TSTP Solution File: SEU261+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU261+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:13 EDT 2022
% Result : Theorem 227.38s 228.05s
% Output : CNFRefutation 232.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 288
% Syntax : Number of formulae : 3860 (1261 unt; 144 typ; 0 def)
% Number of atoms : 43273 (13905 equ; 0 cnn)
% Maximal formula atoms : 15 ( 11 avg)
% Number of connectives : 97135 (16803 ~;17601 |; 826 &;61349 @)
% ( 132 <=>; 424 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 259 ( 259 >; 0 *; 0 +; 0 <<)
% Number of symbols : 147 ( 144 usr; 14 con; 0-5 aty)
% Number of variables : 11281 ( 0 ^11247 !; 34 ?;11281 :)
% 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_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_SY4405,type,
sK13_SY4405: $i > $i > $i ).
thf(tp_sK14_SY4407,type,
sK14_SY4407: $i > $i > $i ).
thf(tp_sK15_F,type,
sK15_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_SY4408,type,
sK17_SY4408: $i > $i > $i > $i ).
thf(tp_sK18_SY4412,type,
sK18_SY4412: $i > $i > $i > $i ).
thf(tp_sK19_B,type,
sK19_B: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY4413,type,
sK20_SY4413: $i > $i ).
thf(tp_sK21_D,type,
sK21_D: $i > $i > $i > $i ).
thf(tp_sK22_SY4414,type,
sK22_SY4414: $i > $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_SY4415,type,
sK24_SY4415: $i > $i > $i ).
thf(tp_sK25_C,type,
sK25_C: $i > $i > $i ).
thf(tp_sK26_SY4416,type,
sK26_SY4416: $i > $i > $i ).
thf(tp_sK27_D,type,
sK27_D: $i > $i > $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_SY4418,type,
sK29_SY4418: $i > $i > $i ).
thf(tp_sK2_SY4402,type,
sK2_SY4402: $i ).
thf(tp_sK30_D,type,
sK30_D: $i > $i > $i > $i ).
thf(tp_sK31_C,type,
sK31_C: $i > $i > $i ).
thf(tp_sK32_SY4420,type,
sK32_SY4420: $i > $i > $i ).
thf(tp_sK33_C,type,
sK33_C: $i > $i > $i ).
thf(tp_sK34_SY4421,type,
sK34_SY4421: $i > $i > $i ).
thf(tp_sK35_D,type,
sK35_D: $i > $i > $i > $i ).
thf(tp_sK36_C,type,
sK36_C: $i > $i > $i ).
thf(tp_sK37_SY4423,type,
sK37_SY4423: $i > $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_C,type,
sK39_C: $i > $i > $i ).
thf(tp_sK3_SY4404,type,
sK3_SY4404: $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY4425,type,
sK41_SY4425: $i > $i > $i ).
thf(tp_sK42_C,type,
sK42_C: $i > $i > $i ).
thf(tp_sK43_B,type,
sK43_B: $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_SY4427,type,
sK45_SY4427: $i > $i > $i ).
thf(tp_sK46_D,type,
sK46_D: $i > $i > $i > $i ).
thf(tp_sK47_C,type,
sK47_C: $i > $i > $i ).
thf(tp_sK48_C,type,
sK48_C: $i > $i > $i ).
thf(tp_sK49_SY4428,type,
sK49_SY4428: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK50_B,type,
sK50_B: $i > $i ).
thf(tp_sK51_E,type,
sK51_E: $i > $i > $i > $i > $i ).
thf(tp_sK52_D,type,
sK52_D: $i > $i > $i > $i ).
thf(tp_sK53_SY4432,type,
sK53_SY4432: $i > $i > $i > $i ).
thf(tp_sK54_E,type,
sK54_E: $i > $i > $i > $i > $i ).
thf(tp_sK55_D,type,
sK55_D: $i > $i > $i > $i ).
thf(tp_sK56_SY4434,type,
sK56_SY4434: $i > $i > $i > $i ).
thf(tp_sK57_D,type,
sK57_D: $i > $i > $i > $i ).
thf(tp_sK58_D,type,
sK58_D: $i > $i > $i > $i ).
thf(tp_sK59_SY4435,type,
sK59_SY4435: $i > $i > $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK60_E,type,
sK60_E: $i > $i > $i > $i > $i ).
thf(tp_sK61_D,type,
sK61_D: $i > $i > $i > $i ).
thf(tp_sK62_SY4437,type,
sK62_SY4437: $i > $i > $i > $i ).
thf(tp_sK63_D,type,
sK63_D: $i > $i > $i > $i ).
thf(tp_sK64_SY4438,type,
sK64_SY4438: $i > $i > $i > $i ).
thf(tp_sK65_C,type,
sK65_C: $i > $i > $i ).
thf(tp_sK66_SY4439,type,
sK66_SY4439: $i > $i > $i ).
thf(tp_sK67_D,type,
sK67_D: $i > $i > $i > $i ).
thf(tp_sK68_B,type,
sK68_B: $i > $i ).
thf(tp_sK69_SY4440,type,
sK69_SY4440: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK70_C,type,
sK70_C: $i > $i > $i ).
thf(tp_sK71_SY4441,type,
sK71_SY4441: $i > $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK73_D,type,
sK73_D: $i > $i > $i > $i ).
thf(tp_sK74_D,type,
sK74_D: $i > $i > $i > $i ).
thf(tp_sK75_B,type,
sK75_B: $i > $i ).
thf(tp_sK76_SY4442,type,
sK76_SY4442: $i > $i ).
thf(tp_sK77_B,type,
sK77_B: $i > $i ).
thf(tp_sK78_SY4443,type,
sK78_SY4443: $i > $i ).
thf(tp_sK79_B,type,
sK79_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK80_SY4444,type,
sK80_SY4444: $i > $i ).
thf(tp_sK81_SY4446,type,
sK81_SY4446: $i > $i ).
thf(tp_sK82_B,type,
sK82_B: $i > $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/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(24,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(26,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(29,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(34,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(36,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(39,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(44,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(46,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(50,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(57,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(62,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(70,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(71,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(81,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(86,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(97,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(108,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
thf(109,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
thf(112,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
thf(113,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(116,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
<=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
<=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
thf(117,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(118,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
thf(119,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_connected_in @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
thf(120,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
thf(122,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/sandbox2/benchmark/theBenchmark.p',d5_wellord1) ).
thf(125,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(128,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_ordering @ A )
<=> ( ( reflexive @ A )
& ( transitive @ A )
& ( antisymmetric @ A )
& ( connected @ A )
& ( well_founded_relation @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
thf(131,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_antisymmetric_in @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
thf(132,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(134,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',d3_wellord1) ).
thf(138,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',d2_wellord1) ).
thf(145,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(149,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( fiber @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
thf(152,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_reflexive_in @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
thf(153,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(156,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_relat_2) ).
thf(157,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
thf(158,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(159,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(161,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(163,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/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
thf(164,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(173,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(174,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(176,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
thf(187,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_wellord1) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',t72_funct_1) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
thf(201,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
thf(202,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
thf(204,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).
thf(207,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord1) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
thf(209,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
thf(213,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( ( ( reflexive @ A )
=> ( reflexive @ B ) )
& ( ( transitive @ A )
=> ( transitive @ B ) )
& ( ( connected @ A )
=> ( connected @ B ) )
& ( ( antisymmetric @ A )
=> ( antisymmetric @ B ) )
& ( ( well_founded_relation @ A )
=> ( well_founded_relation @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t53_wellord1) ).
thf(216,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_wellord1) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
thf(225,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(226,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_wellord1) ).
thf(240,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
thf(247,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_wellord1) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_wellord1) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_wellord1) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(257,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
thf(261,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_wellord1) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
thf(265,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_wellord1) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(278,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/sandbox2/benchmark/theBenchmark.p',t174_relat_1) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(282,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t160_relat_1) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(284,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
thf(285,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/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
thf(288,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(294,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',l82_funct_1) ).
thf(308,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
thf(310,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
thf(314,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
thf(315,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
thf(320,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
thf(321,conjecture,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( well_ordering @ A )
& ( relation_isomorphism @ A @ B @ C ) )
=> ( well_ordering @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_wellord1) ).
thf(322,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( well_ordering @ A )
& ( relation_isomorphism @ A @ B @ C ) )
=> ( well_ordering @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[321]) ).
thf(323,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( well_ordering @ A )
& ( relation_isomorphism @ A @ B @ C ) )
=> ( well_ordering @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[322]) ).
thf(324,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(325,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(326,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(327,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(328,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(329,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(330,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(331,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(333,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(334,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(335,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(336,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(337,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(339,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(340,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)],[52]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(342,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)],[57]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(344,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)],[61]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(347,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)],[68]) ).
thf(348,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)],[69]) ).
thf(349,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(350,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(351,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)],[72]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(354,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(356,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(358,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ( is_reflexive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(361,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)],[112]) ).
thf(362,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)],[113]) ).
thf(363,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)],[114]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
<=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
<=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(365,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)],[117]) ).
thf(366,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(367,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)],[119]) ).
thf(368,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(369,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)],[122]) ).
thf(370,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)],[125]) ).
thf(371,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)],[126]) ).
thf(372,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)],[128]) ).
thf(373,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)],[131]) ).
thf(374,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)],[132]) ).
thf(375,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)],[134]) ).
thf(376,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)],[136]) ).
thf(377,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)],[138]) ).
thf(378,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)],[142]) ).
thf(379,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)],[145]) ).
thf(380,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( fiber @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(381,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)],[152]) ).
thf(382,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)],[153]) ).
thf(383,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ( is_transitive_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(384,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ( is_connected_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(385,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)],[158]) ).
thf(386,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)],[159]) ).
thf(387,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)],[160]) ).
thf(388,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ( is_antisymmetric_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(389,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)],[162]) ).
thf(390,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)],[163]) ).
thf(391,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)],[164]) ).
thf(392,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)],[166]) ).
thf(393,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(394,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(395,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(398,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)],[184]) ).
thf(399,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_orders @ A @ ( relation_field @ A ) )
<=> ( well_ordering @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(400,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)],[188]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(402,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)],[190]) ).
thf(403,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)],[193]) ).
thf(404,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)],[194]) ).
thf(405,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)],[196]) ).
thf(406,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)],[199]) ).
thf(407,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(408,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(409,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(410,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( well_founded_relation @ A )
<=> ( is_well_founded_in @ A @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(411,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)],[208]) ).
thf(412,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(413,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)],[210]) ).
thf(414,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)],[212]) ).
thf(415,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( ( ( reflexive @ A )
=> ( reflexive @ B ) )
& ( ( transitive @ A )
=> ( transitive @ B ) )
& ( ( connected @ A )
=> ( connected @ B ) )
& ( ( antisymmetric @ A )
=> ( antisymmetric @ B ) )
& ( ( well_founded_relation @ A )
=> ( well_founded_relation @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(416,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
=> ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(417,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)],[220]) ).
thf(418,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)],[223]) ).
thf(419,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)],[225]) ).
thf(420,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)],[226]) ).
thf(421,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( well_ordering @ B )
& ( subset @ A @ ( relation_field @ B ) ) )
=> ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(422,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)],[240]) ).
thf(423,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)],[243]) ).
thf(424,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_ordering @ B )
=> ( well_ordering @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(425,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( well_founded_relation @ B )
=> ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(426,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)],[251]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( antisymmetric @ B )
=> ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(428,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)],[256]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( transitive @ B )
=> ( transitive @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( connected @ B )
=> ( connected @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(431,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)],[261]) ).
thf(432,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( reflexive @ B )
=> ( reflexive @ ( relation_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(433,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)],[263]) ).
thf(434,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(435,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(436,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)],[267]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) )
& ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(438,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)],[269]) ).
thf(439,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(442,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)],[277]) ).
thf(443,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)],[278]) ).
thf(444,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(446,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)],[281]) ).
thf(447,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)],[282]) ).
thf(448,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)],[283]) ).
thf(449,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(450,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)],[285]) ).
thf(451,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)],[286]) ).
thf(452,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)],[287]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(454,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)],[289]) ).
thf(455,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)],[290]) ).
thf(456,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)],[294]) ).
thf(457,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(458,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(459,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(460,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)],[299]) ).
thf(461,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)],[303]) ).
thf(462,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)],[308]) ).
thf(463,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)],[310]) ).
thf(464,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)],[314]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(466,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)],[320]) ).
thf(467,plain,
( ( ( relation @ sK1_A )
=> ! [SY4402: $i] :
( ( relation @ SY4402 )
=> ! [SY4403: $i] :
( ( ( relation @ SY4403 )
& ( function @ SY4403 ) )
=> ( ( ( well_ordering @ sK1_A )
& ( relation_isomorphism @ sK1_A @ SY4402 @ SY4403 ) )
=> ( well_ordering @ SY4402 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[323]) ).
thf(468,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[467]) ).
thf(469,plain,
( ( ! [SY4402: $i] :
( ( relation @ SY4402 )
=> ! [SY4403: $i] :
( ( ( relation @ SY4403 )
& ( function @ SY4403 ) )
=> ( ( ( well_ordering @ sK1_A )
& ( relation_isomorphism @ sK1_A @ SY4402 @ SY4403 ) )
=> ( well_ordering @ SY4402 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[467]) ).
thf(470,plain,
( ( ~ ! [SY4402: $i] :
( ( relation @ SY4402 )
=> ! [SY4403: $i] :
( ( ( relation @ SY4403 )
& ( function @ SY4403 ) )
=> ( ( ( well_ordering @ sK1_A )
& ( relation_isomorphism @ sK1_A @ SY4402 @ SY4403 ) )
=> ( well_ordering @ SY4402 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[469]) ).
thf(471,plain,
( ( ( relation @ sK2_SY4402 )
& ( function @ sK3_SY4404 )
& ( relation @ sK3_SY4404 )
& ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
& ( well_ordering @ sK1_A )
& ~ ( well_ordering @ sK2_SY4402 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[470]) ).
thf(472,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A )
& ( function @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(473,plain,
( ( ( relation @ sK5_A )
& ( relation_empty_yielding @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(474,plain,
( ( ( function @ sK6_A )
& ( relation @ sK6_A )
& ( one_to_one @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(475,plain,
( ( ~ ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(476,plain,
( ( ( function @ sK8_A )
& ( relation @ sK8_A )
& ( one_to_one @ sK8_A )
& ( empty @ sK8_A )
& ( epsilon_transitive @ sK8_A )
& ( epsilon_connected @ sK8_A )
& ( ordinal @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(477,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A )
& ( function @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[329]) ).
thf(478,plain,
( ( ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(479,plain,
( ( ( function @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(480,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(481,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)],[333]) ).
thf(482,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(483,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(484,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(485,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(486,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( function @ ( relation_rng_restriction @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(487,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)],[340]) ).
thf(488,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(489,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)],[342]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(491,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[345]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(493,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)],[347]) ).
thf(494,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)],[348]) ).
thf(495,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[350]) ).
thf(496,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)],[351]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(498,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(500,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(501,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(502,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)],[358]) ).
thf(503,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)],[359]) ).
thf(504,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(505,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK12_C @ B @ A ) @ B )
& ( in @ ( sK13_SY4405 @ B @ A ) @ B )
& ( in @ ( sK14_SY4407 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY4405 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_SY4405 @ B @ A ) @ ( sK14_SY4407 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK14_SY4407 @ 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)],[361]) ).
thf(506,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY4411: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ SY4411 ) @ A )
| ~ ( in @ ( ordered_pair @ SY4411 @ ( sK17_SY4408 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK17_SY4408 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK18_SY4412 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK18_SY4412 @ C @ B @ A ) @ ( sK17_SY4408 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK17_SY4408 @ 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 @ ( sK15_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK15_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(507,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK19_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK20_SY4413 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK19_B @ A ) )
= ( apply @ A @ ( sK20_SY4413 @ A ) ) )
& ( ( sK19_B @ A )
!= ( sK20_SY4413 @ 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)],[363]) ).
thf(508,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( sK22_SY4414 @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ ( sK21_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK22_SY4414 @ C @ B @ A ) ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK22_SY4414 @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( apply @ C @ ( sK21_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK22_SY4414 @ C @ B @ A ) ) ) @ B )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) ) )
| ( ( relation_dom @ C )
!= ( relation_field @ A ) )
| ( ( relation_rng @ C )
!= ( relation_field @ B ) )
| ~ ( one_to_one @ C )
| ( relation_isomorphism @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ ( relation_field @ A ) )
| ~ ( in @ E @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ A ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ D @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ E @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_dom @ C )
= ( relation_field @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_rng @ C )
= ( relation_field @ B ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( one_to_one @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(509,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY4415 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ B @ A ) @ ( sK23_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY4415 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ B @ A ) @ ( sK23_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)],[365]) ).
thf(510,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(511,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK25_C @ B @ A )
!= ( sK26_SY4416 @ B @ A ) )
& ( in @ ( sK25_C @ B @ A ) @ B )
& ( in @ ( sK26_SY4416 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK25_C @ B @ A ) @ ( sK26_SY4416 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ B @ A ) @ ( sK25_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)],[367]) ).
thf(512,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(513,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)],[369]) ).
thf(514,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4417: $i] :
~ ( in @ ( ordered_pair @ SY4417 @ ( sK28_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK28_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ B @ A ) @ ( sK28_C @ B @ A ) ) @ A )
| ( in @ ( sK28_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 @ ( sK27_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(515,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4419: $i] :
( ( ( sK31_C @ B @ A )
!= ( apply @ A @ SY4419 ) )
| ~ ( in @ SY4419 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK31_C @ B @ A ) @ B ) )
& ( ( ( ( sK31_C @ B @ A )
= ( apply @ A @ ( sK32_SY4420 @ B @ A ) ) )
& ( in @ ( sK32_SY4420 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK31_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 @ ( sK30_D @ C @ B @ A ) ) )
& ( in @ ( sK30_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(516,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)],[372]) ).
thf(517,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK33_C @ B @ A ) @ B )
& ( in @ ( sK34_SY4421 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK33_C @ B @ A ) @ ( sK34_SY4421 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK34_SY4421 @ B @ A ) @ ( sK33_C @ B @ A ) ) @ A )
& ( ( sK33_C @ B @ A )
!= ( sK34_SY4421 @ 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)],[373]) ).
thf(518,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4422: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ SY4422 ) @ A )
| ~ ( in @ ( sK36_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY4423 @ B @ A ) ) @ A )
| ( in @ ( sK36_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 @ ( sK35_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(519,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)],[375]) ).
thf(520,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY4424: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY4424 ) @ ( sK39_C @ B @ A ) )
| ~ ( in @ SY4424 @ ( sK39_C @ B @ A ) ) )
& ( ( sK39_C @ B @ A )
!= empty_set )
& ( subset @ ( sK39_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK38_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(521,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY4425 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY4425 @ 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)],[377]) ).
thf(522,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY4426: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY4426 ) @ ( sK43_B @ A ) )
| ~ ( in @ SY4426 @ ( sK43_B @ A ) ) )
& ( ( sK43_B @ A )
!= empty_set )
& ( subset @ ( sK43_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK42_C @ B @ A ) ) @ B )
& ( in @ ( sK42_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(523,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ 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)],[379]) ).
thf(524,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ( ( sK46_D @ C @ B @ A )
= B )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ C @ B @ A ) @ B ) @ A )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( ( sK46_D @ C @ B @ A )
!= B )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK46_D @ C @ B @ A ) @ B ) @ A )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( fiber @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( fiber @ A @ B ) )
| ( ! [D: $i] :
( ( D = B )
| ~ ( in @ ( ordered_pair @ D @ B ) @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( D != B ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(525,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK47_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK47_C @ B @ A ) @ ( sK47_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)],[381]) ).
thf(526,plain,
( ( ! [A: $i] :
( ( ! [SY4429: $i,SY4430: $i] :
( ( sK50_B @ A )
!= ( ordered_pair @ SY4429 @ SY4430 ) )
& ( in @ ( sK50_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK48_C @ B @ A ) @ ( sK49_SY4428 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(527,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)],[383]) ).
thf(528,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)],[384]) ).
thf(529,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4431: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ SY4431 ) @ A )
| ~ ( in @ SY4431 @ B ) )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ ( sK53_SY4432 @ C @ B @ A ) ) @ A )
& ( in @ ( sK53_SY4432 @ 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] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK51_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(530,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4433: $i] :
( ~ ( in @ ( ordered_pair @ SY4433 @ ( sK55_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY4433 @ B ) )
| ~ ( in @ ( sK55_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_SY4434 @ C @ B @ A ) @ ( sK55_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK56_SY4434 @ C @ B @ A ) @ B ) )
| ( in @ ( sK55_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 @ ( sK54_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK54_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[386]) ).
