plain,
! [SV499: $i,SV673: $i,SV691: $i,SV782: $i] :
( ( ( in @ ( sK46_E @ SV782 @ SV691 @ SV673 @ SV499 ) @ SV673 )
= $true )
| ( ( in @ SV782 @ SV691 )
= $false )
| ( ( SV691
= ( relation_inverse_image @ SV499 @ SV673 ) )
= $false )
| ( ( relation @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5856]) ).
thf(5915,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) ) )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5860]) ).
thf(5916,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( sK12_SY6429 @ SV642 @ SV468 ) @ SV642 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5861]) ).
thf(5917,plain,
! [SV468: $i,SV743: $i,SV720: $i,SV643: $i,SV750: $i] :
( ( ( in @ SV750 @ SV643 )
= $false )
| ( ( in @ SV720 @ SV643 )
= $false )
| ( ( in @ SV743 @ SV643 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5862]) ).
thf(5918,plain,
! [SV721: $i,SV469: $i,SV696: $i,SV796: $i] :
( ( ( in @ SV796 @ SV696 )
= $false )
| ( ( in @ SV796 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
!= ( apply @ SV469 @ SV796 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5863]) ).
thf(5919,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5864]) ).
thf(5920,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( ~ ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 ) )
= $false )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5864]) ).
thf(5921,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ ( relation_dom @ SV469 ) ) )
= $true )
| ( ( ~ ( in @ SV816 @ SV697 ) )
= $true )
| ( ( ( SV797
!= ( apply @ SV469 @ SV816 ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5865]) ).
thf(5922,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5866]) ).
thf(5923,plain,
! [SV697: $i,SV722: $i,SV469: $i,SV798: $i] :
( ( ( ( SV798
!= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5866]) ).
thf(5924,plain,
! [SV724: $i,SV699: $i,SV799: $i,SV470: $i] :
( ( ( in @ ( apply @ SV470 @ SV799 ) @ SV699 )
= $false )
| ( ( in @ SV799 @ ( relation_dom @ SV470 ) )
= $false )
| ( ( in @ SV799 @ SV724 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(5925,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ SV724 ) )
= $true )
| ( ( in @ SV821 @ ( relation_dom @ SV470 ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5869]) ).
thf(5926,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV724 ) )
= $true )
| ( ( in @ ( apply @ SV470 @ SV822 ) @ SV699 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5870]) ).
thf(5927,plain,
! [SV823: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV823 ) )
= $true )
| ( ( is_reflexive_in @ SV471 @ SV823 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5871]) ).
thf(5928,plain,
! [SV824: $i,SV471: $i] :
( ( ( ~ ( well_orders @ SV471 @ SV824 ) )
= $true )
| ( ( is_transitive_in @ SV471 @ SV824 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5872]) ).
thf(5929,plain,
! [SV472: $i,SV727: $i,SV526: $i] :
( ( ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
= $false )
| ( ( in @ ( sK62_D @ SV727 @ SV526 @ SV472 ) @ ( relation_dom @ SV526 ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(5930,plain,
! [SV472: $i,SV727: $i,SV526: $i] :
( ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV526 )
!= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5874]) ).
thf(5931,plain,
! [SV472: $i,SV759: $i,SV526: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( relation_dom @ SV526 ) )
| ( ( apply @ SV526 @ SV831 )
= ( apply @ SV759 @ SV831 ) ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV759 @ SV472 ) )
= $false )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5875]) ).
thf(5932,plain,
! [SV474: $i,SV648: $i] :
( ( ( in @ ( sK29_C @ SV648 @ SV474 ) @ SV648 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5877]) ).
thf(5933,plain,
! [SV474: $i,SV648: $i] :
( ( ( in @ ( sK30_SY6442 @ SV648 @ SV474 ) @ SV648 )
= $true )
| ( ( is_antisymmetric_in @ SV474 @ SV648 )
= $true )
| ( ( relation @ SV474 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5878]) ).
thf(5934,plain,
! [SV681: $i,SV478: $i,SV812: $i,SV653: $i,SV801: $i] :
( ( ( in @ SV801 @ SV653 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV478 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV681 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5883]) ).
thf(5935,plain,
! [SV478: $i,SV653: $i,SV681: $i,SV825: $i] :
( ( ( ! [SY7445: $i] :
~ ( in @ ( ordered_pair @ SV825 @ SY7445 ) @ SV681 ) )
= $true )
| ( ( in @ SV825 @ SV653 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5884]) ).
thf(5936,plain,
! [SV653: $i,SV478: $i,SV681: $i,SV832: $i,SV826: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV681 )
| ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV478 ) )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5885]) ).
thf(5937,plain,
! [SV683: $i,SV527: $i,SV802: $i,SV480: $i,SV813: $i] :
( ( ( in @ SV813 @ SV480 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV527 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV683 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(5938,plain,
! [SV527: $i,SV480: $i,SV683: $i,SV833: $i,SV827: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV827 @ SV833 ) @ SV683 )
| ( in @ SV833 @ SV480 ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5888]) ).