thf(531,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK57_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)],[387]) ).
thf(532,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)],[388]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK59_SY4435 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK59_SY4435 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ 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)],[389]) ).
thf(534,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4436: $i] :
( ~ ( in @ SY4436 @ ( relation_dom @ A ) )
| ~ ( in @ SY4436 @ B )
| ( ( sK61_D @ C @ B @ A )
!= ( apply @ A @ SY4436 ) ) )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK62_SY4437 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_SY4437 @ C @ B @ A ) @ B )
& ( ( sK61_D @ C @ B @ A )
= ( apply @ A @ ( sK62_SY4437 @ C @ B @ A ) ) ) )
| ( in @ ( sK61_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 @ ( sK60_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK60_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK60_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(535,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ 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)],[391]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK65_C @ B @ A )
!= ( sK66_SY4439 @ B @ A ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ B @ A ) ) @ B ) )
& ( ( ( sK65_C @ B @ A )
= ( sK66_SY4439 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK65_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ 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)],[392]) ).
thf(537,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)],[393]) ).
thf(538,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[394]) ).
thf(539,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[396]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(542,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)],[398]) ).
thf(543,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_orders @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_orders @ A @ ( relation_field @ A ) )
| ( well_ordering @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(544,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)],[400]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(546,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)],[402]) ).
thf(547,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)],[403]) ).
thf(548,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)],[404]) ).
thf(549,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)],[405]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK67_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK67_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK67_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)],[406]) ).
thf(551,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)],[407]) ).
thf(552,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)],[408]) ).
thf(553,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(554,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)],[410]) ).
thf(555,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)],[411]) ).
thf(556,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK68_B @ A ) @ ( sK69_SY4440 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[412]) ).
thf(557,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)],[413]) ).
thf(558,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_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)],[414]) ).
thf(559,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( reflexive @ A )
| ( reflexive @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( transitive @ A )
| ( transitive @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( connected @ A )
| ( connected @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( antisymmetric @ A )
| ( antisymmetric @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( well_founded_relation @ A )
| ( well_founded_relation @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[415]) ).
thf(560,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[416]) ).
thf(561,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)],[417]) ).
thf(562,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)],[418]) ).
thf(563,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)],[419]) ).
thf(564,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)],[420]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[421]) ).
thf(566,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)],[422]) ).
thf(567,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK72_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK72_C @ B @ A ) )
!= ( sK72_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)],[423]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_ordering @ B )
| ( well_ordering @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[424]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_founded_relation @ B )
| ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(570,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)],[426]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( antisymmetric @ B )
| ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(572,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)],[428]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( transitive @ B )
| ( transitive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(574,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( connected @ B )
| ( connected @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[430]) ).
thf(575,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)],[431]) ).
thf(576,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( reflexive @ B )
| ( reflexive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[432]) ).
thf(577,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)],[433]) ).
thf(578,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[434]) ).
thf(579,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[435]) ).
thf(580,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)],[436]) ).
thf(581,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[437]) ).
thf(582,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)],[438]) ).
thf(583,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[439]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[440]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[441]) ).
thf(586,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)],[442]) ).
thf(587,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)],[443]) ).
thf(588,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[444]) ).
thf(589,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[445]) ).
thf(590,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 @ ( sK73_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK73_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK73_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[446]) ).
thf(591,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)],[447]) ).
thf(592,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)],[448]) ).
thf(593,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[449]) ).
thf(594,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)],[450]) ).
thf(595,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)],[451]) ).
thf(596,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)],[452]) ).
thf(597,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[453]) ).
thf(598,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 @ ( sK74_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK74_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK74_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[454]) ).
thf(599,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)],[455]) ).
thf(600,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)],[456]) ).
thf(601,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[457]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[458]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[459]) ).
thf(604,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)],[460]) ).
thf(605,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)],[461]) ).
thf(606,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK75_B @ A )
!= ( sK76_SY4442 @ A ) )
& ( in @ ( sK75_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK76_SY4442 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK75_B @ A ) @ ( sK76_SY4442 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ A ) @ ( sK75_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)],[462]) ).
thf(607,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK77_B @ A ) @ ( sK78_SY4443 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK78_SY4443 @ A ) @ ( sK77_B @ A ) ) @ A )
& ( ( sK77_B @ A )
!= ( sK78_SY4443 @ 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)],[463]) ).
thf(608,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK79_B @ A ) @ ( sK80_SY4444 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK80_SY4444 @ A ) @ ( sK81_SY4446 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK79_B @ A ) @ ( sK81_SY4446 @ 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)],[464]) ).
thf(609,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[465]) ).
thf(610,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK82_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK82_B @ A ) @ ( sK82_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)],[466]) ).
thf(611,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK82_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK82_B @ A ) @ ( sK82_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)],[610]) ).
thf(612,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(613,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK79_B @ A ) @ ( sK80_SY4444 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK80_SY4444 @ A ) @ ( sK81_SY4446 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK79_B @ A ) @ ( sK81_SY4446 @ 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)],[608]) ).
thf(614,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK77_B @ A ) @ ( sK78_SY4443 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK78_SY4443 @ A ) @ ( sK77_B @ A ) ) @ A )
& ( ( sK77_B @ A )
!= ( sK78_SY4443 @ 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)],[607]) ).
thf(615,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK75_B @ A )
!= ( sK76_SY4442 @ A ) )
& ( in @ ( sK75_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK76_SY4442 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK75_B @ A ) @ ( sK76_SY4442 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ A ) @ ( sK75_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)],[606]) ).
thf(616,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)],[605]) ).
thf(617,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)],[604]) ).
thf(618,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(619,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(620,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(621,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)],[600]) ).
thf(622,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)],[599]) ).
thf(623,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 @ ( sK74_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK74_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK74_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(625,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(626,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)],[595]) ).
thf(627,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)],[594]) ).
thf(628,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(629,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)],[592]) ).
thf(630,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)],[591]) ).
thf(631,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 @ ( sK73_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK73_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK73_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(632,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(633,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(634,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)],[587]) ).
thf(635,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)],[586]) ).
thf(636,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(637,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(638,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_field @ ( relation_restriction @ C @ B ) ) )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(639,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)],[582]) ).
thf(640,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ ( relation_field @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_field @ ( relation_restriction @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(641,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)],[580]) ).
thf(642,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(643,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ( subset @ ( fiber @ ( relation_restriction @ C @ A ) @ B ) @ ( fiber @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(644,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)],[577]) ).
thf(645,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( reflexive @ B )
| ( reflexive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(646,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)],[575]) ).
thf(647,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( connected @ B )
| ( connected @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( transitive @ B )
| ( transitive @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(649,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)],[572]) ).
thf(650,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( antisymmetric @ B )
| ( antisymmetric @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(651,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)],[570]) ).
thf(652,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_founded_relation @ B )
| ( well_founded_relation @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(653,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( well_ordering @ B )
| ( well_ordering @ ( relation_restriction @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(654,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK72_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK72_C @ B @ A ) )
!= ( sK72_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)],[567]) ).
thf(655,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)],[566]) ).
thf(656,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ ( relation_field @ B ) )
| ~ ( well_ordering @ B )
| ( ( relation_field @ ( relation_restriction @ B @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(657,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(658,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(659,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)],[562]) ).
thf(660,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)],[561]) ).
thf(661,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( relation_isomorphism @ B @ A @ ( function_inverse @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(662,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( reflexive @ A )
| ( reflexive @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( transitive @ A )
| ( transitive @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( connected @ A )
| ( connected @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( antisymmetric @ A )
| ( antisymmetric @ B ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ~ ( well_founded_relation @ A )
| ( well_founded_relation @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(663,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK71_SY4441 @ B @ A )
= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK70_C @ B @ A )
= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK70_C @ B @ A )
!= ( apply @ A @ ( sK71_SY4441 @ B @ A ) ) )
| ~ ( in @ ( sK71_SY4441 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK71_SY4441 @ B @ A )
!= ( apply @ B @ ( sK70_C @ B @ A ) ) )
| ~ ( in @ ( sK70_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)],[558]) ).
thf(664,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)],[557]) ).
thf(665,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK68_B @ A ) @ ( sK69_SY4440 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(666,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)],[555]) ).
thf(667,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)],[554]) ).
thf(668,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(669,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)],[552]) ).
thf(670,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)],[551]) ).
thf(671,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK67_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK67_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK67_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)],[550]) ).
thf(672,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)],[549]) ).
thf(673,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)],[548]) ).
thf(674,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)],[547]) ).
thf(675,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)],[546]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(677,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)],[544]) ).
thf(678,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_ordering @ A )
| ( well_orders @ A @ ( relation_field @ A ) ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_orders @ A @ ( relation_field @ A ) )
| ( well_ordering @ A ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(679,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)],[542]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(682,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(683,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(684,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)],[537]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK65_C @ B @ A )
!= ( sK66_SY4439 @ B @ A ) )
| ~ ( in @ ( sK65_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ B @ A ) ) @ B ) )
& ( ( ( sK65_C @ B @ A )
= ( sK66_SY4439 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK65_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK65_C @ B @ A ) @ ( sK66_SY4439 @ 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)],[536]) ).
thf(686,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK63_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK63_D @ C @ B @ A ) @ ( sK64_SY4438 @ 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)],[535]) ).
thf(687,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4436: $i] :
( ~ ( in @ SY4436 @ ( relation_dom @ A ) )
| ~ ( in @ SY4436 @ B )
| ( ( sK61_D @ C @ B @ A )
!= ( apply @ A @ SY4436 ) ) )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK62_SY4437 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_SY4437 @ C @ B @ A ) @ B )
& ( ( sK61_D @ C @ B @ A )
= ( apply @ A @ ( sK62_SY4437 @ C @ B @ A ) ) ) )
| ( in @ ( sK61_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 @ ( sK60_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK60_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK60_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(688,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK59_SY4435 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK59_SY4435 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK58_D @ C @ B @ A ) @ ( sK59_SY4435 @ 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)],[533]) ).
thf(689,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)],[532]) ).
thf(690,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK57_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK57_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK57_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK57_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)],[531]) ).
thf(691,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4433: $i] :
( ~ ( in @ ( ordered_pair @ SY4433 @ ( sK55_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY4433 @ B ) )
| ~ ( in @ ( sK55_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_SY4434 @ C @ B @ A ) @ ( sK55_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK56_SY4434 @ C @ B @ A ) @ B ) )
| ( in @ ( sK55_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 @ ( sK54_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK54_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(692,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY4431: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ SY4431 ) @ A )
| ~ ( in @ SY4431 @ B ) )
| ~ ( in @ ( sK52_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK52_D @ C @ B @ A ) @ ( sK53_SY4432 @ C @ B @ A ) ) @ A )
& ( in @ ( sK53_SY4432 @ 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] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK51_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK51_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(693,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)],[528]) ).
thf(694,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)],[527]) ).
thf(695,plain,
( ( ! [A: $i] :
( ( ! [SY4429: $i,SY4430: $i] :
( ( sK50_B @ A )
!= ( ordered_pair @ SY4429 @ SY4430 ) )
& ( in @ ( sK50_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK48_C @ B @ A ) @ ( sK49_SY4428 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(696,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK47_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK47_C @ B @ A ) @ ( sK47_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)],[525]) ).
thf(697,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ( ( sK46_D @ C @ B @ A )
= B )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ C @ B @ A ) @ B ) @ A )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( ( sK46_D @ C @ B @ A )
!= B )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK46_D @ C @ B @ A ) @ B ) @ A )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( fiber @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( fiber @ A @ B ) )
| ( ! [D: $i] :
( ( D = B )
| ~ ( in @ ( ordered_pair @ D @ B ) @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( D != B ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(698,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK44_C @ B @ A ) @ ( sK45_SY4427 @ 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)],[523]) ).
thf(699,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [SY4426: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY4426 ) @ ( sK43_B @ A ) )
| ~ ( in @ SY4426 @ ( sK43_B @ A ) ) )
& ( ( sK43_B @ A )
!= empty_set )
& ( subset @ ( sK43_B @ A ) @ ( relation_field @ A ) ) )
| ( well_founded_relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( well_founded_relation @ A )
| ! [B: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK42_C @ B @ A ) ) @ B )
& ( in @ ( sK42_C @ B @ A ) @ B ) )
| ( B = empty_set )
| ~ ( subset @ B @ ( relation_field @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(700,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY4425 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY4425 @ 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)],[521]) ).
thf(701,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ! [SY4424: $i] :
( ~ ( disjoint @ ( fiber @ A @ SY4424 ) @ ( sK39_C @ B @ A ) )
| ~ ( in @ SY4424 @ ( sK39_C @ B @ A ) ) )
& ( ( sK39_C @ B @ A )
!= empty_set )
& ( subset @ ( sK39_C @ B @ A ) @ B ) )
| ( is_well_founded_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_well_founded_in @ A @ B )
| ! [C: $i] :
( ( ( disjoint @ ( fiber @ A @ ( sK38_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
| ( C = empty_set )
| ~ ( subset @ C @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(702,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)],[519]) ).
thf(703,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4422: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ SY4422 ) @ A )
| ~ ( in @ ( sK36_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY4423 @ B @ A ) ) @ A )
| ( in @ ( sK36_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 @ ( sK35_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(704,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK33_C @ B @ A ) @ B )
& ( in @ ( sK34_SY4421 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK33_C @ B @ A ) @ ( sK34_SY4421 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK34_SY4421 @ B @ A ) @ ( sK33_C @ B @ A ) ) @ A )
& ( ( sK33_C @ B @ A )
!= ( sK34_SY4421 @ 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)],[517]) ).
thf(705,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)],[516]) ).
thf(706,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4419: $i] :
( ( ( sK31_C @ B @ A )
!= ( apply @ A @ SY4419 ) )
| ~ ( in @ SY4419 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK31_C @ B @ A ) @ B ) )
& ( ( ( ( sK31_C @ B @ A )
= ( apply @ A @ ( sK32_SY4420 @ B @ A ) ) )
& ( in @ ( sK32_SY4420 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK31_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 @ ( sK30_D @ C @ B @ A ) ) )
& ( in @ ( sK30_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(707,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY4417: $i] :
~ ( in @ ( ordered_pair @ SY4417 @ ( sK28_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK28_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ B @ A ) @ ( sK28_C @ B @ A ) ) @ A )
| ( in @ ( sK28_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 @ ( sK27_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(708,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)],[513]) ).
thf(709,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(710,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK25_C @ B @ A )
!= ( sK26_SY4416 @ B @ A ) )
& ( in @ ( sK25_C @ B @ A ) @ B )
& ( in @ ( sK26_SY4416 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK25_C @ B @ A ) @ ( sK26_SY4416 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ B @ A ) @ ( sK25_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)],[511]) ).
thf(711,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(712,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY4415 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ B @ A ) @ ( sK23_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK23_C @ B @ A ) @ ( sK24_SY4415 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ B @ A ) @ ( sK23_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)],[509]) ).
thf(713,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( ~ ( in @ ( sK21_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( sK22_SY4414 @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ ( sK21_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK22_SY4414 @ C @ B @ A ) ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK21_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK22_SY4414 @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( apply @ C @ ( sK21_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK22_SY4414 @ C @ B @ A ) ) ) @ B )
| ( in @ ( ordered_pair @ ( sK21_D @ C @ B @ A ) @ ( sK22_SY4414 @ C @ B @ A ) ) @ A ) ) )
| ( ( relation_dom @ C )
!= ( relation_field @ A ) )
| ( ( relation_rng @ C )
!= ( relation_field @ B ) )
| ~ ( one_to_one @ C )
| ( relation_isomorphism @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ ( relation_field @ A ) )
| ~ ( in @ E @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ A ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ D @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ E @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_dom @ C )
= ( relation_field @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_rng @ C )
= ( relation_field @ B ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( one_to_one @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(714,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK19_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK20_SY4413 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK19_B @ A ) )
= ( apply @ A @ ( sK20_SY4413 @ A ) ) )
& ( ( sK19_B @ A )
!= ( sK20_SY4413 @ 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)],[507]) ).
thf(715,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY4411: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ SY4411 ) @ A )
| ~ ( in @ ( ordered_pair @ SY4411 @ ( sK17_SY4408 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK17_SY4408 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK18_SY4412 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK18_SY4412 @ C @ B @ A ) @ ( sK17_SY4408 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ ( sK17_SY4408 @ 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 @ ( sK15_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK15_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(716,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK12_C @ B @ A ) @ B )
& ( in @ ( sK13_SY4405 @ B @ A ) @ B )
& ( in @ ( sK14_SY4407 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY4405 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK13_SY4405 @ B @ A ) @ ( sK14_SY4407 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK14_SY4407 @ 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)],[505]) ).
thf(717,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(718,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)],[503]) ).
thf(719,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)],[502]) ).
thf(720,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(721,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(722,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(723,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(724,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(725,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(726,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)],[496]) ).
thf(727,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(728,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(729,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)],[494]) ).
thf(730,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)],[493]) ).
thf(731,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(732,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(733,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)],[344]) ).
thf(734,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(735,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)],[489]) ).
thf(736,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(737,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)],[487]) ).
thf(738,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(739,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( function @ ( relation_rng_restriction @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(740,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(741,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(742,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(743,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(744,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)],[481]) ).
thf(745,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(746,plain,
( ( ( function @ sK11_A )
& ( relation @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(747,plain,
( ( ( empty @ sK10_A )
& ( relation @ sK10_A ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(748,plain,
( ( ( empty @ sK9_A )
& ( relation @ sK9_A )
& ( function @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(749,plain,
( ( ( function @ sK8_A )
& ( relation @ sK8_A )
& ( one_to_one @ sK8_A )
& ( empty @ sK8_A )
& ( epsilon_transitive @ sK8_A )
& ( epsilon_connected @ sK8_A )
& ( ordinal @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(750,plain,
( ( ~ ( empty @ sK7_A )
& ( relation @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(751,plain,
( ( ( function @ sK6_A )
& ( relation @ sK6_A )
& ( one_to_one @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(752,plain,
( ( ( relation @ sK5_A )
& ( relation_empty_yielding @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(753,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A )
& ( function @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(754,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(755,plain,
( ( ( relation @ sK2_SY4402 )
& ( function @ sK3_SY4404 )
& ( relation @ sK3_SY4404 )
& ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
& ( well_ordering @ sK1_A )
& ~ ( well_ordering @ sK2_SY4402 ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(756,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK20_SY4413 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK19_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK20_SY4413 @ SX0 ) ) ) )
| ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY4413 @ 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)],[714]) ).
thf(757,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(758,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)],[670]) ).
thf(759,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK82_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK82_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)],[611]) ).
thf(760,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ( ( sK71_SY4441 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK71_SY4441 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK70_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK70_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK71_SY4441 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK71_SY4441 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK70_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK70_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)],[663]) ).
thf(761,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)],[674]) ).
thf(762,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)],[718]) ).
thf(763,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK34_SY4421 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SX1 @ SX0 ) @ ( sK34_SY4421 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SX1 @ SX0 ) @ ( sK33_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK33_C @ SX1 @ SX0 )
!= ( sK34_SY4421 @ 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)],[704]) ).
thf(764,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SX2 @ SX1 @ SX0 ) @ ( sK53_SY4432 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK53_SY4432 @ 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] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK51_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(765,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) )
| ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(766,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY4425 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY4425 @ 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)],[700]) ).
thf(767,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)],[708]) ).
thf(768,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)],[705]) ).
thf(769,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(770,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)],[684]) ).
thf(771,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[743]) ).
thf(772,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)],[694]) ).
thf(773,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)],[726]) ).
thf(774,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)],[737]) ).
thf(775,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_orders @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_orders @ SX0 @ ( relation_field @ SX0 ) )
| ( well_ordering @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(776,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)],[677]) ).
thf(777,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 @ ( sK73_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK73_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK73_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(778,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK21_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK21_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK21_D @ SX2 @ SX1 @ SX0 ) @ ( sK22_SY4414 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
| ( ( relation_dom @ SX2 )
!= ( relation_field @ SX0 ) )
| ( ( relation_rng @ SX2 )
!= ( relation_field @ SX1 ) )
| ~ ( one_to_one @ SX2 )
| ( relation_isomorphism @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX4 @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX3 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX4 @ ( relation_field @ SX0 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_dom @ SX2 )
= ( relation_field @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_rng @ SX2 )
= ( relation_field @ SX1 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( one_to_one @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(779,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)],[675]) ).
thf(780,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)],[693]) ).
thf(781,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)],[669]) ).
thf(782,plain,
( ( ~ ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(783,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY4415 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SX1 @ SX0 ) @ ( sK23_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SX1 @ SX0 ) @ ( sK24_SY4415 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SX1 @ SX0 ) @ ( sK23_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)],[712]) ).