thf(5939,plain,
! [SV480: $i,SV527: $i,SV683: $i,SV834: $i,SV828: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV683 )
| ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV527 ) )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5889]) ).
thf(5940,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5890]) ).
thf(5941,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5891]) ).
thf(5942,plain,
! [SV482: $i,SV775: $i] :
( ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) ) )
= $true )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(5943,plain,
! [SV482: $i,SV776: $i] :
( ( ( SV776
= ( function_inverse @ SV482 ) )
= $false )
| ( ( ( relation_dom @ SV776 )
= ( relation_rng @ SV482 ) )
= $true )
| ( ( function @ SV776 )
= $false )
| ( ( relation @ SV776 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5893]) ).
thf(5944,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5894]) ).
thf(5945,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[5894]) ).
thf(5946,plain,
! [SV491: $i,SV665: $i] :
( ( ( in @ ( sK21_C @ SV665 @ SV491 ) @ SV665 )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5897]) ).
thf(5947,plain,
! [SV491: $i,SV665: $i] :
( ( ( in @ ( sK22_SY6437 @ SV665 @ SV491 ) @ SV665 )
= $true )
| ( ( is_connected_in @ SV491 @ SV665 )
= $true )
| ( ( relation @ SV491 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5898]) ).
thf(5948,plain,
! [SV718: $i,SV788: $i,SV493: $i,SV814: $i] :
( ( ( in @ SV814 @ ( relation_dom @ SV493 ) )
= $false )
| ( ( SV788
= ( apply @ SV493 @ SV814 ) )
= $false )
| ( ( in @ SV788 @ SV718 )
= $true )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5900]) ).
thf(5949,plain,
! [SV718: $i,SV493: $i,SV789: $i] :
( ( ( SV789
= ( apply @ SV493 @ ( sK26_D @ SV789 @ SV718 @ SV493 ) ) )
= $true )
| ( ( in @ SV789 @ SV718 )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5901]) ).
thf(5950,plain,
! [SV493: $i,SV718: $i,SV789: $i] :
( ( ( in @ ( sK26_D @ SV789 @ SV718 @ SV493 ) @ ( relation_dom @ SV493 ) )
= $true )
| ( ( in @ SV789 @ SV718 )
= $false )
| ( ( SV718
= ( relation_rng @ SV493 ) )
= $false )
| ( ( function @ SV493 )
= $false )
| ( ( relation @ SV493 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5902]) ).
thf(5951,plain,
! [SV817: $i,SV494: $i,SV577: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SV817 ) @ SV494 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV817 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5903]) ).
thf(5952,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) ) @ SV494 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5904]) ).
thf(5953,plain,
! [SV494: $i,SV577: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY6434 @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5905]) ).
thf(5954,plain,
! [SV741: $i,SV577: $i,SV829: $i,SV494: $i,SV818: $i] :
( ( ( ! [SY7449: $i] :
( ~ ( in @ ( ordered_pair @ SV818 @ SY7449 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SY7449 @ SV829 ) @ SV577 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5906]) ).
thf(5955,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5907]) ).
thf(5956,plain,
! [SV809: $i] :
( ( ( well_ordering @ SV809 )
= $false )
| ( ( reflexive @ SV809 )
= $true )
| ( ( relation @ SV809 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(5957,plain,
! [SV810: $i] :
( ( ( well_ordering @ SV810 )
= $false )
| ( ( transitive @ SV810 )
= $true )
| ( ( relation @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(5958,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
| ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(5959,plain,
! [SV750: $i,SV643: $i,SV468: $i,SV743: $i,SV720: $i] :
( ( ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 )
= $false )
| ( ( in @ SV743 @ SV643 )
= $false )
| ( ( in @ SV720 @ SV643 )
= $false )
| ( ( in @ SV750 @ SV643 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(5960,plain,
! [SV796: $i,SV469: $i,SV696: $i,SV721: $i] :
( ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
= ( apply @ SV469 @ SV796 ) )
= $false )
| ( ( in @ SV796 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( in @ SV796 @ SV696 )
= $false )
| ( ( ~ ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 ) )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(5961,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ ( relation_dom @ SV469 ) )
= $true )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5919]) ).
thf(5962,plain,
! [SV469: $i,SV696: $i,SV721: $i] :
( ( ( in @ ( sK57_SY6458 @ SV721 @ SV696 @ SV469 ) @ SV696 )
= $true )
| ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $true )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5920]) ).
thf(5963,plain,
! [SV722: $i,SV797: $i,SV697: $i,SV469: $i,SV816: $i] :
( ( ( in @ SV816 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( ~ ( in @ SV816 @ SV697 ) )
= $true )
| ( ( ( SV797
!= ( apply @ SV469 @ SV816 ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(5964,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) ) )
= $true )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5922]) ).
thf(5965,plain,
! [SV697: $i,SV722: $i,SV469: $i,SV798: $i] :
( ( ( SV798
= ( apply @ SV469 @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) ) )
= $true )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5923]) ).
thf(5966,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV821: $i] :
( ( ( in @ SV821 @ SV724 )
= $false )
| ( ( in @ SV821 @ ( relation_dom @ SV470 ) )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5925]) ).
thf(5967,plain,
! [SV699: $i,SV470: $i,SV724: $i,SV822: $i] :
( ( ( in @ SV822 @ SV724 )
= $false )
| ( ( in @ ( apply @ SV470 @ SV822 ) @ SV699 )
= $true )
| ( ( SV724
= ( relation_inverse_image @ SV470 @ SV699 ) )
= $false )
| ( ( function @ SV470 )
= $false )
| ( ( relation @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5926]) ).
thf(5968,plain,
! [SV823: $i,SV471: $i] :
( ( ( well_orders @ SV471 @ SV823 )
= $false )
| ( ( is_reflexive_in @ SV471 @ SV823 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5927]) ).
thf(5969,plain,
! [SV824: $i,SV471: $i] :
( ( ( well_orders @ SV471 @ SV824 )
= $false )
| ( ( is_transitive_in @ SV471 @ SV824 )
= $true )
| ( ( relation @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5928]) ).
thf(5970,plain,
! [SV472: $i,SV727: $i,SV526: $i] :
( ( ( ( relation_dom @ SV526 )
= ( set_intersection2 @ ( relation_dom @ SV727 ) @ SV472 ) )
= $false )
| ( ( ( apply @ SV526 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) )
= ( apply @ SV727 @ ( sK62_D @ SV727 @ SV526 @ SV472 ) ) )
= $false )
| ( ( SV526
= ( relation_dom_restriction @ SV727 @ SV472 ) )
= $true )
| ( ( function @ SV727 )
= $false )
| ( ( relation @ SV727 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(5971,plain,
! [SV472: $i,SV759: $i,SV526: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( relation_dom @ SV526 ) ) )
= $true )
| ( ( ( apply @ SV526 @ SV831 )
= ( apply @ SV759 @ SV831 ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV759 @ SV472 ) )
= $false )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5931]) ).
thf(5972,plain,
! [SV681: $i,SV653: $i,SV478: $i,SV812: $i,SV801: $i] :
( ( ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV478 )
= $false )
| ( ( in @ SV801 @ SV653 )
= $false )
| ( ( in @ ( ordered_pair @ SV801 @ SV812 ) @ SV681 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(5973,plain,
! [SV478: $i,SV653: $i,SV681: $i,SV835: $i,SV825: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV825 @ SV835 ) @ SV681 ) )
= $true )
| ( ( in @ SV825 @ SV653 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5935]) ).
thf(5974,plain,
! [SV653: $i,SV478: $i,SV681: $i,SV832: $i,SV826: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV681 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV478 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5936]) ).
thf(5975,plain,
! [SV683: $i,SV480: $i,SV527: $i,SV813: $i,SV802: $i] :
( ( ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV527 )
= $false )
| ( ( in @ SV813 @ SV480 )
= $false )
| ( ( in @ ( ordered_pair @ SV802 @ SV813 ) @ SV683 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(5976,plain,
! [SV527: $i,SV480: $i,SV683: $i,SV833: $i,SV827: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV827 @ SV833 ) @ SV683 ) )
= $true )
| ( ( in @ SV833 @ SV480 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5938]) ).
thf(5977,plain,
! [SV480: $i,SV527: $i,SV683: $i,SV834: $i,SV828: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV683 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV527 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5939]) ).
thf(5978,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5940]) ).
thf(5979,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5941]) ).
thf(5980,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
| ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5942]) ).
thf(5981,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5944]) ).
thf(5982,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[5945]) ).
thf(5983,plain,
! [SV494: $i,SV577: $i,SV740: $i,SV817: $i] :
( ( ( in @ ( ordered_pair @ SV817 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SV817 ) @ SV494 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 ) )
= $true )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5951]) ).
thf(5984,plain,
! [SV741: $i,SV577: $i,SV829: $i,SV494: $i,SV836: $i,SV818: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV818 @ SV836 ) @ SV494 )
| ~ ( in @ ( ordered_pair @ SV836 @ SV829 ) @ SV577 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5954]) ).
thf(5985,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 ) ) )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(5986,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5958]) ).
thf(5987,plain,
! [SV468: $i,SV642: $i] :
( ( ( ~ ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 ) )
= $false )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5958]) ).
thf(5988,plain,
! [SV720: $i,SV643: $i,SV468: $i,SV750: $i,SV743: $i] :
( ( ( in @ ( ordered_pair @ SV743 @ SV750 ) @ SV468 )
= $false )
| ( ( in @ SV750 @ SV643 )
= $false )
| ( ( in @ SV720 @ SV643 )
= $false )
| ( ( in @ SV743 @ SV643 )
= $false )
| ( ( in @ ( ordered_pair @ SV720 @ SV743 ) @ SV468 )
= $false )
| ( ( in @ ( ordered_pair @ SV720 @ SV750 ) @ SV468 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV643 )
= $false )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5959]) ).