thf(784,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK43_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK43_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK42_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(785,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK17_SY4408 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY4408 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY4412 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY4408 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ ( sK17_SY4408 @ 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 @ ( sK15_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(786,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)],[666]) ).
thf(787,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK50_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK50_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK48_C @ SX1 @ SX0 ) @ ( sK49_SY4428 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(788,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY4423 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK36_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 @ ( sK35_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(789,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)],[730]) ).
thf(790,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SX1 @ SX0 )
!= ( sK26_SY4416 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK26_SY4416 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SX1 @ SX0 ) @ ( sK26_SY4416 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SX1 @ SX0 ) @ ( sK25_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)],[710]) ).
thf(791,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SX0 )
!= ( sK76_SY4442 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK76_SY4442 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SX0 ) @ ( sK76_SY4442 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SX0 ) @ ( sK75_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)],[615]) ).
thf(792,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)],[639]) ).
thf(793,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)],[664]) ).
thf(794,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(795,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)],[641]) ).
thf(796,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK13_SY4405 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK14_SY4407 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY4405 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SX1 @ SX0 ) @ ( sK14_SY4407 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK14_SY4407 @ 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)],[716]) ).
thf(797,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( ( sK61_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX3 ) ) )
| ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK62_SY4437 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK61_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK62_SY4437 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK61_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 @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( apply @ SX0 @ ( sK60_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(798,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ( ( sK46_D @ SX2 @ SX1 @ SX0 )
= SX1 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SX2 @ SX1 @ SX0 )
!= SX1 )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( fiber @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( fiber @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ( SX3 = SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 != SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(799,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY4427 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY4427 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY4427 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK44_C @ SX1 @ SX0 ) @ ( sK45_SY4427 @ 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)],[698]) ).
thf(800,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)],[735]) ).
thf(801,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)],[719]) ).
thf(802,plain,
( ( ~ ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(803,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SX1 @ SX0 ) @ ( sK47_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)],[696]) ).
thf(804,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)],[616]) ).
thf(805,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(806,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY4435 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK58_D @ SX2 @ SX1 @ SX0 ) @ ( sK59_SY4435 @ 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)],[688]) ).
thf(807,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)],[655]) ).
thf(808,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX2 ) @ ( sK39_C @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK39_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SX1 @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( is_well_founded_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_well_founded_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK38_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ( SX2 = empty_set )
| ~ ( subset @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(809,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
| ~ ( function @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(810,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK78_SY4443 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK77_B @ SX0 )
!= ( sK78_SY4443 @ 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)],[614]) ).
thf(811,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)],[702]) ).
thf(812,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK31_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK31_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK31_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK32_SY4420 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK31_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 @ ( sK30_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK30_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(813,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_field @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_field @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(814,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[753]) ).
thf(815,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK80_SY4444 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK81_SY4446 @ 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)],[613]) ).
thf(816,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK57_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( apply @ SX0 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( sK57_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)],[690]) ).
thf(817,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)],[733]) ).
thf(818,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
| ~ ( epsilon_connected @ sK8_A ) )
| ~ ( ordinal @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(819,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( reflexive @ SX0 )
| ( reflexive @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( transitive @ SX0 )
| ( transitive @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( connected @ SX0 )
| ( connected @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( antisymmetric @ SX0 )
| ( antisymmetric @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( well_founded_relation @ SX0 )
| ( well_founded_relation @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(820,plain,
( ( ~ ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[752]) ).
thf(821,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)],[649]) ).
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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(823,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[738]) ).
thf(824,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ 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)],[685]) ).
thf(825,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(826,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)],[729]) ).
thf(827,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK28_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SX1 @ SX0 ) @ ( sK28_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK28_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 @ ( sK27_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(828,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 @ ( sK74_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK74_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(829,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)],[689]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( ( ( apply @ SX1 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
!= ( apply @ SX2 @ ( sK67_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)],[671]) ).
thf(831,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(832,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)],[651]) ).
thf(833,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)],[617]) ).
thf(834,plain,
( ( ~ ( ~ ( relation @ sK2_SY4402 )
| ~ ~ ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
| ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(835,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(836,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY4438 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY4438 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY4438 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY4438 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ ( sK64_SY4438 @ 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)],[686]) ).
thf(837,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK55_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SX2 @ SX1 @ SX0 ) @ ( sK55_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK56_SY4434 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK55_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 @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(838,plain,
( ( ~ ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[746]) ).
thf(839,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)],[744]) ).
thf(840,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) )
!= ( sK72_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)],[654]) ).
thf(841,plain,
! [SV1: $i] :
( ( ! [SY4447: $i] :
( ~ ( relation @ SY4447 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SY4447 ) ) @ ( relation_dom @ SY4447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(842,plain,
! [SV2: $i] :
( ( ! [SY4448: $i] :
( ~ ( relation @ SY4448 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SY4448 ) ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(843,plain,
! [SV3: $i] :
( ( ! [SY4449: $i] :
( ~ ( relation @ SY4449 )
| ( subset @ ( relation_rng_restriction @ SV3 @ SY4449 ) @ SY4449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(844,plain,
! [SV4: $i] :
( ( ! [SY4450: $i] :
( ~ ( relation @ SY4450 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY4450 ) ) @ ( relation_rng @ SY4450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(845,plain,
! [SV5: $i] :
( ( ! [SY4451: $i] :
( ~ ( relation @ SY4451 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SY4451 ) )
= ( set_intersection2 @ ( relation_rng @ SY4451 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(846,plain,
! [SV6: $i] :
( ( ! [SY4452: $i,SY4453: $i] :
( ~ ( relation @ SY4453 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV6 @ SY4453 ) @ SY4452 )
= ( relation_rng_restriction @ SV6 @ ( relation_dom_restriction @ SY4453 @ SY4452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(847,plain,
! [SV7: $i] :
( ( ! [SY4454: $i] :
( ~ ( relation @ SY4454 )
| ( subset @ ( relation_image @ SY4454 @ SV7 ) @ ( relation_rng @ SY4454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(848,plain,
! [SV8: $i] :
( ( ! [SY4455: $i] :
( ~ ( function @ SY4455 )
| ~ ( relation @ SY4455 )
| ( subset @ ( relation_image @ SY4455 @ ( relation_inverse_image @ SY4455 @ SV8 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(849,plain,
! [SV9: $i] :
( ( ! [SY4456: $i] :
( ~ ( relation @ SY4456 )
| ( ( relation_image @ SY4456 @ SV9 )
= ( relation_image @ SY4456 @ ( set_intersection2 @ ( relation_dom @ SY4456 ) @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(850,plain,
! [SV10: $i] :
( ( ! [SY4457: $i] :
( ~ ( relation @ SY4457 )
| ~ ( subset @ SV10 @ ( relation_dom @ SY4457 ) )
| ( subset @ SV10 @ ( relation_inverse_image @ SY4457 @ ( relation_image @ SY4457 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(851,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( ( relation_image @ SV11 @ ( relation_dom @ SV11 ) )
= ( relation_rng @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(852,plain,
! [SV12: $i] :
( ( ! [SY4458: $i] :
( ~ ( function @ SY4458 )
| ~ ( relation @ SY4458 )
| ~ ( subset @ SV12 @ ( relation_rng @ SY4458 ) )
| ( ( relation_image @ SY4458 @ ( relation_inverse_image @ SY4458 @ SV12 ) )
= SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(853,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ! [SY4459: $i] :
( ~ ( relation @ SY4459 )
| ( ( relation_rng @ ( relation_composition @ SV13 @ SY4459 ) )
= ( relation_image @ SY4459 @ ( relation_rng @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(854,plain,
! [SV14: $i] :
( ( ! [SY4460: $i] :
( ~ ( relation @ SY4460 )
| ( subset @ ( relation_inverse_image @ SY4460 @ SV14 ) @ ( relation_dom @ SY4460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(855,plain,
! [SV15: $i] :
( ( ! [SY4461: $i] :
( ~ ( relation @ SY4461 )
| ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SY4461 ) )
| ( ( relation_inverse_image @ SY4461 @ SV15 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(856,plain,
! [SV16: $i] :
( ( ! [SY4462: $i,SY4463: $i] :
( ~ ( relation @ SY4463 )
| ~ ( subset @ SV16 @ SY4462 )
| ( subset @ ( relation_inverse_image @ SY4463 @ SV16 ) @ ( relation_inverse_image @ SY4463 @ SY4462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(857,plain,
! [SV17: $i] :
( ( ! [SY4464: $i] :
( ~ ( relation @ SY4464 )
| ( ( relation_restriction @ SY4464 @ SV17 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SY4464 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(858,plain,
! [SV18: $i] :
( ( ! [SY4465: $i] :
( ~ ( relation @ SY4465 )
| ( ( relation_restriction @ SY4465 @ SV18 )
= ( relation_rng_restriction @ SV18 @ ( relation_dom_restriction @ SY4465 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(859,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ( subset @ SV19 @ ( cartesian_product2 @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(860,plain,
! [SV20: $i] :
( ( ! [SY4466: $i,SY4467: $i] :
( ~ ( relation @ SY4467 )
| ( subset @ ( fiber @ ( relation_restriction @ SY4467 @ SV20 ) @ SY4466 ) @ ( fiber @ SY4467 @ SY4466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(861,plain,
! [SV21: $i] :
( ( ! [SY4468: $i] :
( ~ ( function @ SY4468 )
| ~ ( relation @ SY4468 )
| ! [SY4469: $i] :
( ~ ( function @ SY4469 )
| ~ ( relation @ SY4469 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4469 @ SY4468 ) ) )
| ( ( apply @ ( relation_composition @ SY4469 @ SY4468 ) @ SV21 )
= ( apply @ SY4468 @ ( apply @ SY4469 @ SV21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(862,plain,
! [SV22: $i] :
( ( ! [SY4470: $i] :
( ~ ( relation @ SY4470 )
| ~ ( reflexive @ SY4470 )
| ( reflexive @ ( relation_restriction @ SY4470 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(863,plain,
! [SV23: $i] :
( ( ! [SY4471: $i] :
( ~ ( function @ SY4471 )
| ~ ( relation @ SY4471 )
| ! [SY4472: $i] :
( ~ ( function @ SY4472 )
| ~ ( relation @ SY4472 )
| ~ ( in @ SV23 @ ( relation_dom @ SY4471 ) )
| ( ( apply @ ( relation_composition @ SY4471 @ SY4472 ) @ SV23 )
= ( apply @ SY4472 @ ( apply @ SY4471 @ SV23 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(864,plain,
! [SV24: $i] :
( ( ! [SY4473: $i] :
( ~ ( relation @ SY4473 )
| ~ ( connected @ SY4473 )
| ( connected @ ( relation_restriction @ SY4473 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(865,plain,
! [SV25: $i] :
( ( ! [SY4474: $i] :
( ~ ( relation @ SY4474 )
| ~ ( transitive @ SY4474 )
| ( transitive @ ( relation_restriction @ SY4474 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(866,plain,
! [SV26: $i] :
( ( ! [SY4475: $i] :
( ~ ( relation @ SY4475 )
| ~ ( antisymmetric @ SY4475 )
| ( antisymmetric @ ( relation_restriction @ SY4475 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(867,plain,
! [SV27: $i] :
( ( ! [SY4476: $i] :
( ~ ( relation @ SY4476 )
| ~ ( well_founded_relation @ SY4476 )
| ( well_founded_relation @ ( relation_restriction @ SY4476 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(868,plain,
! [SV28: $i] :
( ( ! [SY4477: $i] :
( ~ ( relation @ SY4477 )
| ~ ( well_ordering @ SY4477 )
| ( well_ordering @ ( relation_restriction @ SY4477 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(869,plain,
! [SV29: $i] :
( ( ! [SY4478: $i] :
( ~ ( relation @ SY4478 )
| ~ ( subset @ SV29 @ ( relation_field @ SY4478 ) )
| ~ ( well_ordering @ SY4478 )
| ( ( relation_field @ ( relation_restriction @ SY4478 @ SV29 ) )
= SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(870,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY4479: $i] :
( ~ ( relation @ SY4479 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SY4479 ) ) @ ( relation_dom @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(871,plain,
! [SV31: $i] :
( ( ~ ( relation @ SV31 )
| ! [SY4480: $i] :
( ~ ( relation @ SY4480 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SY4480 ) ) @ ( relation_rng @ SY4480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(872,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY4481: $i] :
( ~ ( relation @ SY4481 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY4481 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY4481 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(873,plain,
! [SV33: $i] :
( ( ~ ( relation @ SV33 )
| ! [SY4482: $i] :
( ~ ( relation @ SY4482 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY4482 ) )
| ( ( relation_rng @ ( relation_composition @ SY4482 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(874,plain,
! [SV34: $i] :
( ( ~ ( relation @ SV34 )
| ! [SY4483: $i] :
( ~ ( relation @ SY4483 )
| ! [SY4484: $i] :
( ~ ( function @ SY4484 )
| ~ ( relation @ SY4484 )
| ~ ( relation_isomorphism @ SV34 @ SY4483 @ SY4484 )
| ( relation_isomorphism @ SY4483 @ SV34 @ ( function_inverse @ SY4484 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(875,plain,
! [SV35: $i] :
( ( ~ ( relation @ SV35 )
| ( in @ ( ordered_pair @ ( sK68_B @ SV35 ) @ ( sK69_SY4440 @ SV35 ) ) @ SV35 )
| ( SV35 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(876,plain,
! [SV36: $i] :
( ( ~ ( function @ SV36 )
| ~ ( relation @ SV36 )
| ~ ( one_to_one @ SV36 )
| ( one_to_one @ ( function_inverse @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(877,plain,
! [SV37: $i] :
( ( ! [SY4485: $i,SY4486: $i] :
( ~ ( function @ SY4486 )
| ~ ( relation @ SY4486 )
| ~ ( in @ SY4485 @ ( relation_dom @ ( relation_dom_restriction @ SY4486 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY4486 @ SV37 ) @ SY4485 )
= ( apply @ SY4486 @ SY4485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(878,plain,
! [SV38: $i] :
( ( ! [SY4487: $i,SY4488: $i] :
( ~ ( function @ SY4488 )
| ~ ( relation @ SY4488 )
| ~ ( in @ SY4487 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SY4488 @ SV38 ) @ SY4487 )
= ( apply @ SY4488 @ SY4487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(879,plain,
! [SV39: $i] :
( ( ! [SY4489: $i] :
( ~ ( relation @ SY4489 )
| ( subset @ ( relation_dom_restriction @ SY4489 @ SV39 ) @ SY4489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(880,plain,
! [SV40: $i] :
( ( ! [SY4490: $i] :
( ~ ( relation @ SY4490 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY4490 @ SV40 ) )
= ( set_intersection2 @ ( relation_dom @ SY4490 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(881,plain,
! [SV41: $i] :
( ( ! [SY4491: $i] :
( ~ ( relation @ SY4491 )
| ( ( relation_dom_restriction @ SY4491 @ SV41 )
= ( relation_composition @ ( identity_relation @ SV41 ) @ SY4491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(882,plain,
! [SV42: $i] :
( ( ! [SY4492: $i] :
( ~ ( relation @ SY4492 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY4492 @ SV42 ) ) @ ( relation_rng @ SY4492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(883,plain,
! [SV43: $i] :
( ( ~ ( empty @ SV43 )
| ( function @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(884,plain,
! [SV44: $i] :
( ( ~ ( empty @ SV44 )
| ( relation @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(885,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ( ( relation_field @ SV45 )
= ( set_union2 @ ( relation_dom @ SV45 ) @ ( relation_rng @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(886,plain,
! [SV46: $i] :
( ( ~ ( relation @ SV46 )
| ! [SY4493: $i] :
( ( relation_restriction @ SV46 @ SY4493 )
= ( set_intersection2 @ SV46 @ ( cartesian_product2 @ SY4493 @ SY4493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(887,plain,
! [SV47: $i] :
( ( ~ ( function @ SV47 )
| ~ ( relation @ SV47 )
| ~ ( one_to_one @ SV47 )
| ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(888,plain,
! [SV48: $i] :
( ( ~ ( relation @ SV48 )
| ! [SY4494: $i] : ( relation @ ( relation_restriction @ SV48 @ SY4494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(889,plain,
! [SV49: $i] :
( ( ~ ( relation @ SV49 )
| ( relation @ ( relation_inverse @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(890,plain,
! [SV50: $i] :
( ( ! [SY4495: $i] :
( ~ ( relation @ SV50 )
| ~ ( relation @ SY4495 )
| ( relation @ ( relation_composition @ SV50 @ SY4495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(891,plain,
! [SV51: $i] :
( ( relation @ ( identity_relation @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(892,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ! [SY4496: $i] : ( relation @ ( relation_dom_restriction @ SV52 @ SY4496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(893,plain,
! [SV53: $i] :
( ( ! [SY4497: $i] :
( ~ ( relation @ SY4497 )
| ( relation @ ( relation_rng_restriction @ SV53 @ SY4497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(894,plain,
! [SV54: $i] :
( ( ! [SY4498: $i] :
( ~ ( relation @ SV54 )
| ~ ( relation @ SY4498 )
| ( relation @ ( set_intersection2 @ SV54 @ SY4498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(895,plain,
! [SV55: $i] :
( ( ! [SY4499: $i] :
( ~ ( relation @ SV55 )
| ~ ( relation @ SY4499 )
| ( relation @ ( set_union2 @ SV55 @ SY4499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(896,plain,
! [SV56: $i] :
( ( ! [SY4500: $i] :
( ~ ( relation @ SV56 )
| ~ ( relation @ SY4500 )
| ( relation @ ( set_difference @ SV56 @ SY4500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(897,plain,
! [SV57: $i] :
( ( ( empty @ SV57 )
| ~ ( relation @ SV57 )
| ~ ( empty @ ( relation_dom @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(898,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
| ~ ( relation @ SV58 )
| ~ ( empty @ ( relation_rng @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(899,plain,
! [SV59: $i] :
( ( ~ ( relation @ SV59 )
| ( ( relation_inverse @ ( relation_inverse @ SV59 ) )
= SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(900,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK20_SY4413 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK19_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK20_SY4413 @ SX0 ) ) ) )
| ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY4413 @ 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)],[756]) ).
thf(901,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(902,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)],[758]) ).
thf(903,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK82_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK82_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)],[759]) ).
thf(904,plain,
! [SV60: $i] :
( ( ~ ( function @ SV60 )
| ~ ( relation @ SV60 )
| ~ ( one_to_one @ SV60 )
| ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(905,plain,
! [SV61: $i] :
( ( ! [SY4512: $i] :
~ ( ~ ! [SY4513: $i,SY4514: $i] :
( ~ ( relation @ SY4514 )
| ~ ( in @ SV61 @ SY4513 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY4512 ) @ SY4514 )
| ( in @ ( ordered_pair @ SV61 @ SY4512 ) @ ( relation_composition @ ( identity_relation @ SY4513 ) @ SY4514 ) ) )
| ~ ~ ( ~ ! [SY4515: $i,SY4516: $i] :
( ~ ( relation @ SY4516 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY4512 ) @ ( relation_composition @ ( identity_relation @ SY4515 ) @ SY4516 ) )
| ( in @ SV61 @ SY4515 ) )
| ~ ! [SY4517: $i,SY4518: $i] :
( ~ ( relation @ SY4518 )
| ~ ( in @ ( ordered_pair @ SV61 @ SY4512 ) @ ( relation_composition @ ( identity_relation @ SY4517 ) @ SY4518 ) )
| ( in @ ( ordered_pair @ SV61 @ SY4512 ) @ SY4518 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(906,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)],[762]) ).
thf(907,plain,
! [SV62: $i] :
( ( ~ ( relation @ SV62 )
| ~ ( ~ ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) )
| ~ ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(908,plain,
! [SV63: $i] :
( ( ~ ( relation @ SV63 )
| ~ ( ~ ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) )
| ~ ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(909,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY4531: $i,SY4532: $i] :
( ~ ( relation @ SY4532 )
| ~ ( in @ SV64 @ SY4532 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SY4531 @ SY4531 ) )
| ( in @ SV64 @ ( relation_restriction @ SY4532 @ SY4531 ) ) )
| ~ ~ ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) )
| ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(910,plain,
! [SV65: $i] :
( ( ~ ( relation @ SV65 )
| ~ ( ~ ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) )
| ~ ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(911,plain,
! [SV66: $i] :
( ( ~ ( relation @ SV66 )
| ~ ( ~ ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(912,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)],[768]) ).
thf(913,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
| ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(914,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)],[770]) ).
thf(915,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(916,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)],[772]) ).
thf(917,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)],[773]) ).
thf(918,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)],[774]) ).