thf(5989,plain,
! [SV796: $i,SV469: $i,SV696: $i,SV721: $i] :
( ( ( in @ ( sK56_D @ SV721 @ SV696 @ SV469 ) @ SV721 )
= $false )
| ( ( in @ SV796 @ SV696 )
= $false )
| ( ( in @ SV796 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( ( sK56_D @ SV721 @ SV696 @ SV469 )
= ( apply @ SV469 @ SV796 ) )
= $false )
| ( ( SV721
= ( relation_image @ SV469 @ SV696 ) )
= $true )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5960]) ).
thf(5990,plain,
! [SV722: $i,SV797: $i,SV469: $i,SV697: $i,SV816: $i] :
( ( ( in @ SV816 @ SV697 )
= $false )
| ( ( in @ SV816 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( ( SV797
!= ( apply @ SV469 @ SV816 ) ) )
= $true )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5963]) ).
thf(5991,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
| ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(5992,plain,
! [SV472: $i,SV759: $i,SV526: $i,SV831: $i] :
( ( ( in @ SV831 @ ( relation_dom @ SV526 ) )
= $false )
| ( ( ( apply @ SV526 @ SV831 )
= ( apply @ SV759 @ SV831 ) )
= $true )
| ( ( SV526
= ( relation_dom_restriction @ SV759 @ SV472 ) )
= $false )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( function @ SV526 )
= $false )
| ( ( relation @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(5993,plain,
! [SV478: $i,SV653: $i,SV681: $i,SV835: $i,SV825: $i] :
( ( ( in @ ( ordered_pair @ SV825 @ SV835 ) @ SV681 )
= $false )
| ( ( in @ SV825 @ SV653 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(5994,plain,
! [SV653: $i,SV478: $i,SV681: $i,SV832: $i,SV826: $i] :
( ( ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV681 )
= $false )
| ( ( in @ ( ordered_pair @ SV826 @ SV832 ) @ SV478 )
= $true )
| ( ( SV681
= ( relation_dom_restriction @ SV478 @ SV653 ) )
= $false )
| ( ( relation @ SV681 )
= $false )
| ( ( relation @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5974]) ).
thf(5995,plain,
! [SV527: $i,SV480: $i,SV683: $i,SV833: $i,SV827: $i] :
( ( ( in @ ( ordered_pair @ SV827 @ SV833 ) @ SV683 )
= $false )
| ( ( in @ SV833 @ SV480 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5976]) ).
thf(5996,plain,
! [SV480: $i,SV527: $i,SV683: $i,SV834: $i,SV828: $i] :
( ( ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV683 )
= $false )
| ( ( in @ ( ordered_pair @ SV828 @ SV834 ) @ SV527 )
= $true )
| ( ( SV683
= ( relation_rng_restriction @ SV480 @ SV527 ) )
= $false )
| ( ( relation @ SV683 )
= $false )
| ( ( relation @ SV527 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5977]) ).
thf(5997,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5978]) ).
thf(5998,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5978]) ).
thf(5999,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5979]) ).
thf(6000,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5979]) ).
thf(6001,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5980]) ).
thf(6002,plain,
! [SV775: $i,SV482: $i] :
( ( ( ~ ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5980]) ).
thf(6003,plain,
! [SV817: $i,SV494: $i,SV577: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV740 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK14_D @ SV740 @ SV577 @ SV494 ) @ SV817 ) @ SV494 )
= $false )
| ( ( in @ ( ordered_pair @ SV817 @ ( sK15_SY6430 @ SV740 @ SV577 @ SV494 ) ) @ SV577 )
= $false )
| ( ( SV740
= ( relation_composition @ SV494 @ SV577 ) )
= $true )
| ( ( relation @ SV740 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5983]) ).
thf(6004,plain,
! [SV741: $i,SV577: $i,SV829: $i,SV494: $i,SV836: $i,SV818: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV818 @ SV836 ) @ SV494 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV836 @ SV829 ) @ SV577 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5984]) ).
thf(6005,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
| ~ ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6006,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( sK10_C @ SV642 @ SV468 ) @ SV642 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5986]) ).
thf(6007,plain,
! [SV468: $i,SV642: $i] :
( ( ( in @ ( sK11_SY6427 @ SV642 @ SV468 ) @ SV642 )
= $true )
| ( ( is_transitive_in @ SV468 @ SV642 )
= $true )
| ( ( relation @ SV468 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5987]) ).
thf(6008,plain,
! [SV722: $i,SV697: $i,SV816: $i,SV469: $i,SV797: $i] :
( ( ( SV797
= ( apply @ SV469 @ SV816 ) )
= $false )
| ( ( in @ SV816 @ ( relation_dom @ SV469 ) )
= $false )
| ( ( in @ SV816 @ SV697 )
= $false )
| ( ( in @ SV797 @ SV722 )
= $true )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5990]) ).
thf(6009,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5991]) ).
thf(6010,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 ) )
= $false )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5991]) ).
thf(6011,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5997]) ).
thf(6012,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5998]) ).
thf(6013,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5999]) ).
thf(6014,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6000]) ).
thf(6015,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6001]) ).
thf(6016,plain,
! [SV775: $i,SV482: $i] :
( ( ( ~ ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6002]) ).
thf(6017,plain,
! [SV741: $i,SV577: $i,SV829: $i,SV494: $i,SV836: $i,SV818: $i] :
( ( ( in @ ( ordered_pair @ SV818 @ SV836 ) @ SV494 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV836 @ SV829 ) @ SV577 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6004]) ).
thf(6018,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6005]) ).
thf(6019,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV819: $i,SV830: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6005]) ).
thf(6020,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ ( relation_dom @ SV469 ) )
= $true )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6009]) ).
thf(6021,plain,
! [SV469: $i,SV697: $i,SV722: $i,SV798: $i] :
( ( ( in @ ( sK55_E @ SV798 @ SV722 @ SV697 @ SV469 ) @ SV697 )
= $true )
| ( ( in @ SV798 @ SV722 )
= $false )
| ( ( SV722
= ( relation_image @ SV469 @ SV697 ) )
= $false )
| ( ( function @ SV469 )
= $false )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6010]) ).
thf(6022,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6023,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6012]) ).
thf(6024,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6013]) ).
thf(6025,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6014]) ).
thf(6026,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) )
| ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6015]) ).
thf(6027,plain,
! [SV775: $i,SV482: $i] :
( ( ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) )
| ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6016]) ).
thf(6028,plain,
! [SV741: $i,SV494: $i,SV818: $i,SV577: $i,SV829: $i,SV836: $i] :
( ( ( in @ ( ordered_pair @ SV836 @ SV829 ) @ SV577 )
= $false )
| ( ( in @ ( ordered_pair @ SV818 @ SV836 ) @ SV494 )
= $false )
| ( ( in @ ( ordered_pair @ SV818 @ SV829 ) @ SV741 )
= $true )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6029,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV830: $i,SV819: $i] :
( ( ( in @ ( ordered_pair @ SV819 @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) ) @ SV494 )
= $true )
| ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6018]) ).
thf(6030,plain,
! [SV494: $i,SV577: $i,SV741: $i,SV819: $i,SV830: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_F @ SV830 @ SV819 @ SV741 @ SV577 @ SV494 ) @ SV830 ) @ SV577 )
= $true )
| ( ( in @ ( ordered_pair @ SV819 @ SV830 ) @ SV741 )
= $false )
| ( ( SV741
= ( relation_composition @ SV494 @ SV577 ) )
= $false )
| ( ( relation @ SV741 )
= $false )
| ( ( relation @ SV577 )
= $false )
| ( ( relation @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6019]) ).
thf(6031,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6022]) ).
thf(6032,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6022]) ).
thf(6033,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6023]) ).
thf(6034,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6023]) ).
thf(6035,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6024]) ).
thf(6036,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6024]) ).
thf(6037,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6025]) ).
thf(6038,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6026]) ).
thf(6039,plain,
! [SV482: $i,SV775: $i] :
( ( ( ~ ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6026]) ).
thf(6040,plain,
! [SV775: $i,SV482: $i] :
( ( ( ~ ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6027]) ).
thf(6041,plain,
! [SV775: $i,SV482: $i] :
( ( ( ~ ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) )
= $false )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6027]) ).
thf(6042,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6031]) ).
thf(6043,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6032]) ).
thf(6044,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6033]) ).
thf(6045,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6034]) ).
thf(6046,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6035]) ).
thf(6047,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6036]) ).
thf(6048,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6049,plain,
! [SV482: $i,SV775: $i] :
( ( ( ! [SY7423: $i,SY7424: $i] :
( ( SY7424
!= ( apply @ SV775 @ SY7423 ) )
| ~ ( in @ SY7423 @ ( relation_rng @ SV482 ) )
| ( SY7423
= ( apply @ SV482 @ SY7424 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6038]) ).
thf(6050,plain,
! [SV482: $i,SV775: $i] :
( ( ( ! [SY7425: $i,SY7426: $i] :
( ( SY7426
!= ( apply @ SV775 @ SY7425 ) )
| ~ ( in @ SY7425 @ ( relation_rng @ SV482 ) )
| ( in @ SY7426 @ ( relation_dom @ SV482 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6039]) ).
thf(6051,plain,
! [SV775: $i,SV482: $i] :
( ( ( ! [SY7427: $i,SY7428: $i] :
( ( SY7427
!= ( apply @ SV482 @ SY7428 ) )
| ~ ( in @ SY7428 @ ( relation_dom @ SV482 ) )
| ( SY7428
= ( apply @ SV775 @ SY7427 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6040]) ).
thf(6052,plain,
! [SV775: $i,SV482: $i] :
( ( ( ! [SY7102: $i] :
( ! [SY7103: $i] :
( ( SY7102
!= ( apply @ SV482 @ SY7103 ) )
| ~ ( in @ SY7103 @ ( relation_dom @ SV482 ) ) )
| ( in @ SY7102 @ ( relation_rng @ SV482 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6041]) ).