thf(919,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_orders @ SX0 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_orders @ SX0 @ ( relation_field @ SX0 ) )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(920,plain,
! [SV67: $i] :
( ( ~ ( ~ ! [SY4547: $i,SY4548: $i] :
( ~ ( function @ SY4548 )
| ~ ( relation @ SY4548 )
| ( SY4547
!= ( apply @ SY4548 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SY4548 ) )
| ( in @ ( ordered_pair @ SV67 @ SY4547 ) @ SY4548 ) )
| ~ ~ ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) )
| ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(921,plain,
! [SV68: $i] :
( ( ~ ( ~ ! [SY4553: $i,SY4554: $i] :
( ~ ( relation @ SY4554 )
| ! [SY4555: $i] :
( ~ ( in @ SY4555 @ ( relation_rng @ SY4554 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4555 ) @ SY4554 )
| ~ ( in @ SY4555 @ SY4553 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SY4554 @ SY4553 ) ) )
| ~ ! [SY4556: $i,SY4557: $i] :
( ~ ( relation @ SY4557 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SY4557 @ SY4556 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ ( relation_rng @ SY4557 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) ) @ SY4557 ) )
| ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ SY4556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(922,plain,
! [SV69: $i] :
( ( ~ ( relation @ SV69 )
| ! [SY4558: $i] :
( ~ ( relation @ SY4558 )
| ~ ( ~ ! [SY4559: $i] :
( ~ ( function @ SY4559 )
| ~ ( relation @ SY4559 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4559 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4559 )
!= ( relation_field @ SY4558 ) )
| ~ ( one_to_one @ SY4559 )
| ( relation_isomorphism @ SV69 @ SY4558 @ SY4559 ) )
| ~ ~ ( ~ ! [SY4560: $i] :
( ~ ( function @ SY4560 )
| ~ ( relation @ SY4560 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4560 )
| ~ ( ~ ! [SY4561: $i,SY4562: $i] :
( ~ ( in @ SY4561 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4562 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4561 ) @ ( apply @ SY4560 @ SY4562 ) ) @ SY4558 )
| ( in @ ( ordered_pair @ SY4561 @ SY4562 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4567: $i,SY4568: $i] :
( ~ ( in @ ( ordered_pair @ SY4567 @ SY4568 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4567 ) @ ( apply @ SY4560 @ SY4568 ) ) @ SY4558 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4569: $i] :
( ~ ( function @ SY4569 )
| ~ ( relation @ SY4569 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4569 )
| ( ( relation_dom @ SY4569 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4570: $i] :
( ~ ( function @ SY4570 )
| ~ ( relation @ SY4570 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4570 )
| ( ( relation_rng @ SY4570 )
= ( relation_field @ SY4558 ) ) ) )
| ~ ! [SY4571: $i] :
( ~ ( function @ SY4571 )
| ~ ( relation @ SY4571 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4571 )
| ( one_to_one @ SY4571 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(923,plain,
! [SV70: $i] :
( ( ~ ( ~ ! [SY4572: $i,SY4573: $i] :
( ~ ( relation @ SY4573 )
| ~ ( in @ SV70 @ SY4572 )
| ~ ( in @ SV70 @ ( relation_dom @ SY4573 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4573 @ SY4572 ) ) ) )
| ~ ~ ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) )
| ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(924,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)],[780]) ).
thf(925,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)],[781]) ).
thf(926,plain,
( ( ~ ~ ( empty @ sK7_A )
| ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(927,plain,
! [SV71: $i] :
( ( ~ ( relation @ SV71 )
| ~ ( ~ ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) )
| ~ ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(928,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK43_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK43_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK42_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(929,plain,
! [SV72: $i] :
( ( ~ ( relation @ SV72 )
| ! [SY4584: $i] :
( ~ ( relation @ SY4584 )
| ~ ( ~ ! [SY4585: $i] :
( ~ ( relation @ SY4585 )
| ~ ( ~ ( ! [SY4586: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ SY4586 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4586 @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) ) )
| ( SY4585
= ( relation_composition @ SV72 @ SY4584 ) ) )
| ~ ! [SY4587: $i] :
( ~ ( relation @ SY4587 )
| ( SY4587
!= ( relation_composition @ SV72 @ SY4584 ) )
| ~ ( ~ ! [SY4588: $i,SY4589: $i] :
( ! [SY4590: $i] :
( ~ ( in @ ( ordered_pair @ SY4588 @ SY4590 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4590 @ SY4589 ) @ SY4584 ) )
| ( in @ ( ordered_pair @ SY4588 @ SY4589 ) @ SY4587 ) )
| ~ ! [SY4591: $i,SY4592: $i] :
( ~ ( in @ ( ordered_pair @ SY4591 @ SY4592 ) @ SY4587 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4591 @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) @ SY4592 ) @ SY4584 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(930,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)],[786]) ).
thf(931,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK50_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK50_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK48_C @ SX1 @ SX0 ) @ ( sK49_SY4428 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(932,plain,
! [SV73: $i] :
( ( ~ ( relation @ SV73 )
| ~ ( ~ ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) )
| ~ ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(933,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)],[789]) ).
thf(934,plain,
! [SV74: $i] :
( ( ~ ( relation @ SV74 )
| ~ ( ~ ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) )
| ~ ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(935,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SX0 )
!= ( sK76_SY4442 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK76_SY4442 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SX0 ) @ ( sK76_SY4442 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SX0 ) @ ( sK75_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)],[791]) ).
thf(936,plain,
! [SV75: $i] :
( ( ~ ( ~ ! [SY4603: $i,SY4604: $i] :
( ~ ( relation @ SY4604 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4603 ) @ SY4604 )
| ( in @ SV75 @ ( relation_dom @ SY4604 ) ) )
| ~ ! [SY4605: $i,SY4606: $i] :
( ~ ( relation @ SY4606 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4605 ) @ SY4606 )
| ( in @ SY4605 @ ( relation_rng @ SY4606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(937,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)],[793]) ).
thf(938,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(939,plain,
! [SV76: $i] :
( ( ! [SY4607: $i] :
( ~ ( function @ SY4607 )
| ~ ( relation @ SY4607 )
| ~ ( ~ ! [SY4608: $i] :
( ~ ( function @ SY4608 )
| ~ ( relation @ SY4608 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4608 ) )
| ~ ( in @ ( apply @ SY4608 @ SV76 ) @ ( relation_dom @ SY4607 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4608 @ SY4607 ) ) ) )
| ~ ~ ( ~ ! [SY4609: $i] :
( ~ ( function @ SY4609 )
| ~ ( relation @ SY4609 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4609 @ SY4607 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4609 ) ) )
| ~ ! [SY4610: $i] :
( ~ ( function @ SY4610 )
| ~ ( relation @ SY4610 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4610 @ SY4607 ) ) )
| ( in @ ( apply @ SY4610 @ SV76 ) @ ( relation_dom @ SY4607 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(940,plain,
! [SV77: $i] :
( ( ~ ( relation @ SV77 )
| ~ ( ~ ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) )
| ~ ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(941,plain,
! [SV78: $i] :
( ( ~ ( function @ SV78 )
| ~ ( relation @ SV78 )
| ~ ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(942,plain,
! [SV79: $i] :
( ( ~ ( relation @ SV79 )
| ~ ( ~ ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) )
| ~ ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(943,plain,
! [SV80: $i] :
( ( ~ ( relation @ SV80 )
| ~ ( ~ ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) )
| ~ ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(944,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)],[800]) ).
thf(945,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)],[801]) ).
thf(946,plain,
( ( ~ ( empty @ sK10_A )
| ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(947,plain,
! [SV81: $i] :
( ( ~ ( relation @ SV81 )
| ~ ( ~ ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) )
| ~ ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(948,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY4640: $i,SY4641: $i] :
( ~ ( function @ SY4641 )
| ~ ( relation @ SY4641 )
| ~ ( in @ SY4640 @ ( relation_dom @ SY4641 ) )
| ~ ( in @ SY4640 @ SV82 )
| ( in @ SY4640 @ ( relation_dom @ ( relation_dom_restriction @ SY4641 @ SV82 ) ) ) )
| ~ ~ ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) )
| ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(949,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(950,plain,
! [SV83: $i] :
( ( ! [SY4646: $i] :
( ~ ( relation @ SY4646 )
| ~ ( ~ ! [SY4647: $i] :
( ~ ( relation @ SY4647 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4647 @ SY4646 @ SV83 ) @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) ) @ SY4646 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4647 @ SY4646 @ SV83 ) @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) ) @ SY4647 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4647 @ SY4646 @ SV83 ) @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) ) @ SY4647 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4647 @ SY4646 @ SV83 ) @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) ) @ SY4646 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4647 @ SY4646 @ SV83 ) @ ( sK59_SY4435 @ SY4647 @ SY4646 @ SV83 ) ) @ SY4647 ) ) ) )
| ( SY4647
= ( relation_rng_restriction @ SV83 @ SY4646 ) ) )
| ~ ! [SY4648: $i] :
( ~ ( relation @ SY4648 )
| ( SY4648
!= ( relation_rng_restriction @ SV83 @ SY4646 ) )
| ~ ( ~ ! [SY4649: $i,SY4650: $i] :
( ~ ( in @ SY4650 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4649 @ SY4650 ) @ SY4646 )
| ( in @ ( ordered_pair @ SY4649 @ SY4650 ) @ SY4648 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4648 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4648 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4646 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(951,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)],[807]) ).
thf(952,plain,
! [SV84: $i] :
( ( ~ ( relation @ SV84 )
| ~ ( ~ ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) )
| ~ ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(953,plain,
( ( ~ ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
| ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(954,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK78_SY4443 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK77_B @ SX0 )
!= ( sK78_SY4443 @ 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)],[810]) ).
thf(955,plain,
! [SV85: $i] :
( ( ~ ( function @ SV85 )
| ~ ( relation @ SV85 )
| ~ ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(956,plain,
! [SV86: $i] :
( ( ~ ( function @ SV86 )
| ~ ( relation @ SV86 )
| ~ ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(957,plain,
! [SV87: $i] :
( ( ~ ( ~ ! [SY4673: $i,SY4674: $i] :
( ~ ( relation @ SY4674 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4674 @ SY4673 ) ) )
| ( in @ SV87 @ ( relation_field @ SY4674 ) ) )
| ~ ! [SY4675: $i,SY4676: $i] :
( ~ ( relation @ SY4676 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4676 @ SY4675 ) ) )
| ( in @ SV87 @ SY4675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(958,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
| ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(959,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK80_SY4444 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK81_SY4446 @ 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)],[815]) ).
thf(960,plain,
! [SV88: $i] :
( ( ~ ( function @ SV88 )
| ~ ( relation @ SV88 )
| ~ ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(961,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)],[817]) ).
thf(962,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
| ~ ( epsilon_connected @ sK8_A ) )
| ~ ( ordinal @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(963,plain,
! [SV89: $i] :
( ( ~ ( relation @ SV89 )
| ! [SY4684: $i] :
( ~ ( relation @ SY4684 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4685: $i] :
( ~ ( function @ SY4685 )
| ~ ( relation @ SY4685 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4685 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SY4684 ) )
| ~ ! [SY4686: $i] :
( ~ ( function @ SY4686 )
| ~ ( relation @ SY4686 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4686 )
| ~ ( transitive @ SV89 )
| ( transitive @ SY4684 ) ) )
| ~ ! [SY4687: $i] :
( ~ ( function @ SY4687 )
| ~ ( relation @ SY4687 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4687 )
| ~ ( connected @ SV89 )
| ( connected @ SY4684 ) ) )
| ~ ! [SY4688: $i] :
( ~ ( function @ SY4688 )
| ~ ( relation @ SY4688 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4688 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SY4684 ) ) )
| ~ ! [SY4689: $i] :
( ~ ( function @ SY4689 )
| ~ ( relation @ SY4689 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4689 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SY4684 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(964,plain,
( ( ~ ( relation @ sK5_A )
| ~ ( relation_empty_yielding @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(965,plain,
! [SV90: $i] :
( ( ~ ( relation @ SV90 )
| ~ ( ~ ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) )
| ~ ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(966,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)],[822]) ).
thf(967,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(968,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ 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)],[824]) ).
thf(969,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(970,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)],[826]) ).
thf(971,plain,
! [SV91: $i] :
( ( ~ ( relation @ SV91 )
| ~ ( ~ ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) )
| ~ ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(972,plain,
! [SV92: $i] :
( ( ~ ( ~ ! [SY4698: $i,SY4699: $i] :
( ~ ( relation @ SY4699 )
| ! [SY4700: $i] :
( ~ ( in @ SY4700 @ ( relation_dom @ SY4699 ) )
| ~ ( in @ ( ordered_pair @ SY4700 @ SV92 ) @ SY4699 )
| ~ ( in @ SY4700 @ SY4698 ) )
| ( in @ SV92 @ ( relation_image @ SY4699 @ SY4698 ) ) )
| ~ ! [SY4701: $i,SY4702: $i] :
( ~ ( relation @ SY4702 )
| ~ ( in @ SV92 @ ( relation_image @ SY4702 @ SY4701 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ ( relation_dom @ SY4702 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SV92 ) @ SY4702 ) )
| ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SY4701 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(973,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)],[829]) ).
thf(974,plain,
! [SV93: $i] :
( ( ! [SY4703: $i] :
( ~ ( function @ SY4703 )
| ~ ( relation @ SY4703 )
| ~ ( ~ ! [SY4704: $i] :
( ~ ( function @ SY4704 )
| ~ ( relation @ SY4704 )
| ~ ( ~ ( in @ ( sK67_D @ SY4704 @ SY4703 @ SV93 ) @ ( relation_dom @ SY4703 ) )
| ~ ( ( ( apply @ SY4703 @ ( sK67_D @ SY4704 @ SY4703 @ SV93 ) )
!= ( apply @ SY4704 @ ( sK67_D @ SY4704 @ SY4703 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SY4703 )
!= ( set_intersection2 @ ( relation_dom @ SY4704 ) @ SV93 ) )
| ( SY4703
= ( relation_dom_restriction @ SY4704 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4705: $i] :
( ~ ( function @ SY4705 )
| ~ ( relation @ SY4705 )
| ( SY4703
!= ( relation_dom_restriction @ SY4705 @ SV93 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY4703 ) )
| ( ( apply @ SY4703 @ SX3 )
= ( apply @ SY4705 @ SX3 ) ) ) )
| ~ ! [SY4707: $i] :
( ~ ( function @ SY4707 )
| ~ ( relation @ SY4707 )
| ( SY4703
!= ( relation_dom_restriction @ SY4707 @ SV93 ) )
| ( ( relation_dom @ SY4703 )
= ( set_intersection2 @ ( relation_dom @ SY4707 ) @ SV93 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(975,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(976,plain,
! [SV94: $i] :
( ( ~ ( ~ ! [SY4708: $i,SY4709: $i] :
( ~ ( relation @ SY4709 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4708 ) @ SY4709 )
| ( in @ SV94 @ ( relation_field @ SY4709 ) ) )
| ~ ! [SY4710: $i,SY4711: $i] :
( ~ ( relation @ SY4711 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4710 ) @ SY4711 )
| ( in @ SY4710 @ ( relation_field @ SY4711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(977,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY4712: $i,SY4713: $i] :
( ~ ( relation @ SY4713 )
| ~ ( in @ SV95 @ SY4712 )
| ~ ( in @ SV95 @ ( relation_rng @ SY4713 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4712 @ SY4713 ) ) ) )
| ~ ~ ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) )
| ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(978,plain,
( ( ~ ( relation @ sK2_SY4402 )
| ~ ~ ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
| ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(979,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(980,plain,
! [SV96: $i] :
( ( ~ ( relation @ SV96 )
| ~ ( ~ ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) )
| ~ ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(981,plain,
! [SV97: $i] :
( ( ~ ( relation @ SV97 )
| ~ ( ~ ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) )
| ~ ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(982,plain,
( ( ~ ( function @ sK11_A )
| ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(983,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)],[839]) ).
thf(984,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) )
!= ( sK72_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)],[840]) ).