thf(6053,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6042]) ).
thf(6054,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6043]) ).
thf(6055,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
| ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6044]) ).
thf(6056,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6045]) ).
thf(6057,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6046]) ).
thf(6058,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6047]) ).
thf(6059,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6048]) ).
thf(6060,plain,
! [SV482: $i,SV837: $i,SV775: $i] :
( ( ( ! [SY7450: $i] :
( ( SY7450
!= ( apply @ SV775 @ SV837 ) )
| ~ ( in @ SV837 @ ( relation_rng @ SV482 ) )
| ( SV837
= ( apply @ SV482 @ SY7450 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6049]) ).
thf(6061,plain,
! [SV482: $i,SV838: $i,SV775: $i] :
( ( ( ! [SY7451: $i] :
( ( SY7451
!= ( apply @ SV775 @ SV838 ) )
| ~ ( in @ SV838 @ ( relation_rng @ SV482 ) )
| ( in @ SY7451 @ ( relation_dom @ SV482 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6050]) ).
thf(6062,plain,
! [SV775: $i,SV482: $i,SV839: $i] :
( ( ( ! [SY7452: $i] :
( ( SV839
!= ( apply @ SV482 @ SY7452 ) )
| ~ ( in @ SY7452 @ ( relation_dom @ SV482 ) )
| ( SY7452
= ( apply @ SV775 @ SV839 ) ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6051]) ).
thf(6063,plain,
! [SV775: $i,SV482: $i,SV840: $i] :
( ( ( ! [SY7453: $i] :
( ( SV840
!= ( apply @ SV482 @ SY7453 ) )
| ~ ( in @ SY7453 @ ( relation_dom @ SV482 ) ) )
| ( in @ SV840 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6052]) ).
thf(6064,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6053]) ).
thf(6065,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6053]) ).
thf(6066,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6054]) ).
thf(6067,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6055]) ).
thf(6068,plain,
! [SV482: $i,SV745: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[6055]) ).
thf(6069,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6056]) ).
thf(6070,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6057]) ).
thf(6071,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK65_C @ SV745 @ SV482 )
!= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6058]) ).
thf(6072,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
!= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6059]) ).
thf(6073,plain,
! [SV482: $i,SV837: $i,SV775: $i,SV841: $i] :
( ( ( ( SV841
!= ( apply @ SV775 @ SV837 ) )
| ~ ( in @ SV837 @ ( relation_rng @ SV482 ) )
| ( SV837
= ( apply @ SV482 @ SV841 ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6074,plain,
! [SV482: $i,SV838: $i,SV775: $i,SV842: $i] :
( ( ( ( SV842
!= ( apply @ SV775 @ SV838 ) )
| ~ ( in @ SV838 @ ( relation_rng @ SV482 ) )
| ( in @ SV842 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6061]) ).
thf(6075,plain,
! [SV775: $i,SV843: $i,SV482: $i,SV839: $i] :
( ( ( ( SV839
!= ( apply @ SV482 @ SV843 ) )
| ~ ( in @ SV843 @ ( relation_dom @ SV482 ) )
| ( SV843
= ( apply @ SV775 @ SV839 ) ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6062]) ).
thf(6076,plain,
! [SV775: $i,SV482: $i,SV840: $i] :
( ( ( ! [SY7453: $i] :
( ( SV840
!= ( apply @ SV482 @ SY7453 ) )
| ~ ( in @ SY7453 @ ( relation_dom @ SV482 ) ) ) )
= $true )
| ( ( in @ SV840 @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6063]) ).
thf(6077,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6064]) ).
thf(6078,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6065]) ).
thf(6079,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(6080,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6067]) ).
thf(6081,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
| ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[6068]) ).
thf(6082,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(6083,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6084,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6071]) ).
thf(6085,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6072]) ).
thf(6086,plain,
! [SV482: $i,SV837: $i,SV775: $i,SV841: $i] :
( ( ( ( SV841
!= ( apply @ SV775 @ SV837 ) )
| ~ ( in @ SV837 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV482 @ SV841 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6073]) ).
thf(6087,plain,
! [SV482: $i,SV838: $i,SV775: $i,SV842: $i] :
( ( ( ( SV842
!= ( apply @ SV775 @ SV838 ) )
| ~ ( in @ SV838 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( in @ SV842 @ ( relation_dom @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6074]) ).
thf(6088,plain,
! [SV775: $i,SV843: $i,SV482: $i,SV839: $i] :
( ( ( ( SV839
!= ( apply @ SV482 @ SV843 ) )
| ~ ( in @ SV843 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( SV843
= ( apply @ SV775 @ SV839 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6089,plain,
! [SV775: $i,SV844: $i,SV482: $i,SV840: $i] :
( ( ( ( SV840
!= ( apply @ SV482 @ SV844 ) )
| ~ ( in @ SV844 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ SV840 @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6076]) ).
thf(6090,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6077]) ).
thf(6091,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6078]) ).
thf(6092,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6079]) ).
thf(6093,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6080]) ).