thf(985,plain,
! [SV1: $i,SV98: $i] :
( ( ~ ( relation @ SV98 )
| ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV98 ) ) @ ( relation_dom @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(986,plain,
! [SV2: $i,SV99: $i] :
( ( ~ ( relation @ SV99 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV99 ) ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(987,plain,
! [SV3: $i,SV100: $i] :
( ( ~ ( relation @ SV100 )
| ( subset @ ( relation_rng_restriction @ SV3 @ SV100 ) @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(988,plain,
! [SV4: $i,SV101: $i] :
( ( ~ ( relation @ SV101 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV101 ) ) @ ( relation_rng @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(989,plain,
! [SV5: $i,SV102: $i] :
( ( ~ ( relation @ SV102 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV102 ) )
= ( set_intersection2 @ ( relation_rng @ SV102 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(990,plain,
! [SV103: $i,SV6: $i] :
( ( ! [SY4736: $i] :
( ~ ( relation @ SY4736 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV6 @ SY4736 ) @ SV103 )
= ( relation_rng_restriction @ SV6 @ ( relation_dom_restriction @ SY4736 @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(991,plain,
! [SV7: $i,SV104: $i] :
( ( ~ ( relation @ SV104 )
| ( subset @ ( relation_image @ SV104 @ SV7 ) @ ( relation_rng @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(992,plain,
! [SV8: $i,SV105: $i] :
( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 )
| ( subset @ ( relation_image @ SV105 @ ( relation_inverse_image @ SV105 @ SV8 ) ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(993,plain,
! [SV9: $i,SV106: $i] :
( ( ~ ( relation @ SV106 )
| ( ( relation_image @ SV106 @ SV9 )
= ( relation_image @ SV106 @ ( set_intersection2 @ ( relation_dom @ SV106 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(994,plain,
! [SV10: $i,SV107: $i] :
( ( ~ ( relation @ SV107 )
| ~ ( subset @ SV10 @ ( relation_dom @ SV107 ) )
| ( subset @ SV10 @ ( relation_inverse_image @ SV107 @ ( relation_image @ SV107 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(995,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ( relation_image @ SV11 @ ( relation_dom @ SV11 ) )
= ( relation_rng @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(996,plain,
! [SV12: $i,SV108: $i] :
( ( ~ ( function @ SV108 )
| ~ ( relation @ SV108 )
| ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) )
| ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(997,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ! [SY4459: $i] :
( ~ ( relation @ SY4459 )
| ( ( relation_rng @ ( relation_composition @ SV13 @ SY4459 ) )
= ( relation_image @ SY4459 @ ( relation_rng @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(998,plain,
! [SV14: $i,SV109: $i] :
( ( ~ ( relation @ SV109 )
| ( subset @ ( relation_inverse_image @ SV109 @ SV14 ) @ ( relation_dom @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(999,plain,
! [SV15: $i,SV110: $i] :
( ( ~ ( relation @ SV110 )
| ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV110 ) )
| ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1000,plain,
! [SV111: $i,SV16: $i] :
( ( ! [SY4737: $i] :
( ~ ( relation @ SY4737 )
| ~ ( subset @ SV16 @ SV111 )
| ( subset @ ( relation_inverse_image @ SY4737 @ SV16 ) @ ( relation_inverse_image @ SY4737 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1001,plain,
! [SV17: $i,SV112: $i] :
( ( ~ ( relation @ SV112 )
| ( ( relation_restriction @ SV112 @ SV17 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV112 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1002,plain,
! [SV18: $i,SV113: $i] :
( ( ~ ( relation @ SV113 )
| ( ( relation_restriction @ SV113 @ SV18 )
= ( relation_rng_restriction @ SV18 @ ( relation_dom_restriction @ SV113 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1003,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( subset @ SV19 @ ( cartesian_product2 @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(1004,plain,
! [SV114: $i,SV20: $i] :
( ( ! [SY4738: $i] :
( ~ ( relation @ SY4738 )
| ( subset @ ( fiber @ ( relation_restriction @ SY4738 @ SV20 ) @ SV114 ) @ ( fiber @ SY4738 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1005,plain,
! [SV21: $i,SV115: $i] :
( ( ~ ( function @ SV115 )
| ~ ( relation @ SV115 )
| ! [SY4739: $i] :
( ~ ( function @ SY4739 )
| ~ ( relation @ SY4739 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4739 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SY4739 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SY4739 @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1006,plain,
! [SV22: $i,SV116: $i] :
( ( ~ ( relation @ SV116 )
| ~ ( reflexive @ SV116 )
| ( reflexive @ ( relation_restriction @ SV116 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1007,plain,
! [SV23: $i,SV117: $i] :
( ( ~ ( function @ SV117 )
| ~ ( relation @ SV117 )
| ! [SY4740: $i] :
( ~ ( function @ SY4740 )
| ~ ( relation @ SY4740 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SY4740 ) @ SV23 )
= ( apply @ SY4740 @ ( apply @ SV117 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1008,plain,
! [SV24: $i,SV118: $i] :
( ( ~ ( relation @ SV118 )
| ~ ( connected @ SV118 )
| ( connected @ ( relation_restriction @ SV118 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1009,plain,
! [SV25: $i,SV119: $i] :
( ( ~ ( relation @ SV119 )
| ~ ( transitive @ SV119 )
| ( transitive @ ( relation_restriction @ SV119 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1010,plain,
! [SV26: $i,SV120: $i] :
( ( ~ ( relation @ SV120 )
| ~ ( antisymmetric @ SV120 )
| ( antisymmetric @ ( relation_restriction @ SV120 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1011,plain,
! [SV27: $i,SV121: $i] :
( ( ~ ( relation @ SV121 )
| ~ ( well_founded_relation @ SV121 )
| ( well_founded_relation @ ( relation_restriction @ SV121 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1012,plain,
! [SV28: $i,SV122: $i] :
( ( ~ ( relation @ SV122 )
| ~ ( well_ordering @ SV122 )
| ( well_ordering @ ( relation_restriction @ SV122 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1013,plain,
! [SV29: $i,SV123: $i] :
( ( ~ ( relation @ SV123 )
| ~ ( subset @ SV29 @ ( relation_field @ SV123 ) )
| ~ ( well_ordering @ SV123 )
| ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1014,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY4479: $i] :
( ~ ( relation @ SY4479 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SY4479 ) ) @ ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(1015,plain,
! [SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ! [SY4480: $i] :
( ~ ( relation @ SY4480 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SY4480 ) ) @ ( relation_rng @ SY4480 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1016,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY4481: $i] :
( ~ ( relation @ SY4481 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY4481 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY4481 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1017,plain,
! [SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ! [SY4482: $i] :
( ~ ( relation @ SY4482 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY4482 ) )
| ( ( relation_rng @ ( relation_composition @ SY4482 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1018,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ! [SY4483: $i] :
( ~ ( relation @ SY4483 )
| ! [SY4484: $i] :
( ~ ( function @ SY4484 )
| ~ ( relation @ SY4484 )
| ~ ( relation_isomorphism @ SV34 @ SY4483 @ SY4484 )
| ( relation_isomorphism @ SY4483 @ SV34 @ ( function_inverse @ SY4484 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(1019,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK68_B @ SV35 ) @ ( sK69_SY4440 @ SV35 ) ) @ SV35 )
| ( SV35 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1020,plain,
! [SV36: $i] :
( ( ( ~ ( function @ SV36 )
| ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( one_to_one @ SV36 )
| ( one_to_one @ ( function_inverse @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1021,plain,
! [SV37: $i,SV124: $i] :
( ( ! [SY4741: $i] :
( ~ ( function @ SY4741 )
| ~ ( relation @ SY4741 )
| ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SY4741 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY4741 @ SV37 ) @ SV124 )
= ( apply @ SY4741 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1022,plain,
! [SV38: $i,SV125: $i] :
( ( ! [SY4742: $i] :
( ~ ( function @ SY4742 )
| ~ ( relation @ SY4742 )
| ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SY4742 @ SV38 ) @ SV125 )
= ( apply @ SY4742 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1023,plain,
! [SV39: $i,SV126: $i] :
( ( ~ ( relation @ SV126 )
| ( subset @ ( relation_dom_restriction @ SV126 @ SV39 ) @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1024,plain,
! [SV40: $i,SV127: $i] :
( ( ~ ( relation @ SV127 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV127 @ SV40 ) )
= ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1025,plain,
! [SV41: $i,SV128: $i] :
( ( ~ ( relation @ SV128 )
| ( ( relation_dom_restriction @ SV128 @ SV41 )
= ( relation_composition @ ( identity_relation @ SV41 ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1026,plain,
! [SV42: $i,SV129: $i] :
( ( ~ ( relation @ SV129 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV129 @ SV42 ) ) @ ( relation_rng @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1027,plain,
! [SV43: $i] :
( ( ( ~ ( empty @ SV43 ) )
= $true )
| ( ( function @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(1028,plain,
! [SV44: $i] :
( ( ( ~ ( empty @ SV44 ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1029,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ( relation_field @ SV45 )
= ( set_union2 @ ( relation_dom @ SV45 ) @ ( relation_rng @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(1030,plain,
! [SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ! [SY4493: $i] :
( ( relation_restriction @ SV46 @ SY4493 )
= ( set_intersection2 @ SV46 @ ( cartesian_product2 @ SY4493 @ SY4493 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(1031,plain,
! [SV47: $i] :
( ( ( ~ ( function @ SV47 )
| ~ ( relation @ SV47 ) )
= $true )
| ( ( ~ ( one_to_one @ SV47 )
| ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1032,plain,
! [SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( ! [SY4494: $i] : ( relation @ ( relation_restriction @ SV48 @ SY4494 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1033,plain,
! [SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1034,plain,
! [SV130: $i,SV50: $i] :
( ( ~ ( relation @ SV50 )
| ~ ( relation @ SV130 )
| ( relation @ ( relation_composition @ SV50 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1035,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ! [SY4496: $i] : ( relation @ ( relation_dom_restriction @ SV52 @ SY4496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1036,plain,
! [SV53: $i,SV131: $i] :
( ( ~ ( relation @ SV131 )
| ( relation @ ( relation_rng_restriction @ SV53 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1037,plain,
! [SV132: $i,SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( relation @ SV132 )
| ( relation @ ( set_intersection2 @ SV54 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1038,plain,
! [SV133: $i,SV55: $i] :
( ( ~ ( relation @ SV55 )
| ~ ( relation @ SV133 )
| ( relation @ ( set_union2 @ SV55 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1039,plain,
! [SV134: $i,SV56: $i] :
( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV134 )
| ( relation @ ( set_difference @ SV56 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1040,plain,
! [SV57: $i] :
( ( ( ( empty @ SV57 )
| ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1041,plain,
! [SV58: $i] :
( ( ( ( empty @ SV58 )
| ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(1042,plain,
! [SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV59 ) )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(1043,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK20_SY4413 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK19_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK20_SY4413 @ SX0 ) ) ) )
| ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY4413 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(1044,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)],[900]) ).
thf(1045,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(1046,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(1047,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(1048,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(1049,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK82_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(1050,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)],[903]) ).
thf(1051,plain,
! [SV60: $i] :
( ( ( ~ ( function @ SV60 )
| ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( one_to_one @ SV60 )
| ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(1052,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ( ~ ! [SY4743: $i,SY4744: $i] :
( ~ ( relation @ SY4744 )
| ~ ( in @ SV61 @ SY4743 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4744 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4743 ) @ SY4744 ) ) )
| ~ ~ ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) )
| ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1053,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(1054,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(1055,plain,
! [SV62: $i] :
( ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( ~ ( ~ ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) )
| ~ ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1056,plain,
! [SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( ~ ( ~ ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) )
| ~ ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1057,plain,
! [SV64: $i] :
( ( ~ ! [SY4531: $i,SY4532: $i] :
( ~ ( relation @ SY4532 )
| ~ ( in @ SV64 @ SY4532 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SY4531 @ SY4531 ) )
| ( in @ SV64 @ ( relation_restriction @ SY4532 @ SY4531 ) ) )
| ~ ~ ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) )
| ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1058,plain,
! [SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ~ ( ~ ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) )
| ~ ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1059,plain,
! [SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( ~ ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1060,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)],[912]) ).
thf(1061,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)],[912]) ).
thf(1062,plain,
( ( ~ ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(1063,plain,
( ( ~ ( one_to_one @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(1064,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)],[914]) ).
thf(1065,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(1066,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1067,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(1068,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(1069,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(1070,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(1071,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[917]) ).
thf(1072,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(1073,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(1074,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_orders @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(1075,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_orders @ SX0 @ ( relation_field @ SX0 ) )
| ( well_ordering @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(1076,plain,
! [SV67: $i] :
( ( ~ ! [SY4547: $i,SY4548: $i] :
( ~ ( function @ SY4548 )
| ~ ( relation @ SY4548 )
| ( SY4547
!= ( apply @ SY4548 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SY4548 ) )
| ( in @ ( ordered_pair @ SV67 @ SY4547 ) @ SY4548 ) )
| ~ ~ ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) )
| ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1077,plain,
! [SV68: $i] :
( ( ~ ! [SY4553: $i,SY4554: $i] :
( ~ ( relation @ SY4554 )
| ! [SY4555: $i] :
( ~ ( in @ SY4555 @ ( relation_rng @ SY4554 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4555 ) @ SY4554 )
| ~ ( in @ SY4555 @ SY4553 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SY4554 @ SY4553 ) ) )
| ~ ! [SY4556: $i,SY4557: $i] :
( ~ ( relation @ SY4557 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SY4557 @ SY4556 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ ( relation_rng @ SY4557 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) ) @ SY4557 ) )
| ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ SY4556 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1078,plain,
! [SV69: $i] :
( ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( ! [SY4558: $i] :
( ~ ( relation @ SY4558 )
| ~ ( ~ ! [SY4559: $i] :
( ~ ( function @ SY4559 )
| ~ ( relation @ SY4559 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4559 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4559 )
!= ( relation_field @ SY4558 ) )
| ~ ( one_to_one @ SY4559 )
| ( relation_isomorphism @ SV69 @ SY4558 @ SY4559 ) )
| ~ ~ ( ~ ! [SY4560: $i] :
( ~ ( function @ SY4560 )
| ~ ( relation @ SY4560 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4560 )
| ~ ( ~ ! [SY4561: $i,SY4562: $i] :
( ~ ( in @ SY4561 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4562 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4561 ) @ ( apply @ SY4560 @ SY4562 ) ) @ SY4558 )
| ( in @ ( ordered_pair @ SY4561 @ SY4562 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4567: $i,SY4568: $i] :
( ~ ( in @ ( ordered_pair @ SY4567 @ SY4568 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4567 ) @ ( apply @ SY4560 @ SY4568 ) ) @ SY4558 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4569: $i] :
( ~ ( function @ SY4569 )
| ~ ( relation @ SY4569 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4569 )
| ( ( relation_dom @ SY4569 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4570: $i] :
( ~ ( function @ SY4570 )
| ~ ( relation @ SY4570 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4570 )
| ( ( relation_rng @ SY4570 )
= ( relation_field @ SY4558 ) ) ) )
| ~ ! [SY4571: $i] :
( ~ ( function @ SY4571 )
| ~ ( relation @ SY4571 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4571 )
| ( one_to_one @ SY4571 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1079,plain,
! [SV70: $i] :
( ( ~ ! [SY4572: $i,SY4573: $i] :
( ~ ( relation @ SY4573 )
| ~ ( in @ SV70 @ SY4572 )
| ~ ( in @ SV70 @ ( relation_dom @ SY4573 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4573 @ SY4572 ) ) ) )
| ~ ~ ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) )
| ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1080,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(1081,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(1082,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1083,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(1084,plain,
( ( ~ ~ ( empty @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1085,plain,
( ( ~ ( relation @ sK7_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(1086,plain,
! [SV71: $i] :
( ( ( ~ ( relation @ SV71 ) )
= $true )
| ( ( ~ ( ~ ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) )
| ~ ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1087,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK43_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK43_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1088,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK42_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(1089,plain,
! [SV72: $i] :
( ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( ! [SY4584: $i] :
( ~ ( relation @ SY4584 )
| ~ ( ~ ! [SY4585: $i] :
( ~ ( relation @ SY4585 )
| ~ ( ~ ( ! [SY4586: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ SY4586 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4586 @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) ) )
| ( SY4585
= ( relation_composition @ SV72 @ SY4584 ) ) )
| ~ ! [SY4587: $i] :
( ~ ( relation @ SY4587 )
| ( SY4587
!= ( relation_composition @ SV72 @ SY4584 ) )
| ~ ( ~ ! [SY4588: $i,SY4589: $i] :
( ! [SY4590: $i] :
( ~ ( in @ ( ordered_pair @ SY4588 @ SY4590 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4590 @ SY4589 ) @ SY4584 ) )
| ( in @ ( ordered_pair @ SY4588 @ SY4589 ) @ SY4587 ) )
| ~ ! [SY4591: $i,SY4592: $i] :
( ~ ( in @ ( ordered_pair @ SY4591 @ SY4592 ) @ SY4587 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4591 @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) @ SY4592 ) @ SY4584 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1090,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)],[930]) ).
thf(1091,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)],[930]) ).
thf(1092,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK50_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK50_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1093,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK48_C @ SX1 @ SX0 ) @ ( sK49_SY4428 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[931]) ).
thf(1094,plain,
! [SV73: $i] :
( ( ( ~ ( relation @ SV73 ) )
= $true )
| ( ( ~ ( ~ ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) )
| ~ ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1095,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)],[933]) ).
thf(1096,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)],[933]) ).
thf(1097,plain,
! [SV74: $i] :
( ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( ~ ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) )
| ~ ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(1098,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SX0 )
!= ( sK76_SY4442 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK76_SY4442 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SX0 ) @ ( sK76_SY4442 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SX0 ) @ ( sK75_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(1099,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)],[935]) ).
thf(1100,plain,
! [SV75: $i] :
( ( ~ ! [SY4603: $i,SY4604: $i] :
( ~ ( relation @ SY4604 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4603 ) @ SY4604 )
| ( in @ SV75 @ ( relation_dom @ SY4604 ) ) )
| ~ ! [SY4605: $i,SY4606: $i] :
( ~ ( relation @ SY4606 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4605 ) @ SY4606 )
| ( in @ SY4605 @ ( relation_rng @ SY4606 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1101,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)],[937]) ).
thf(1102,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)],[937]) ).
thf(1103,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1104,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1105,plain,
! [SV76: $i,SV136: $i] :
( ( ~ ( function @ SV136 )
| ~ ( relation @ SV136 )
| ~ ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1106,plain,
! [SV77: $i] :
( ( ( ~ ( relation @ SV77 ) )
= $true )
| ( ( ~ ( ~ ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) )
| ~ ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1107,plain,
! [SV78: $i] :
( ( ( ~ ( function @ SV78 )
| ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1108,plain,
! [SV79: $i] :
( ( ( ~ ( relation @ SV79 ) )
= $true )
| ( ( ~ ( ~ ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) )
| ~ ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1109,plain,
! [SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ~ ( ~ ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) )
| ~ ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1110,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1111,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1112,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1113,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(1114,plain,
( ( ~ ( empty @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1115,plain,
( ( ~ ( relation @ sK10_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1116,plain,
! [SV81: $i] :
( ( ( ~ ( relation @ SV81 ) )
= $true )
| ( ( ~ ( ~ ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) )
| ~ ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1117,plain,
! [SV82: $i] :
( ( ~ ! [SY4640: $i,SY4641: $i] :
( ~ ( function @ SY4641 )
| ~ ( relation @ SY4641 )
| ~ ( in @ SY4640 @ ( relation_dom @ SY4641 ) )
| ~ ( in @ SY4640 @ SV82 )
| ( in @ SY4640 @ ( relation_dom @ ( relation_dom_restriction @ SY4641 @ SV82 ) ) ) )
| ~ ~ ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) )
| ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1118,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1119,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1120,plain,
! [SV83: $i,SV137: $i] :
( ( ~ ( relation @ SV137 )
| ~ ( ~ ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
| ~ ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1121,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1122,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1123,plain,
! [SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( ~ ( ~ ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) )
| ~ ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1124,plain,
( ( ~ ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1125,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[953]) ).
thf(1126,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK78_SY4443 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK77_B @ SX0 )
!= ( sK78_SY4443 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(1127,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)],[954]) ).
thf(1128,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 )
| ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1129,plain,
! [SV86: $i] :
( ( ( ~ ( function @ SV86 )
| ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1130,plain,
! [SV87: $i] :
( ( ~ ! [SY4673: $i,SY4674: $i] :
( ~ ( relation @ SY4674 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4674 @ SY4673 ) ) )
| ( in @ SV87 @ ( relation_field @ SY4674 ) ) )
| ~ ! [SY4675: $i,SY4676: $i] :
( ~ ( relation @ SY4676 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4676 @ SY4675 ) ) )
| ( in @ SV87 @ SY4675 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1131,plain,
( ( ~ ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1132,plain,
( ( ~ ( function @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1133,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK80_SY4444 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1134,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)],[959]) ).
thf(1135,plain,
! [SV88: $i] :
( ( ( ~ ( function @ SV88 )
| ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1136,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)],[961]) ).
thf(1137,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[961]) ).
thf(1138,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
| ~ ( epsilon_connected @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1139,plain,
( ( ~ ( ordinal @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(1140,plain,
! [SV89: $i] :
( ( ( ~ ( relation @ SV89 ) )
= $true )
| ( ( ! [SY4684: $i] :
( ~ ( relation @ SY4684 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4685: $i] :
( ~ ( function @ SY4685 )
| ~ ( relation @ SY4685 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4685 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SY4684 ) )
| ~ ! [SY4686: $i] :
( ~ ( function @ SY4686 )
| ~ ( relation @ SY4686 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4686 )
| ~ ( transitive @ SV89 )
| ( transitive @ SY4684 ) ) )
| ~ ! [SY4687: $i] :
( ~ ( function @ SY4687 )
| ~ ( relation @ SY4687 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4687 )
| ~ ( connected @ SV89 )
| ( connected @ SY4684 ) ) )
| ~ ! [SY4688: $i] :
( ~ ( function @ SY4688 )
| ~ ( relation @ SY4688 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4688 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SY4684 ) ) )
| ~ ! [SY4689: $i] :
( ~ ( function @ SY4689 )
| ~ ( relation @ SY4689 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4689 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SY4684 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1141,plain,
( ( ~ ( relation @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1142,plain,
( ( ~ ( relation_empty_yielding @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(1143,plain,
! [SV90: $i] :
( ( ( ~ ( relation @ SV90 ) )
= $true )
| ( ( ~ ( ~ ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) )
| ~ ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1144,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1145,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1146,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1147,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1148,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[968]) ).
thf(1149,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)],[968]) ).
thf(1150,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1151,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1152,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(1153,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)],[970]) ).
thf(1154,plain,
! [SV91: $i] :
( ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( ~ ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) )
| ~ ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1155,plain,
! [SV92: $i] :
( ( ~ ! [SY4698: $i,SY4699: $i] :
( ~ ( relation @ SY4699 )
| ! [SY4700: $i] :
( ~ ( in @ SY4700 @ ( relation_dom @ SY4699 ) )
| ~ ( in @ ( ordered_pair @ SY4700 @ SV92 ) @ SY4699 )
| ~ ( in @ SY4700 @ SY4698 ) )
| ( in @ SV92 @ ( relation_image @ SY4699 @ SY4698 ) ) )
| ~ ! [SY4701: $i,SY4702: $i] :
( ~ ( relation @ SY4702 )
| ~ ( in @ SV92 @ ( relation_image @ SY4702 @ SY4701 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ ( relation_dom @ SY4702 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SV92 ) @ SY4702 ) )
| ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SY4701 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1156,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1157,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1158,plain,
! [SV93: $i,SV138: $i] :
( ( ~ ( function @ SV138 )
| ~ ( relation @ SV138 )
| ~ ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1159,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1160,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1161,plain,
! [SV94: $i] :
( ( ~ ! [SY4708: $i,SY4709: $i] :
( ~ ( relation @ SY4709 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4708 ) @ SY4709 )
| ( in @ SV94 @ ( relation_field @ SY4709 ) ) )
| ~ ! [SY4710: $i,SY4711: $i] :
( ~ ( relation @ SY4711 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4710 ) @ SY4711 )
| ( in @ SY4710 @ ( relation_field @ SY4711 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1162,plain,
! [SV95: $i] :
( ( ~ ! [SY4712: $i,SY4713: $i] :
( ~ ( relation @ SY4713 )
| ~ ( in @ SV95 @ SY4712 )
| ~ ( in @ SV95 @ ( relation_rng @ SY4713 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4712 @ SY4713 ) ) ) )
| ~ ~ ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) )
| ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1163,plain,
( ( ~ ( relation @ sK2_SY4402 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1164,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
| ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(1165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1166,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1167,plain,
! [SV96: $i] :
( ( ( ~ ( relation @ SV96 ) )
= $true )
| ( ( ~ ( ~ ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) )
| ~ ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1168,plain,
! [SV97: $i] :
( ( ( ~ ( relation @ SV97 ) )
= $true )
| ( ( ~ ( ~ ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) )
| ~ ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1169,plain,
( ( ~ ( function @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1170,plain,
( ( ~ ( relation @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1171,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1172,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1173,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) )
!= ( sK72_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1174,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)],[984]) ).
thf(1175,plain,
! [SV1: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV98 ) ) @ ( relation_dom @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1176,plain,
! [SV2: $i,SV99: $i] :
( ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV99 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1177,plain,
! [SV3: $i,SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV3 @ SV100 ) @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1178,plain,
! [SV4: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV101 ) ) @ ( relation_rng @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1179,plain,
! [SV5: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV102 ) )
= ( set_intersection2 @ ( relation_rng @ SV102 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1180,plain,
! [SV103: $i,SV6: $i,SV139: $i] :
( ( ~ ( relation @ SV139 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV6 @ SV139 ) @ SV103 )
= ( relation_rng_restriction @ SV6 @ ( relation_dom_restriction @ SV139 @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1181,plain,
! [SV7: $i,SV104: $i] :
( ( ( ~ ( relation @ SV104 ) )
= $true )
| ( ( subset @ ( relation_image @ SV104 @ SV7 ) @ ( relation_rng @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1182,plain,
! [SV8: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 )
| ~ ( relation @ SV105 ) )
= $true )
| ( ( subset @ ( relation_image @ SV105 @ ( relation_inverse_image @ SV105 @ SV8 ) ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1183,plain,
! [SV9: $i,SV106: $i] :
( ( ( ~ ( relation @ SV106 ) )
= $true )
| ( ( ( relation_image @ SV106 @ SV9 )
= ( relation_image @ SV106 @ ( set_intersection2 @ ( relation_dom @ SV106 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1184,plain,
! [SV10: $i,SV107: $i] :
( ( ( ~ ( relation @ SV107 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ ( relation_dom @ SV107 ) )
| ( subset @ SV10 @ ( relation_inverse_image @ SV107 @ ( relation_image @ SV107 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1185,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ( relation_image @ SV11 @ ( relation_dom @ SV11 ) )
= ( relation_rng @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1186,plain,
! [SV12: $i,SV108: $i] :
( ( ( ~ ( function @ SV108 )
| ~ ( relation @ SV108 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) )
| ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1187,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ! [SY4459: $i] :
( ~ ( relation @ SY4459 )
| ( ( relation_rng @ ( relation_composition @ SV13 @ SY4459 ) )
= ( relation_image @ SY4459 @ ( relation_rng @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1188,plain,
! [SV14: $i,SV109: $i] :
( ( ( ~ ( relation @ SV109 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV109 @ SV14 ) @ ( relation_dom @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1189,plain,
! [SV15: $i,SV110: $i] :
( ( ( ~ ( relation @ SV110 ) )
= $true )
| ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV110 ) )
| ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1190,plain,
! [SV111: $i,SV16: $i,SV140: $i] :
( ( ~ ( relation @ SV140 )
| ~ ( subset @ SV16 @ SV111 )
| ( subset @ ( relation_inverse_image @ SV140 @ SV16 ) @ ( relation_inverse_image @ SV140 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1191,plain,
! [SV17: $i,SV112: $i] :
( ( ( ~ ( relation @ SV112 ) )
= $true )
| ( ( ( relation_restriction @ SV112 @ SV17 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV112 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1192,plain,
! [SV18: $i,SV113: $i] :
( ( ( ~ ( relation @ SV113 ) )
= $true )
| ( ( ( relation_restriction @ SV113 @ SV18 )
= ( relation_rng_restriction @ SV18 @ ( relation_dom_restriction @ SV113 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1193,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( subset @ SV19 @ ( cartesian_product2 @ ( relation_dom @ SV19 ) @ ( relation_rng @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1194,plain,
! [SV114: $i,SV20: $i,SV141: $i] :
( ( ~ ( relation @ SV141 )
| ( subset @ ( fiber @ ( relation_restriction @ SV141 @ SV20 ) @ SV114 ) @ ( fiber @ SV141 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1195,plain,
! [SV21: $i,SV115: $i] :
( ( ( ~ ( function @ SV115 )
| ~ ( relation @ SV115 ) )
= $true )
| ( ( ! [SY4739: $i] :
( ~ ( function @ SY4739 )
| ~ ( relation @ SY4739 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4739 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SY4739 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SY4739 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1196,plain,
! [SV22: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( reflexive @ SV116 )
| ( reflexive @ ( relation_restriction @ SV116 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1197,plain,
! [SV23: $i,SV117: $i] :
( ( ( ~ ( function @ SV117 )
| ~ ( relation @ SV117 ) )
= $true )
| ( ( ! [SY4740: $i] :
( ~ ( function @ SY4740 )
| ~ ( relation @ SY4740 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SY4740 ) @ SV23 )
= ( apply @ SY4740 @ ( apply @ SV117 @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1198,plain,
! [SV24: $i,SV118: $i] :
( ( ( ~ ( relation @ SV118 ) )
= $true )
| ( ( ~ ( connected @ SV118 )
| ( connected @ ( relation_restriction @ SV118 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1199,plain,
! [SV25: $i,SV119: $i] :
( ( ( ~ ( relation @ SV119 ) )
= $true )
| ( ( ~ ( transitive @ SV119 )
| ( transitive @ ( relation_restriction @ SV119 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1200,plain,
! [SV26: $i,SV120: $i] :
( ( ( ~ ( relation @ SV120 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV120 )
| ( antisymmetric @ ( relation_restriction @ SV120 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1201,plain,
! [SV27: $i,SV121: $i] :
( ( ( ~ ( relation @ SV121 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV121 )
| ( well_founded_relation @ ( relation_restriction @ SV121 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1202,plain,
! [SV28: $i,SV122: $i] :
( ( ( ~ ( relation @ SV122 ) )
= $true )
| ( ( ~ ( well_ordering @ SV122 )
| ( well_ordering @ ( relation_restriction @ SV122 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1203,plain,
! [SV29: $i,SV123: $i] :
( ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ ( relation_field @ SV123 ) )
| ~ ( well_ordering @ SV123 )
| ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1204,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY4479: $i] :
( ~ ( relation @ SY4479 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SY4479 ) ) @ ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1205,plain,
! [SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ! [SY4480: $i] :
( ~ ( relation @ SY4480 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SY4480 ) ) @ ( relation_rng @ SY4480 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1206,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY4481: $i] :
( ~ ( relation @ SY4481 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SY4481 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SY4481 ) )
= ( relation_dom @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1207,plain,
! [SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ! [SY4482: $i] :
( ~ ( relation @ SY4482 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SY4482 ) )
| ( ( relation_rng @ ( relation_composition @ SY4482 @ SV33 ) )
= ( relation_rng @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1208,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ! [SY4483: $i] :
( ~ ( relation @ SY4483 )
| ! [SY4484: $i] :
( ~ ( function @ SY4484 )
| ~ ( relation @ SY4484 )
| ~ ( relation_isomorphism @ SV34 @ SY4483 @ SY4484 )
| ( relation_isomorphism @ SY4483 @ SV34 @ ( function_inverse @ SY4484 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1209,plain,
! [SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK68_B @ SV35 ) @ ( sK69_SY4440 @ SV35 ) ) @ SV35 )
| ( SV35 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1210,plain,
! [SV36: $i] :
( ( ( ~ ( function @ SV36 ) )
= $true )
| ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( one_to_one @ SV36 )
| ( one_to_one @ ( function_inverse @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1211,plain,
! [SV37: $i,SV124: $i,SV142: $i] :
( ( ~ ( function @ SV142 )
| ~ ( relation @ SV142 )
| ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1212,plain,
! [SV38: $i,SV125: $i,SV143: $i] :
( ( ~ ( function @ SV143 )
| ~ ( relation @ SV143 )
| ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1213,plain,
! [SV39: $i,SV126: $i] :
( ( ( ~ ( relation @ SV126 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV126 @ SV39 ) @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1214,plain,
! [SV40: $i,SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV127 @ SV40 ) )
= ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1215,plain,
! [SV41: $i,SV128: $i] :
( ( ( ~ ( relation @ SV128 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV128 @ SV41 )
= ( relation_composition @ ( identity_relation @ SV41 ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1216,plain,
! [SV42: $i,SV129: $i] :
( ( ( ~ ( relation @ SV129 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV129 @ SV42 ) ) @ ( relation_rng @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1217,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
= $false )
| ( ( function @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1218,plain,
! [SV44: $i] :
( ( ( empty @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1219,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ( relation_field @ SV45 )
= ( set_union2 @ ( relation_dom @ SV45 ) @ ( relation_rng @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1220,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ! [SY4493: $i] :
( ( relation_restriction @ SV46 @ SY4493 )
= ( set_intersection2 @ SV46 @ ( cartesian_product2 @ SY4493 @ SY4493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1221,plain,
! [SV47: $i] :
( ( ( ~ ( function @ SV47 ) )
= $true )
| ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ~ ( one_to_one @ SV47 )
| ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1222,plain,
! [SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( ! [SY4494: $i] : ( relation @ ( relation_restriction @ SV48 @ SY4494 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1223,plain,
! [SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( relation @ ( relation_inverse @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1224,plain,
! [SV130: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 )
| ~ ( relation @ SV130 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV50 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1225,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( ! [SY4496: $i] : ( relation @ ( relation_dom_restriction @ SV52 @ SY4496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1226,plain,
! [SV53: $i,SV131: $i] :
( ( ( ~ ( relation @ SV131 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV53 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1227,plain,
! [SV132: $i,SV54: $i] :
( ( ( ~ ( relation @ SV54 )
| ~ ( relation @ SV132 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1228,plain,
! [SV133: $i,SV55: $i] :
( ( ( ~ ( relation @ SV55 )
| ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1229,plain,
! [SV134: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV134 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1230,plain,
! [SV57: $i] :
( ( ( empty @ SV57 )
= $true )
| ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1231,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
= $true )
| ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1232,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV59 ) )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1233,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK20_SY4413 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK19_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK20_SY4413 @ SX0 ) ) ) )
| ~ ( ( ( sK19_B @ SX0 )
!= ( sK20_SY4413 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1234,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)],[1044]) ).
thf(1235,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1237,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1238,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1239,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK82_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1240,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)],[1050]) ).
thf(1241,plain,
! [SV60: $i] :
( ( ( ~ ( function @ SV60 ) )
= $true )
| ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( one_to_one @ SV60 )
| ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1242,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ! [SY4743: $i,SY4744: $i] :
( ~ ( relation @ SY4744 )
| ~ ( in @ SV61 @ SY4743 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4744 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4743 ) @ SY4744 ) ) )
| ~ ~ ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) )
| ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1243,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1244,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ( is_reflexive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1245,plain,
! [SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( ~ ( ~ ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) )
| ~ ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1246,plain,
! [SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( ~ ( ~ ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) )
| ~ ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1247,plain,
! [SV64: $i] :
( ( ~ ! [SY4531: $i,SY4532: $i] :
( ~ ( relation @ SY4532 )
| ~ ( in @ SV64 @ SY4532 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SY4531 @ SY4531 ) )
| ( in @ SV64 @ ( relation_restriction @ SY4532 @ SY4531 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1248,plain,
! [SV64: $i] :
( ( ~ ~ ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) )
| ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1249,plain,
! [SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ~ ( ~ ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) )
| ~ ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1250,plain,
! [SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( ~ ( ~ ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1251,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)],[1060]) ).
thf(1252,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)],[1061]) ).
thf(1253,plain,
( ( ~ ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1254,plain,
( ( one_to_one @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1255,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)],[1064]) ).
thf(1256,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1257,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1258,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1259,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1260,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ( is_transitive_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1261,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1262,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1263,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1264,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1265,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_orders @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1266,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_orders @ SX0 @ ( relation_field @ SX0 ) )
| ( well_ordering @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1075]) ).
thf(1267,plain,
! [SV67: $i] :
( ( ~ ! [SY4547: $i,SY4548: $i] :
( ~ ( function @ SY4548 )
| ~ ( relation @ SY4548 )
| ( SY4547
!= ( apply @ SY4548 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SY4548 ) )
| ( in @ ( ordered_pair @ SV67 @ SY4547 ) @ SY4548 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1268,plain,
! [SV67: $i] :
( ( ~ ~ ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) )
| ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1269,plain,
! [SV68: $i] :
( ( ~ ! [SY4553: $i,SY4554: $i] :
( ~ ( relation @ SY4554 )
| ! [SY4555: $i] :
( ~ ( in @ SY4555 @ ( relation_rng @ SY4554 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4555 ) @ SY4554 )
| ~ ( in @ SY4555 @ SY4553 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SY4554 @ SY4553 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1270,plain,
! [SV68: $i] :
( ( ~ ! [SY4556: $i,SY4557: $i] :
( ~ ( relation @ SY4557 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SY4557 @ SY4556 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ ( relation_rng @ SY4557 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) ) @ SY4557 ) )
| ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ SY4556 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1271,plain,
! [SV69: $i] :
( ( ( relation @ SV69 )
= $false )
| ( ( ! [SY4558: $i] :
( ~ ( relation @ SY4558 )
| ~ ( ~ ! [SY4559: $i] :
( ~ ( function @ SY4559 )
| ~ ( relation @ SY4559 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4559 @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) ) @ ( apply @ SY4559 @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) ) @ SY4558 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4559 @ SY4558 @ SV69 ) @ ( sK22_SY4414 @ SY4559 @ SY4558 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4559 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4559 )
!= ( relation_field @ SY4558 ) )
| ~ ( one_to_one @ SY4559 )
| ( relation_isomorphism @ SV69 @ SY4558 @ SY4559 ) )
| ~ ~ ( ~ ! [SY4560: $i] :
( ~ ( function @ SY4560 )
| ~ ( relation @ SY4560 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4560 )
| ~ ( ~ ! [SY4561: $i,SY4562: $i] :
( ~ ( in @ SY4561 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4562 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4561 ) @ ( apply @ SY4560 @ SY4562 ) ) @ SY4558 )
| ( in @ ( ordered_pair @ SY4561 @ SY4562 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4567: $i,SY4568: $i] :
( ~ ( in @ ( ordered_pair @ SY4567 @ SY4568 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4560 @ SY4567 ) @ ( apply @ SY4560 @ SY4568 ) ) @ SY4558 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4569: $i] :
( ~ ( function @ SY4569 )
| ~ ( relation @ SY4569 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4569 )
| ( ( relation_dom @ SY4569 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4570: $i] :
( ~ ( function @ SY4570 )
| ~ ( relation @ SY4570 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4570 )
| ( ( relation_rng @ SY4570 )
= ( relation_field @ SY4558 ) ) ) )
| ~ ! [SY4571: $i] :
( ~ ( function @ SY4571 )
| ~ ( relation @ SY4571 )
| ~ ( relation_isomorphism @ SV69 @ SY4558 @ SY4571 )
| ( one_to_one @ SY4571 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1272,plain,
! [SV70: $i] :
( ( ~ ! [SY4572: $i,SY4573: $i] :
( ~ ( relation @ SY4573 )
| ~ ( in @ SV70 @ SY4572 )
| ~ ( in @ SV70 @ ( relation_dom @ SY4573 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4573 @ SY4572 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1273,plain,
! [SV70: $i] :
( ( ~ ~ ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) )
| ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1274,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1275,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_connected_in @ SX0 @ ( relation_field @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1276,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1277,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1278,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1279,plain,
( ( relation @ sK7_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1280,plain,
! [SV71: $i] :
( ( ( relation @ SV71 )
= $false )
| ( ( ~ ( ~ ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) )
| ~ ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1281,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( disjoint @ ( fiber @ SX0 @ SX1 ) @ ( sK43_B @ SX0 ) )
| ~ ( in @ SX1 @ ( sK43_B @ SX0 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SX0 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1282,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ! [SX1: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SX0 @ ( sK42_C @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK42_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set )
| ~ ( subset @ SX1 @ ( relation_field @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1283,plain,
! [SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( ! [SY4584: $i] :
( ~ ( relation @ SY4584 )
| ~ ( ~ ! [SY4585: $i] :
( ~ ( relation @ SY4585 )
| ~ ( ~ ( ! [SY4586: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ SY4586 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4586 @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4584 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4585 @ SY4584 @ SV72 ) @ ( sK17_SY4408 @ SY4585 @ SY4584 @ SV72 ) ) @ SY4585 ) ) )
| ( SY4585
= ( relation_composition @ SV72 @ SY4584 ) ) )
| ~ ! [SY4587: $i] :
( ~ ( relation @ SY4587 )
| ( SY4587
!= ( relation_composition @ SV72 @ SY4584 ) )
| ~ ( ~ ! [SY4588: $i,SY4589: $i] :
( ! [SY4590: $i] :
( ~ ( in @ ( ordered_pair @ SY4588 @ SY4590 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4590 @ SY4589 ) @ SY4584 ) )
| ( in @ ( ordered_pair @ SY4588 @ SY4589 ) @ SY4587 ) )
| ~ ! [SY4591: $i,SY4592: $i] :
( ~ ( in @ ( ordered_pair @ SY4591 @ SY4592 ) @ SY4587 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4591 @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4592 @ SY4591 @ SY4587 @ SY4584 @ SV72 ) @ SY4592 ) @ SY4584 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1284,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)],[1090]) ).
thf(1285,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)],[1091]) ).
thf(1286,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK50_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK50_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1287,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK48_C @ SX1 @ SX0 ) @ ( sK49_SY4428 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1288,plain,
! [SV73: $i] :
( ( ( relation @ SV73 )
= $false )
| ( ( ~ ( ~ ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) )
| ~ ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1289,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)],[1095]) ).
thf(1290,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)],[1096]) ).
thf(1291,plain,
! [SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( ~ ( ~ ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) )
| ~ ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1292,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SX0 )
!= ( sK76_SY4442 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK76_SY4442 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SX0 ) @ ( sK76_SY4442 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SX0 ) @ ( sK75_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1293,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)],[1099]) ).
thf(1294,plain,
! [SV75: $i] :
( ( ~ ! [SY4603: $i,SY4604: $i] :
( ~ ( relation @ SY4604 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4603 ) @ SY4604 )
| ( in @ SV75 @ ( relation_dom @ SY4604 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1295,plain,
! [SV75: $i] :
( ( ~ ! [SY4605: $i,SY4606: $i] :
( ~ ( relation @ SY4606 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4605 ) @ SY4606 )
| ( in @ SY4605 @ ( relation_rng @ SY4606 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1296,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)],[1101]) ).
thf(1297,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)],[1102]) ).
thf(1298,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1299,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1300,plain,
! [SV76: $i,SV136: $i] :
( ( ( ~ ( function @ SV136 )
| ~ ( relation @ SV136 ) )
= $true )
| ( ( ~ ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1301,plain,
! [SV77: $i] :
( ( ( relation @ SV77 )
= $false )
| ( ( ~ ( ~ ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) )
| ~ ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1302,plain,
! [SV78: $i] :
( ( ( ~ ( function @ SV78 ) )
= $true )
| ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1303,plain,
! [SV79: $i] :
( ( ( relation @ SV79 )
= $false )
| ( ( ~ ( ~ ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) )
| ~ ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1304,plain,
! [SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( ~ ( ~ ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) )
| ~ ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1305,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1306,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1307,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1308,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1309,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1310,plain,
( ( relation @ sK10_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1311,plain,
! [SV81: $i] :
( ( ( relation @ SV81 )
= $false )
| ( ( ~ ( ~ ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) )
| ~ ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1312,plain,
! [SV82: $i] :
( ( ~ ! [SY4640: $i,SY4641: $i] :
( ~ ( function @ SY4641 )
| ~ ( relation @ SY4641 )
| ~ ( in @ SY4640 @ ( relation_dom @ SY4641 ) )
| ~ ( in @ SY4640 @ SV82 )
| ( in @ SY4640 @ ( relation_dom @ ( relation_dom_restriction @ SY4641 @ SV82 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1313,plain,
! [SV82: $i] :
( ( ~ ~ ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) )
| ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1314,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1315,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1316,plain,
! [SV83: $i,SV137: $i] :
( ( ( ~ ( relation @ SV137 ) )
= $true )
| ( ( ~ ( ~ ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
| ~ ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1317,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1318,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1319,plain,
! [SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( ~ ( ~ ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) )
| ~ ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1320,plain,
( ( ~ ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1321,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1322,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SX0 ) @ ( sK78_SY4443 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SX0 ) @ ( sK77_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK77_B @ SX0 )
!= ( sK78_SY4443 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1323,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)],[1127]) ).
thf(1324,plain,
! [SV85: $i] :
( ( ( ~ ( function @ SV85 ) )
= $true )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1325,plain,
! [SV86: $i] :
( ( ( ~ ( function @ SV86 ) )
= $true )
| ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1326,plain,
! [SV87: $i] :
( ( ~ ! [SY4673: $i,SY4674: $i] :
( ~ ( relation @ SY4674 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4674 @ SY4673 ) ) )
| ( in @ SV87 @ ( relation_field @ SY4674 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1327,plain,
! [SV87: $i] :
( ( ~ ! [SY4675: $i,SY4676: $i] :
( ~ ( relation @ SY4676 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4676 @ SY4675 ) ) )
| ( in @ SV87 @ SY4675 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1328,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1329,plain,
( ( function @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1132]) ).