thf(6094,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6081]) ).
thf(6095,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6082]) ).
thf(6096,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6083]) ).
thf(6097,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6084]) ).
thf(6098,plain,
! [SV482: $i,SV745: $i] :
( ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( ( relation_dom @ SV745 )
!= ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(6099,plain,
! [SV482: $i,SV837: $i,SV775: $i,SV841: $i] :
( ( ( ( SV841
!= ( apply @ SV775 @ SV837 ) ) )
= $true )
| ( ( ~ ( in @ SV837 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV482 @ SV841 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6086]) ).
thf(6100,plain,
! [SV482: $i,SV838: $i,SV775: $i,SV842: $i] :
( ( ( ( SV842
!= ( apply @ SV775 @ SV838 ) ) )
= $true )
| ( ( ~ ( in @ SV838 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( in @ SV842 @ ( relation_dom @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6087]) ).
thf(6101,plain,
! [SV775: $i,SV843: $i,SV482: $i,SV839: $i] :
( ( ( ( SV839
!= ( apply @ SV482 @ SV843 ) ) )
= $true )
| ( ( ~ ( in @ SV843 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( SV843
= ( apply @ SV775 @ SV839 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6088]) ).
thf(6102,plain,
! [SV775: $i,SV844: $i,SV482: $i,SV840: $i] :
( ( ( ( SV840
!= ( apply @ SV482 @ SV844 ) ) )
= $true )
| ( ( ~ ( in @ SV844 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ SV840 @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6089]) ).
thf(6103,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(6104,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(6105,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6092]) ).
thf(6106,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(6107,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6094]) ).
thf(6108,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $true )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6095]) ).
thf(6109,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6096]) ).
thf(6110,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $true )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6097]) ).
thf(6111,plain,
! [SV482: $i,SV745: $i] :
( ( ( ( relation_dom @ SV745 )
= ( relation_rng @ SV482 ) )
= $false )
| ( ( in @ ( sK66_SY6462 @ SV745 @ SV482 ) @ ( relation_dom @ SV482 ) )
= $false )
| ( ( ( sK65_C @ SV745 @ SV482 )
= ( apply @ SV482 @ ( sK66_SY6462 @ SV745 @ SV482 ) ) )
= $false )
| ( ( ( sK66_SY6462 @ SV745 @ SV482 )
= ( apply @ SV745 @ ( sK65_C @ SV745 @ SV482 ) ) )
= $false )
| ( ( in @ ( sK65_C @ SV745 @ SV482 ) @ ( relation_rng @ SV482 ) )
= $false )
| ( ( SV745
= ( function_inverse @ SV482 ) )
= $true )
| ( ( function @ SV745 )
= $false )
| ( ( relation @ SV745 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6098]) ).
thf(6112,plain,
! [SV482: $i,SV837: $i,SV775: $i,SV841: $i] :
( ( ( SV841
= ( apply @ SV775 @ SV837 ) )
= $false )
| ( ( ~ ( in @ SV837 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV482 @ SV841 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(6113,plain,
! [SV482: $i,SV838: $i,SV775: $i,SV842: $i] :
( ( ( SV842
= ( apply @ SV775 @ SV838 ) )
= $false )
| ( ( ~ ( in @ SV838 @ ( relation_rng @ SV482 ) ) )
= $true )
| ( ( in @ SV842 @ ( relation_dom @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6100]) ).
thf(6114,plain,
! [SV775: $i,SV843: $i,SV482: $i,SV839: $i] :
( ( ( SV839
= ( apply @ SV482 @ SV843 ) )
= $false )
| ( ( ~ ( in @ SV843 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( SV843
= ( apply @ SV775 @ SV839 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6101]) ).
thf(6115,plain,
! [SV775: $i,SV844: $i,SV482: $i,SV840: $i] :
( ( ( SV840
= ( apply @ SV482 @ SV844 ) )
= $false )
| ( ( ~ ( in @ SV844 @ ( relation_dom @ SV482 ) ) )
= $true )
| ( ( in @ SV840 @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6102]) ).
thf(6116,plain,
! [SV775: $i,SV841: $i,SV482: $i,SV837: $i] :
( ( ( in @ SV837 @ ( relation_rng @ SV482 ) )
= $false )
| ( ( SV841
= ( apply @ SV775 @ SV837 ) )
= $false )
| ( ( SV837
= ( apply @ SV482 @ SV841 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6112]) ).
thf(6117,plain,
! [SV775: $i,SV842: $i,SV482: $i,SV838: $i] :
( ( ( in @ SV838 @ ( relation_rng @ SV482 ) )
= $false )
| ( ( SV842
= ( apply @ SV775 @ SV838 ) )
= $false )
| ( ( in @ SV842 @ ( relation_dom @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6118,plain,
! [SV775: $i,SV839: $i,SV482: $i,SV843: $i] :
( ( ( in @ SV843 @ ( relation_dom @ SV482 ) )
= $false )
| ( ( SV839
= ( apply @ SV482 @ SV843 ) )
= $false )
| ( ( SV843
= ( apply @ SV775 @ SV839 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6114]) ).