thf(1330,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK80_SY4444 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SX0 ) @ ( sK81_SY4446 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1331,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)],[1134]) ).
thf(1332,plain,
! [SV88: $i] :
( ( ( ~ ( function @ SV88 ) )
= $true )
| ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1333,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)],[1136]) ).
thf(1334,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1335,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
| ~ ( epsilon_connected @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1336,plain,
( ( ordinal @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1337,plain,
! [SV89: $i] :
( ( ( relation @ SV89 )
= $false )
| ( ( ! [SY4684: $i] :
( ~ ( relation @ SY4684 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4685: $i] :
( ~ ( function @ SY4685 )
| ~ ( relation @ SY4685 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4685 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SY4684 ) )
| ~ ! [SY4686: $i] :
( ~ ( function @ SY4686 )
| ~ ( relation @ SY4686 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4686 )
| ~ ( transitive @ SV89 )
| ( transitive @ SY4684 ) ) )
| ~ ! [SY4687: $i] :
( ~ ( function @ SY4687 )
| ~ ( relation @ SY4687 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4687 )
| ~ ( connected @ SV89 )
| ( connected @ SY4684 ) ) )
| ~ ! [SY4688: $i] :
( ~ ( function @ SY4688 )
| ~ ( relation @ SY4688 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4688 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SY4684 ) ) )
| ~ ! [SY4689: $i] :
( ~ ( function @ SY4689 )
| ~ ( relation @ SY4689 )
| ~ ( relation_isomorphism @ SV89 @ SY4684 @ SY4689 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SY4684 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1338,plain,
( ( relation @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1339,plain,
( ( relation_empty_yielding @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1340,plain,
! [SV90: $i] :
( ( ( relation @ SV90 )
= $false )
| ( ( ~ ( ~ ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) )
| ~ ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1341,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1342,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_founded_relation @ SX0 )
| ( is_well_founded_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1343,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1344,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1345,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
!= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SX1 @ SX0 )
= ( sK66_SY4439 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK65_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_C @ SX1 @ SX0 ) @ ( sK66_SY4439 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1346,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)],[1149]) ).
thf(1347,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1348,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1349,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1350,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)],[1153]) ).
thf(1351,plain,
! [SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( ~ ( ~ ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) )
| ~ ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1352,plain,
! [SV92: $i] :
( ( ~ ! [SY4698: $i,SY4699: $i] :
( ~ ( relation @ SY4699 )
| ! [SY4700: $i] :
( ~ ( in @ SY4700 @ ( relation_dom @ SY4699 ) )
| ~ ( in @ ( ordered_pair @ SY4700 @ SV92 ) @ SY4699 )
| ~ ( in @ SY4700 @ SY4698 ) )
| ( in @ SV92 @ ( relation_image @ SY4699 @ SY4698 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1353,plain,
! [SV92: $i] :
( ( ~ ! [SY4701: $i,SY4702: $i] :
( ~ ( relation @ SY4702 )
| ~ ( in @ SV92 @ ( relation_image @ SY4702 @ SY4701 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ ( relation_dom @ SY4702 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SV92 ) @ SY4702 ) )
| ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SY4701 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1354,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1355,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( is_antisymmetric_in @ SX0 @ ( relation_field @ SX0 ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1356,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ( function @ SV138 )
| ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1357,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1358,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1359,plain,
! [SV94: $i] :
( ( ~ ! [SY4708: $i,SY4709: $i] :
( ~ ( relation @ SY4709 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4708 ) @ SY4709 )
| ( in @ SV94 @ ( relation_field @ SY4709 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1360,plain,
! [SV94: $i] :
( ( ~ ! [SY4710: $i,SY4711: $i] :
( ~ ( relation @ SY4711 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4710 ) @ SY4711 )
| ( in @ SY4710 @ ( relation_field @ SY4711 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1161]) ).
thf(1361,plain,
! [SV95: $i] :
( ( ~ ! [SY4712: $i,SY4713: $i] :
( ~ ( relation @ SY4713 )
| ~ ( in @ SV95 @ SY4712 )
| ~ ( in @ SV95 @ ( relation_rng @ SY4713 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4712 @ SY4713 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1362,plain,
! [SV95: $i] :
( ( ~ ~ ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) )
| ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1363,plain,
( ( relation @ sK2_SY4402 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1364,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
| ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1365,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ ( relation_field @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1366,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_field @ ( relation_restriction @ SX1 @ SX0 ) ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1367,plain,
! [SV96: $i] :
( ( ( relation @ SV96 )
= $false )
| ( ( ~ ( ~ ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) )
| ~ ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1368,plain,
! [SV97: $i] :
( ( ( relation @ SV97 )
= $false )
| ( ( ~ ( ~ ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) )
| ~ ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1369,plain,
( ( function @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1370,plain,
( ( relation @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1371,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1372,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1373,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) )
!= ( sK72_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1374,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)],[1174]) ).
thf(1375,plain,
! [SV1: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_rng_restriction @ SV1 @ SV98 ) ) @ ( relation_dom @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1376,plain,
! [SV2: $i,SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV99 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1377,plain,
! [SV3: $i,SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV3 @ SV100 ) @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1378,plain,
! [SV4: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV101 ) ) @ ( relation_rng @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1379,plain,
! [SV5: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV102 ) )
= ( set_intersection2 @ ( relation_rng @ SV102 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1380,plain,
! [SV103: $i,SV6: $i,SV139: $i] :
( ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV6 @ SV139 ) @ SV103 )
= ( relation_rng_restriction @ SV6 @ ( relation_dom_restriction @ SV139 @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1381,plain,
! [SV7: $i,SV104: $i] :
( ( ( relation @ SV104 )
= $false )
| ( ( subset @ ( relation_image @ SV104 @ SV7 ) @ ( relation_rng @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1382,plain,
! [SV8: $i,SV105: $i] :
( ( ( ~ ( function @ SV105 ) )
= $true )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( subset @ ( relation_image @ SV105 @ ( relation_inverse_image @ SV105 @ SV8 ) ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1383,plain,
! [SV9: $i,SV106: $i] :
( ( ( relation @ SV106 )
= $false )
| ( ( ( relation_image @ SV106 @ SV9 )
= ( relation_image @ SV106 @ ( set_intersection2 @ ( relation_dom @ SV106 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1384,plain,
! [SV10: $i,SV107: $i] :
( ( ( relation @ SV107 )
= $false )
| ( ( ~ ( subset @ SV10 @ ( relation_dom @ SV107 ) )
| ( subset @ SV10 @ ( relation_inverse_image @ SV107 @ ( relation_image @ SV107 @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1385,plain,
! [SV12: $i,SV108: $i] :
( ( ( ~ ( function @ SV108 ) )
= $true )
| ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) )
| ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1386,plain,
! [SV13: $i,SV144: $i] :
( ( ( ~ ( relation @ SV144 )
| ( ( relation_rng @ ( relation_composition @ SV13 @ SV144 ) )
= ( relation_image @ SV144 @ ( relation_rng @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1387,plain,
! [SV14: $i,SV109: $i] :
( ( ( relation @ SV109 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV109 @ SV14 ) @ ( relation_dom @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1388,plain,
! [SV15: $i,SV110: $i] :
( ( ( relation @ SV110 )
= $false )
| ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV110 ) )
| ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1389,plain,
! [SV111: $i,SV16: $i,SV140: $i] :
( ( ( ~ ( relation @ SV140 ) )
= $true )
| ( ( ~ ( subset @ SV16 @ SV111 )
| ( subset @ ( relation_inverse_image @ SV140 @ SV16 ) @ ( relation_inverse_image @ SV140 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1390,plain,
! [SV17: $i,SV112: $i] :
( ( ( relation @ SV112 )
= $false )
| ( ( ( relation_restriction @ SV112 @ SV17 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV112 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1391,plain,
! [SV18: $i,SV113: $i] :
( ( ( relation @ SV113 )
= $false )
| ( ( ( relation_restriction @ SV113 @ SV18 )
= ( relation_rng_restriction @ SV18 @ ( relation_dom_restriction @ SV113 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1392,plain,
! [SV114: $i,SV20: $i,SV141: $i] :
( ( ( ~ ( relation @ SV141 ) )
= $true )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV141 @ SV20 ) @ SV114 ) @ ( fiber @ SV141 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1393,plain,
! [SV21: $i,SV115: $i] :
( ( ( ~ ( function @ SV115 ) )
= $true )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ! [SY4739: $i] :
( ~ ( function @ SY4739 )
| ~ ( relation @ SY4739 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4739 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SY4739 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SY4739 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1394,plain,
! [SV22: $i,SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( ~ ( reflexive @ SV116 )
| ( reflexive @ ( relation_restriction @ SV116 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1395,plain,
! [SV23: $i,SV117: $i] :
( ( ( ~ ( function @ SV117 ) )
= $true )
| ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( ! [SY4740: $i] :
( ~ ( function @ SY4740 )
| ~ ( relation @ SY4740 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SY4740 ) @ SV23 )
= ( apply @ SY4740 @ ( apply @ SV117 @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1396,plain,
! [SV24: $i,SV118: $i] :
( ( ( relation @ SV118 )
= $false )
| ( ( ~ ( connected @ SV118 )
| ( connected @ ( relation_restriction @ SV118 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1397,plain,
! [SV25: $i,SV119: $i] :
( ( ( relation @ SV119 )
= $false )
| ( ( ~ ( transitive @ SV119 )
| ( transitive @ ( relation_restriction @ SV119 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1398,plain,
! [SV26: $i,SV120: $i] :
( ( ( relation @ SV120 )
= $false )
| ( ( ~ ( antisymmetric @ SV120 )
| ( antisymmetric @ ( relation_restriction @ SV120 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1399,plain,
! [SV27: $i,SV121: $i] :
( ( ( relation @ SV121 )
= $false )
| ( ( ~ ( well_founded_relation @ SV121 )
| ( well_founded_relation @ ( relation_restriction @ SV121 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1400,plain,
! [SV28: $i,SV122: $i] :
( ( ( relation @ SV122 )
= $false )
| ( ( ~ ( well_ordering @ SV122 )
| ( well_ordering @ ( relation_restriction @ SV122 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1401,plain,
! [SV29: $i,SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( ~ ( subset @ SV29 @ ( relation_field @ SV123 ) )
| ~ ( well_ordering @ SV123 )
| ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1402,plain,
! [SV30: $i,SV145: $i] :
( ( ( ~ ( relation @ SV145 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SV145 ) ) @ ( relation_dom @ SV30 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1403,plain,
! [SV31: $i,SV146: $i] :
( ( ( ~ ( relation @ SV146 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SV146 ) ) @ ( relation_rng @ SV146 ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1404,plain,
! [SV32: $i,SV147: $i] :
( ( ( ~ ( relation @ SV147 )
| ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV147 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV147 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1405,plain,
! [SV33: $i,SV148: $i] :
( ( ( ~ ( relation @ SV148 )
| ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV148 ) )
| ( ( relation_rng @ ( relation_composition @ SV148 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1406,plain,
! [SV34: $i,SV149: $i] :
( ( ( ~ ( relation @ SV149 )
| ! [SY4764: $i] :
( ~ ( function @ SY4764 )
| ~ ( relation @ SY4764 )
| ~ ( relation_isomorphism @ SV34 @ SV149 @ SY4764 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SY4764 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1407,plain,
! [SV35: $i] :
( ( ( in @ ( ordered_pair @ ( sK68_B @ SV35 ) @ ( sK69_SY4440 @ SV35 ) ) @ SV35 )
= $true )
| ( ( SV35 = empty_set )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1408,plain,
! [SV36: $i] :
( ( ( function @ SV36 )
= $false )
| ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ~ ( one_to_one @ SV36 )
| ( one_to_one @ ( function_inverse @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1409,plain,
! [SV37: $i,SV124: $i,SV142: $i] :
( ( ( ~ ( function @ SV142 )
| ~ ( relation @ SV142 ) )
= $true )
| ( ( ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1410,plain,
! [SV38: $i,SV125: $i,SV143: $i] :
( ( ( ~ ( function @ SV143 )
| ~ ( relation @ SV143 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1411,plain,
! [SV39: $i,SV126: $i] :
( ( ( relation @ SV126 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV126 @ SV39 ) @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1412,plain,
! [SV40: $i,SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV127 @ SV40 ) )
= ( set_intersection2 @ ( relation_dom @ SV127 ) @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1413,plain,
! [SV41: $i,SV128: $i] :
( ( ( relation @ SV128 )
= $false )
| ( ( ( relation_dom_restriction @ SV128 @ SV41 )
= ( relation_composition @ ( identity_relation @ SV41 ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1414,plain,
! [SV42: $i,SV129: $i] :
( ( ( relation @ SV129 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV129 @ SV42 ) ) @ ( relation_rng @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1415,plain,
! [SV150: $i,SV46: $i] :
( ( ( ( relation_restriction @ SV46 @ SV150 )
= ( set_intersection2 @ SV46 @ ( cartesian_product2 @ SV150 @ SV150 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1416,plain,
! [SV47: $i] :
( ( ( function @ SV47 )
= $false )
| ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( ~ ( one_to_one @ SV47 )
| ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1417,plain,
! [SV151: $i,SV48: $i] :
( ( ( relation @ ( relation_restriction @ SV48 @ SV151 ) )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1418,plain,
! [SV130: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV50 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1419,plain,
! [SV152: $i,SV52: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV52 @ SV152 ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1420,plain,
! [SV53: $i,SV131: $i] :
( ( ( relation @ SV131 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV53 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1421,plain,
! [SV132: $i,SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1422,plain,
! [SV133: $i,SV55: $i] :
( ( ( ~ ( relation @ SV55 ) )
= $true )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1423,plain,
! [SV134: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1424,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1425,plain,
! [SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1426,plain,
! [SV153: $i] :
( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
| ( one_to_one @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1427,plain,
! [SV154: $i] :
( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 )
| ~ ( one_to_one @ SV154 )
| ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1428,plain,
! [SV155: $i] :
( ( ! [SY4767: $i] :
( ~ ( function @ SY4767 )
| ~ ( relation @ SY4767 )
| ( function @ ( relation_rng_restriction @ SV155 @ SY4767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1429,plain,
! [SV156: $i] :
( ( ! [SY4768: $i] :
( ~ ( function @ SY4768 )
| ~ ( relation @ SY4768 )
| ( relation @ ( relation_rng_restriction @ SV156 @ SY4768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1430,plain,
! [SV157: $i] :
( ( ~ ( relation @ SV157 )
| ( ( relation_dom @ SV157 )
!= empty_set )
| ( ( relation_rng @ SV157 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1431,plain,
! [SV158: $i] :
( ( ~ ( relation @ SV158 )
| ( ( relation_rng @ SV158 )
!= empty_set )
| ( ( relation_dom @ SV158 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1432,plain,
! [SV159: $i] :
( ( ~ ( relation @ SV159 )
| ~ ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
| ( reflexive @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1433,plain,
! [SV160: $i] :
( ( ~ ( relation @ SV160 )
| ~ ( reflexive @ SV160 )
| ! [SY4769: $i] :
( ~ ( in @ SY4769 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SY4769 @ SY4769 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1434,plain,
! [SV60: $i] :
( ( ( function @ SV60 )
= $false )
| ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( ~ ( one_to_one @ SV60 )
| ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1435,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ! [SY4743: $i,SY4744: $i] :
( ~ ( relation @ SY4744 )
| ~ ( in @ SV61 @ SY4743 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4744 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4743 ) @ SY4744 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1436,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ~ ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) )
| ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1437,plain,
! [SV161: $i] :
( ( ~ ( relation @ SV161 )
| ~ ( is_reflexive_in @ SV161 @ ( relation_field @ SV161 ) )
| ( reflexive @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1438,plain,
! [SV162: $i] :
( ( ~ ( relation @ SV162 )
| ~ ( reflexive @ SV162 )
| ( is_reflexive_in @ SV162 @ ( relation_field @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1439,plain,
! [SV62: $i] :
( ( ( ~ ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) )
| ~ ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1440,plain,
! [SV63: $i] :
( ( ( ~ ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) )
| ~ ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1441,plain,
! [SV64: $i] :
( ( ! [SY4531: $i,SY4532: $i] :
( ~ ( relation @ SY4532 )
| ~ ( in @ SV64 @ SY4532 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SY4531 @ SY4531 ) )
| ( in @ SV64 @ ( relation_restriction @ SY4532 @ SY4531 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1442,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) )
| ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1443,plain,
! [SV65: $i] :
( ( ( ~ ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) )
| ~ ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1444,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1445,plain,
! [SV163: $i] :
( ( ~ ( relation @ SV163 )
| ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 )
| ~ ( connected @ SV163 )
| ~ ( well_founded_relation @ SV163 )
| ( well_ordering @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1446,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)],[1252]) ).
thf(1447,plain,
( ( ~ ( function @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1448,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)],[1255]) ).
thf(1449,plain,
! [SV164: $i] :
( ( ~ ( empty @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( function @ SV164 )
| ( one_to_one @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1450,plain,
! [SV165: $i] :
( ( ~ ( empty @ SV165 )
| ( empty @ ( relation_rng @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1451,plain,
! [SV166: $i] :
( ( ~ ( empty @ SV166 )
| ( relation @ ( relation_rng @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1452,plain,
! [SV167: $i] :
( ( ~ ( relation @ SV167 )
| ~ ( is_transitive_in @ SV167 @ ( relation_field @ SV167 ) )
| ( transitive @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1453,plain,
! [SV168: $i] :
( ( ~ ( relation @ SV168 )
| ~ ( transitive @ SV168 )
| ( is_transitive_in @ SV168 @ ( relation_field @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1454,plain,
! [SV169: $i] :
( ( ! [SY4770: $i] :
( ~ ( empty @ SV169 )
| ~ ( relation @ SY4770 )
| ( empty @ ( relation_composition @ SY4770 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1455,plain,
! [SV170: $i] :
( ( ! [SY4771: $i] :
( ~ ( empty @ SV170 )
| ~ ( relation @ SY4771 )
| ( relation @ ( relation_composition @ SY4771 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1456,plain,
! [SV171: $i] :
( ( ~ ( function @ SV171 )
| ~ ( relation @ SV171 )
| ! [SY4772: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY4772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1457,plain,
! [SV172: $i] :
( ( ~ ( function @ SV172 )
| ~ ( relation @ SV172 )
| ! [SY4773: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY4773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1458,plain,
! [SV173: $i] :
( ( ~ ( relation @ SV173 )
| ~ ( well_ordering @ SV173 )
| ( well_orders @ SV173 @ ( relation_field @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1459,plain,
! [SV174: $i] :
( ( ~ ( relation @ SV174 )
| ~ ( well_orders @ SV174 @ ( relation_field @ SV174 ) )
| ( well_ordering @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1460,plain,
! [SV67: $i] :
( ( ! [SY4547: $i,SY4548: $i] :
( ~ ( function @ SY4548 )
| ~ ( relation @ SY4548 )
| ( SY4547
!= ( apply @ SY4548 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SY4548 ) )
| ( in @ ( ordered_pair @ SV67 @ SY4547 ) @ SY4548 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1461,plain,
! [SV67: $i] :
( ( ~ ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) )
| ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1462,plain,
! [SV68: $i] :
( ( ! [SY4553: $i,SY4554: $i] :
( ~ ( relation @ SY4554 )
| ! [SY4555: $i] :
( ~ ( in @ SY4555 @ ( relation_rng @ SY4554 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4555 ) @ SY4554 )
| ~ ( in @ SY4555 @ SY4553 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SY4554 @ SY4553 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1463,plain,
! [SV68: $i] :
( ( ! [SY4556: $i,SY4557: $i] :
( ~ ( relation @ SY4557 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SY4557 @ SY4556 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ ( relation_rng @ SY4557 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) ) @ SY4557 ) )
| ~ ( in @ ( sK73_D @ SY4557 @ SY4556 @ SV68 ) @ SY4556 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1464,plain,
! [SV69: $i,SV175: $i] :
( ( ( ~ ( relation @ SV175 )
| ~ ( ~ ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) )
| ~ ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1465,plain,
! [SV70: $i] :
( ( ! [SY4572: $i,SY4573: $i] :
( ~ ( relation @ SY4573 )
| ~ ( in @ SV70 @ SY4572 )
| ~ ( in @ SV70 @ ( relation_dom @ SY4573 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4573 @ SY4572 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1272]) ).