thf(6119,plain,
! [SV775: $i,SV840: $i,SV482: $i,SV844: $i] :
( ( ( in @ SV844 @ ( relation_dom @ SV482 ) )
= $false )
| ( ( SV840
= ( apply @ SV482 @ SV844 ) )
= $false )
| ( ( in @ SV840 @ ( relation_rng @ SV482 ) )
= $true )
| ( ( SV775
= ( function_inverse @ SV482 ) )
= $false )
| ( ( function @ SV775 )
= $false )
| ( ( relation @ SV775 )
= $false )
| ( ( one_to_one @ SV482 )
= $false )
| ( ( function @ SV482 )
= $false )
| ( ( relation @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6115]) ).
thf(6120,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[3454,6119,6118,6117,6116,6111,6110,6109,6108,6107,6106,6105,6104,6103,6030,6029,6028,6021,6020,6008,6007,6006,6003,5996,5995,5994,5993,5992,5989,5988,5982,5981,5975,5972,5970,5969,5968,5967,5966,5965,5962,5961,5957,5956,5953,5952,5950,5949,5948,5947,5946,5943,5933,5932,5929,5924,5916,5914,5913,5912,5909,5908,5899,5896,5895,5886,5882,5881,5880,5879,5876,5867,5859,5858,5857,5853,5852,5851,5850,5845,5844,5843,5834,5831,5830,5825,5824,5820,5819,5814,5813,5811,5810,5801,5795,5794,5790,5782,5781,5774,5771,5770,5758,5757,5755,5727,5725,5717,5704,5698,5695,5694,5687,5686,5685,5679,5676,5659,5658,5657,5656,5650,5644,5638,5637,5635,5629,5608,5607,5603,5596,5586,5585,5584,5580,5579,5567,5566,5564,5559,5555,5554,5551,5550,5549,5548,5537,5535,5528,5527,5520,5518,5514,5495,5484,5473,5472,5470,5461,5451,5450,5439,5431,5430,5429,5423,5405,5402,5381,5366,5354,5349,5329,5328,5315,5311,5310,5309,5308,5302,5288,5287,5283,5282,5281,5280,5279,5278,5277,5245,5244,5198,5193,5182,5181,5178,5161,5153,5145,5139,5135,5130,5121,5104,5076,5068,5067,5064,5063,5056,5052,5016,5000,4987,4986,4960,4959,4941,4917,4916,4897,4894,4893,4861,4860,4837,4836,4816,4768,4754,4753,4752,4744,4743,4740,4739,4734,4733,4727,4726,4699,4698,4690,4689,4666,4665,4656,4655,4626,4625,4616,4604,4603,4600,4599,4596,4595,4467,4464,4459,4456,4455,4443,4442,4425,4424,4415,4414,4404,4403,4399,4368,4367,4348,4337,4336,4333,4332,4317,4316,4315,4314,4307,4306,4301,4299,4298,4163,4162,4141,4138,4137,4095,4094,4021,4020,4017,4016,4015,4014,4010,4001,3997,3995,3993,3992,3991,3990,3961,3951,3942,3939,3938,3936,3935,3934,3933,3929,3913,3912,3888,3887,3886,3877,3860,3851,3849,3848,3833,3827,3568]) ).
thf(6121,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6120,3333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU244+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:54:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46 ........
% 0.20/0.58
% 0.20/0.58 No.of.Axioms: 298
% 0.20/0.58
% 0.20/0.58 Length.of.Defs: 0
% 0.20/0.58
% 0.20/0.58 Contains.Choice.Funs: false
% 0.48/0.66 ...................
% 0.61/0.77 (rf:2,axioms:212,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:300,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.16/75.35 ......................ignored arguments false
% 75.39/75.56 .........
% 75.48/75.70 (rf:0,axioms:298,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:300,loop_count:0,foatp_calls:0,translation:fof_full)...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.46/150.77 ...................................
% 150.69/150.99 (rf:2,axioms:212,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:300,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 225.52/225.86 ...........................
% 225.79/226.10 (rf:-1,axioms:120,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:300,loop_count:0,foatp_calls:0,translation:fof_full)................................................................................................................................................................................................................................................................................................................................................................................................................
% 232.38/232.69
% 232.38/232.69 ********************************
% 232.38/232.69 * All subproblems solved! *
% 232.38/232.69 ********************************
% 232.38/232.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:-1,axioms:121,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:68,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6120,loop_count:0,foatp_calls:1,translation:fof_full)
% 247.06/247.38
% 247.06/247.38 %**** Beginning of derivation protocol ****
% 247.06/247.38 % SZS output start CNFRefutation
% See solution above
% 247.09/247.42
% 247.09/247.42 %**** End of derivation protocol ****
% 247.09/247.42 %**** no. of clauses in derivation: 5943 ****
% 247.09/247.42 %**** clause counter: 6120 ****
% 247.09/247.42
% 247.09/247.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:-1,axioms:121,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:68,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6120,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------