thf(1466,plain,
! [SV70: $i] :
( ( ~ ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) )
| ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1467,plain,
! [SV176: $i] :
( ( ~ ( relation @ SV176 )
| ~ ( connected @ SV176 )
| ( is_connected_in @ SV176 @ ( relation_field @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1468,plain,
! [SV177: $i] :
( ( ~ ( relation @ SV177 )
| ~ ( is_connected_in @ SV177 @ ( relation_field @ SV177 ) )
| ( connected @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1469,plain,
! [SV178: $i] :
( ( ~ ( relation @ SV178 )
| ( ( relation_dom @ SV178 )
!= empty_set )
| ( SV178 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1470,plain,
! [SV179: $i] :
( ( ~ ( relation @ SV179 )
| ( ( relation_rng @ SV179 )
!= empty_set )
| ( SV179 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1471,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1472,plain,
! [SV71: $i] :
( ( ( ~ ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) )
| ~ ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1473,plain,
! [SV180: $i] :
( ( ~ ( relation @ SV180 )
| ~ ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
| ( well_founded_relation @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1474,plain,
! [SV181: $i] :
( ( ~ ( relation @ SV181 )
| ~ ( well_founded_relation @ SV181 )
| ! [SY4788: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SY4788 @ SV181 ) ) @ SY4788 )
| ~ ( in @ ( sK42_C @ SY4788 @ SV181 ) @ SY4788 ) )
| ( SY4788 = empty_set )
| ~ ( subset @ SY4788 @ ( relation_field @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1475,plain,
! [SV72: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 )
| ~ ( ~ ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) )
| ~ ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1476,plain,
! [SV183: $i] :
( ( ! [SY4797: $i] :
( ~ ( function @ SY4797 )
| ~ ( relation @ SY4797 )
| ~ ( in @ SV183 @ ( relation_rng @ SY4797 ) )
| ~ ( one_to_one @ SY4797 )
| ( SV183
= ( apply @ SY4797 @ ( apply @ ( function_inverse @ SY4797 ) @ SV183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1477,plain,
! [SV184: $i] :
( ( ! [SY4798: $i] :
( ~ ( function @ SY4798 )
| ~ ( relation @ SY4798 )
| ~ ( in @ SV184 @ ( relation_rng @ SY4798 ) )
| ~ ( one_to_one @ SY4798 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SY4798 ) @ SY4798 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1478,plain,
! [SV185: $i] :
( ( ~ ( ~ ! [SY4799: $i,SY4800: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SY4799 @ SY4800 ) )
| ~ ( in @ ( sK50_B @ SV185 ) @ SV185 ) )
| ( relation @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1479,plain,
! [SV186: $i] :
( ( ~ ( relation @ SV186 )
| ! [SY4801: $i] :
( ( SY4801
= ( ordered_pair @ ( sK48_C @ SY4801 @ SV186 ) @ ( sK49_SY4428 @ SY4801 @ SV186 ) ) )
| ~ ( in @ SY4801 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1480,plain,
! [SV73: $i] :
( ( ( ~ ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) )
| ~ ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1481,plain,
! [SV187: $i] :
( ( ! [SY4802: $i] :
( ~ ( function @ SV187 )
| ~ ( relation @ SV187 )
| ~ ( relation @ SY4802 )
| ~ ( function @ SY4802 )
| ( function @ ( relation_composition @ SV187 @ SY4802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1482,plain,
! [SV188: $i] :
( ( ! [SY4803: $i] :
( ~ ( function @ SV188 )
| ~ ( relation @ SV188 )
| ~ ( relation @ SY4803 )
| ~ ( function @ SY4803 )
| ( relation @ ( relation_composition @ SV188 @ SY4803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1483,plain,
! [SV74: $i] :
( ( ( ~ ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) )
| ~ ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1484,plain,
! [SV189: $i] :
( ( ~ ( relation @ SV189 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
| ( connected @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1485,plain,
! [SV190: $i] :
( ( ~ ( relation @ SV190 )
| ~ ( connected @ SV190 )
| ! [SY4804: $i,SY4805: $i] :
( ( SY4804 = SY4805 )
| ~ ( in @ SY4804 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4805 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SY4804 @ SY4805 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4805 @ SY4804 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1486,plain,
! [SV75: $i] :
( ( ! [SY4603: $i,SY4604: $i] :
( ~ ( relation @ SY4604 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4603 ) @ SY4604 )
| ( in @ SV75 @ ( relation_dom @ SY4604 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1487,plain,
! [SV75: $i] :
( ( ! [SY4605: $i,SY4606: $i] :
( ~ ( relation @ SY4606 )
| ~ ( in @ ( ordered_pair @ SV75 @ SY4605 ) @ SY4606 )
| ( in @ SY4605 @ ( relation_rng @ SY4606 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1488,plain,
! [SV191: $i] :
( ( ~ ( function @ SV191 )
| ~ ( relation @ SV191 )
| ~ ( one_to_one @ SV191 )
| ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1489,plain,
! [SV192: $i] :
( ( ~ ( function @ SV192 )
| ~ ( relation @ SV192 )
| ~ ( one_to_one @ SV192 )
| ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1490,plain,
! [SV193: $i] :
( ( ~ ( empty @ SV193 )
| ( empty @ ( relation_dom @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1491,plain,
! [SV194: $i] :
( ( ~ ( empty @ SV194 )
| ( relation @ ( relation_dom @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1492,plain,
! [SV76: $i,SV136: $i] :
( ( ( ~ ( function @ SV136 ) )
= $true )
| ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( ~ ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1493,plain,
! [SV77: $i] :
( ( ( ~ ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) )
| ~ ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1494,plain,
! [SV78: $i] :
( ( ( function @ SV78 )
= $false )
| ( ( ~ ( relation @ SV78 ) )
= $true )
| ( ( ~ ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1495,plain,
! [SV79: $i] :
( ( ( ~ ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) )
| ~ ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1496,plain,
! [SV80: $i] :
( ( ( ~ ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) )
| ~ ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1497,plain,
! [SV195: $i] :
( ( ~ ( function @ SV195 )
| ~ ( relation @ SV195 )
| ~ ( one_to_one @ SV195 )
| ( function @ ( relation_inverse @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1498,plain,
! [SV196: $i] :
( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 )
| ~ ( one_to_one @ SV196 )
| ( relation @ ( relation_inverse @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1499,plain,
! [SV197: $i] :
( ( ~ ( function @ SV197 )
| ~ ( relation @ SV197 )
| ( function @ ( function_inverse @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1500,plain,
! [SV198: $i] :
( ( ~ ( function @ SV198 )
| ~ ( relation @ SV198 )
| ( relation @ ( function_inverse @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1501,plain,
! [SV81: $i] :
( ( ( ~ ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) )
| ~ ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1502,plain,
! [SV82: $i] :
( ( ! [SY4640: $i,SY4641: $i] :
( ~ ( function @ SY4641 )
| ~ ( relation @ SY4641 )
| ~ ( in @ SY4640 @ ( relation_dom @ SY4641 ) )
| ~ ( in @ SY4640 @ SV82 )
| ( in @ SY4640 @ ( relation_dom @ ( relation_dom_restriction @ SY4641 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1503,plain,
! [SV82: $i] :
( ( ~ ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) )
| ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1504,plain,
! [SV199: $i] :
( ( function @ ( identity_relation @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1505,plain,
! [SV200: $i] :
( ( relation @ ( identity_relation @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1506,plain,
! [SV83: $i,SV137: $i] :
( ( ( relation @ SV137 )
= $false )
| ( ( ~ ( ~ ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
| ~ ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1507,plain,
! [SV201: $i] :
( ( ~ ( relation @ SV201 )
| ( ( relation_rng @ SV201 )
= ( relation_dom @ ( relation_inverse @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1508,plain,
! [SV202: $i] :
( ( ~ ( relation @ SV202 )
| ( ( relation_dom @ SV202 )
= ( relation_rng @ ( relation_inverse @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1509,plain,
! [SV84: $i] :
( ( ( ~ ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) )
| ~ ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1510,plain,
( ( ~ ( empty @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1511,plain,
! [SV203: $i] :
( ( ~ ( relation @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
| ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) )
| ( antisymmetric @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1512,plain,
! [SV204: $i] :
( ( ~ ( relation @ SV204 )
| ~ ( antisymmetric @ SV204 )
| ! [SY4806: $i,SY4807: $i] :
( ~ ( in @ ( ordered_pair @ SY4806 @ SY4807 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4807 @ SY4806 ) @ SV204 )
| ( SY4806 = SY4807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1513,plain,
! [SV85: $i] :
( ( ( function @ SV85 )
= $false )
| ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1514,plain,
! [SV86: $i] :
( ( ( function @ SV86 )
= $false )
| ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ~ ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1515,plain,
! [SV87: $i] :
( ( ! [SY4673: $i,SY4674: $i] :
( ~ ( relation @ SY4674 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4674 @ SY4673 ) ) )
| ( in @ SV87 @ ( relation_field @ SY4674 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1516,plain,
! [SV87: $i] :
( ( ! [SY4675: $i,SY4676: $i] :
( ~ ( relation @ SY4676 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4676 @ SY4675 ) ) )
| ( in @ SV87 @ SY4675 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1517,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1518,plain,
! [SV205: $i] :
( ( ~ ( relation @ SV205 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ( transitive @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1519,plain,
! [SV206: $i] :
( ( ~ ( relation @ SV206 )
| ~ ( transitive @ SV206 )
| ! [SY4808: $i,SY4809: $i,SY4810: $i] :
( ~ ( in @ ( ordered_pair @ SY4808 @ SY4809 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4809 @ SY4810 ) @ SV206 )
| ( in @ ( ordered_pair @ SY4808 @ SY4810 ) @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1520,plain,
! [SV88: $i] :
( ( ( function @ SV88 )
= $false )
| ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ~ ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1521,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)],[1333]) ).
thf(1522,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
| ~ ( epsilon_connected @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1523,plain,
! [SV89: $i,SV207: $i] :
( ( ( ~ ( relation @ SV207 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
| ~ ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1524,plain,
! [SV90: $i] :
( ( ( ~ ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) )
| ~ ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1525,plain,
! [SV208: $i] :
( ( ~ ( relation @ SV208 )
| ~ ( is_well_founded_in @ SV208 @ ( relation_field @ SV208 ) )
| ( well_founded_relation @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1526,plain,
! [SV209: $i] :
( ( ~ ( relation @ SV209 )
| ~ ( well_founded_relation @ SV209 )
| ( is_well_founded_in @ SV209 @ ( relation_field @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1527,plain,
! [SV210: $i] :
( ( ! [SY4816: $i] :
( ~ ( relation @ SY4816 )
| ~ ( ~ ( ( ( sK65_C @ SY4816 @ SV210 )
!= ( sK66_SY4439 @ SY4816 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SY4816 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SY4816 @ SV210 ) @ ( sK66_SY4439 @ SY4816 @ SV210 ) ) @ SY4816 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SY4816 @ SV210 )
= ( sK66_SY4439 @ SY4816 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SY4816 @ SV210 ) @ ( sK66_SY4439 @ SY4816 @ SV210 ) ) @ SY4816 ) )
| ~ ( ( in @ ( sK65_C @ SY4816 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SY4816 @ SV210 ) @ ( sK66_SY4439 @ SY4816 @ SV210 ) ) @ SY4816 ) ) ) )
| ( SY4816
= ( identity_relation @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1528,plain,
! [SV211: $i] :
( ( ! [SY4817: $i] :
( ~ ( relation @ SY4817 )
| ( SY4817
!= ( identity_relation @ SV211 ) )
| ~ ( ~ ! [SY4818: $i,SY4819: $i] :
( ( SY4818 != SY4819 )
| ~ ( in @ SY4818 @ SV211 )
| ( in @ ( ordered_pair @ SY4818 @ SY4819 ) @ SY4817 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY4817 )
| ( SX2 = SX3 ) )
| ~ ! [SY4822: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY4822 @ SX3 ) @ SY4817 )
| ( in @ SY4822 @ SV211 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1529,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1530,plain,
! [SV212: $i] :
( ( ~ ( relation @ SV212 )
| ~ ( relation_empty_yielding @ SV212 )
| ! [SY4824: $i] : ( relation @ ( relation_dom_restriction @ SV212 @ SY4824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1531,plain,
! [SV213: $i] :
( ( ~ ( relation @ SV213 )
| ~ ( relation_empty_yielding @ SV213 )
| ! [SY4825: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SY4825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1532,plain,
! [SV91: $i] :
( ( ( ~ ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) )
| ~ ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1533,plain,
! [SV92: $i] :
( ( ! [SY4698: $i,SY4699: $i] :
( ~ ( relation @ SY4699 )
| ! [SY4700: $i] :
( ~ ( in @ SY4700 @ ( relation_dom @ SY4699 ) )
| ~ ( in @ ( ordered_pair @ SY4700 @ SV92 ) @ SY4699 )
| ~ ( in @ SY4700 @ SY4698 ) )
| ( in @ SV92 @ ( relation_image @ SY4699 @ SY4698 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1534,plain,
! [SV92: $i] :
( ( ! [SY4701: $i,SY4702: $i] :
( ~ ( relation @ SY4702 )
| ~ ( in @ SV92 @ ( relation_image @ SY4702 @ SY4701 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ ( relation_dom @ SY4702 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SV92 ) @ SY4702 ) )
| ~ ( in @ ( sK74_D @ SY4702 @ SY4701 @ SV92 ) @ SY4701 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1535,plain,
! [SV214: $i] :
( ( ~ ( relation @ SV214 )
| ~ ( antisymmetric @ SV214 )
| ( is_antisymmetric_in @ SV214 @ ( relation_field @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1536,plain,
! [SV215: $i] :
( ( ~ ( relation @ SV215 )
| ~ ( is_antisymmetric_in @ SV215 @ ( relation_field @ SV215 ) )
| ( antisymmetric @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1537,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ( function @ SV138 ) )
= $true )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1538,plain,
! [SV216: $i] :
( ( ~ ( empty @ SV216 )
| ( empty @ ( relation_inverse @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1539,plain,
! [SV217: $i] :
( ( ~ ( empty @ SV217 )
| ( relation @ ( relation_inverse @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1540,plain,
! [SV94: $i] :
( ( ! [SY4708: $i,SY4709: $i] :
( ~ ( relation @ SY4709 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4708 ) @ SY4709 )
| ( in @ SV94 @ ( relation_field @ SY4709 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1541,plain,
! [SV94: $i] :
( ( ! [SY4710: $i,SY4711: $i] :
( ~ ( relation @ SY4711 )
| ~ ( in @ ( ordered_pair @ SV94 @ SY4710 ) @ SY4711 )
| ( in @ SY4710 @ ( relation_field @ SY4711 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1542,plain,
! [SV95: $i] :
( ( ! [SY4712: $i,SY4713: $i] :
( ~ ( relation @ SY4713 )
| ~ ( in @ SV95 @ SY4712 )
| ~ ( in @ SV95 @ ( relation_rng @ SY4713 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4712 @ SY4713 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1543,plain,
! [SV95: $i] :
( ( ~ ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) )
| ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1544,plain,
( ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
| ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1545,plain,
! [SV218: $i] :
( ( ! [SY4826: $i] :
( ~ ( relation @ SY4826 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY4826 @ SV218 ) ) @ ( relation_field @ SY4826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1546,plain,
! [SV219: $i] :
( ( ! [SY4827: $i] :
( ~ ( relation @ SY4827 )
| ( subset @ ( relation_field @ ( relation_restriction @ SY4827 @ SV219 ) ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1547,plain,
! [SV96: $i] :
( ( ( ~ ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) )
| ~ ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1548,plain,
! [SV97: $i] :
( ( ( ~ ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) )
| ~ ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1549,plain,
! [SV220: $i] :
( ( ! [SY4828: $i] :
( ~ ( empty @ SV220 )
| ~ ( relation @ SY4828 )
| ( empty @ ( relation_composition @ SV220 @ SY4828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1550,plain,
! [SV221: $i] :
( ( ! [SY4829: $i] :
( ~ ( empty @ SV221 )
| ~ ( relation @ SY4829 )
| ( relation @ ( relation_composition @ SV221 @ SY4829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1551,plain,
! [SV222: $i] :
( ( ! [SY4830: $i] :
( ~ ( function @ SY4830 )
| ~ ( relation @ SY4830 )
| ~ ( ~ ( in @ ( sK72_C @ SY4830 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SY4830 @ ( sK72_C @ SY4830 @ SV222 ) )
!= ( sK72_C @ SY4830 @ SV222 ) ) ) )
| ( ( relation_dom @ SY4830 )
!= SV222 )
| ( SY4830
= ( identity_relation @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1552,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)],[1374]) ).
thf(1553,plain,
! [SV103: $i,SV6: $i,SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV6 @ SV139 ) @ SV103 )
= ( relation_rng_restriction @ SV6 @ ( relation_dom_restriction @ SV139 @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1554,plain,
! [SV8: $i,SV105: $i] :
( ( ( function @ SV105 )
= $false )
| ( ( ~ ( relation @ SV105 ) )
= $true )
| ( ( subset @ ( relation_image @ SV105 @ ( relation_inverse_image @ SV105 @ SV8 ) ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1555,plain,
! [SV107: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ ( relation_dom @ SV107 ) ) )
= $true )
| ( ( subset @ SV10 @ ( relation_inverse_image @ SV107 @ ( relation_image @ SV107 @ SV10 ) ) )
= $true )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1556,plain,
! [SV12: $i,SV108: $i] :
( ( ( function @ SV108 )
= $false )
| ( ( ~ ( relation @ SV108 ) )
= $true )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) )
| ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1557,plain,
! [SV13: $i,SV144: $i] :
( ( ( ~ ( relation @ SV144 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV13 @ SV144 ) )
= ( relation_image @ SV144 @ ( relation_rng @ SV13 ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1558,plain,
! [SV110: $i,SV15: $i] :
( ( ( ( SV15 = empty_set )
| ~ ( subset @ SV15 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1559,plain,
! [SV111: $i,SV16: $i,SV140: $i] :
( ( ( relation @ SV140 )
= $false )
| ( ( ~ ( subset @ SV16 @ SV111 )
| ( subset @ ( relation_inverse_image @ SV140 @ SV16 ) @ ( relation_inverse_image @ SV140 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1560,plain,
! [SV114: $i,SV20: $i,SV141: $i] :
( ( ( relation @ SV141 )
= $false )
| ( ( subset @ ( fiber @ ( relation_restriction @ SV141 @ SV20 ) @ SV114 ) @ ( fiber @ SV141 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1561,plain,
! [SV21: $i,SV115: $i] :
( ( ( function @ SV115 )
= $false )
| ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ! [SY4739: $i] :
( ~ ( function @ SY4739 )
| ~ ( relation @ SY4739 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4739 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SY4739 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SY4739 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1562,plain,
! [SV22: $i,SV116: $i] :
( ( ( ~ ( reflexive @ SV116 ) )
= $true )
| ( ( reflexive @ ( relation_restriction @ SV116 @ SV22 ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1563,plain,
! [SV23: $i,SV117: $i] :
( ( ( function @ SV117 )
= $false )
| ( ( ~ ( relation @ SV117 ) )
= $true )
| ( ( ! [SY4740: $i] :
( ~ ( function @ SY4740 )
| ~ ( relation @ SY4740 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SY4740 ) @ SV23 )
= ( apply @ SY4740 @ ( apply @ SV117 @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1564,plain,
! [SV24: $i,SV118: $i] :
( ( ( ~ ( connected @ SV118 ) )
= $true )
| ( ( connected @ ( relation_restriction @ SV118 @ SV24 ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1565,plain,
! [SV25: $i,SV119: $i] :
( ( ( ~ ( transitive @ SV119 ) )
= $true )
| ( ( transitive @ ( relation_restriction @ SV119 @ SV25 ) )
= $true )
| ( ( relation @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1566,plain,
! [SV26: $i,SV120: $i] :
( ( ( ~ ( antisymmetric @ SV120 ) )
= $true )
| ( ( antisymmetric @ ( relation_restriction @ SV120 @ SV26 ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1567,plain,
! [SV27: $i,SV121: $i] :
( ( ( ~ ( well_founded_relation @ SV121 ) )
= $true )
| ( ( well_founded_relation @ ( relation_restriction @ SV121 @ SV27 ) )
= $true )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1568,plain,
! [SV28: $i,SV122: $i] :
( ( ( ~ ( well_ordering @ SV122 ) )
= $true )
| ( ( well_ordering @ ( relation_restriction @ SV122 @ SV28 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1569,plain,
! [SV123: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ ( relation_field @ SV123 ) )
| ~ ( well_ordering @ SV123 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1570,plain,
! [SV30: $i,SV145: $i] :
( ( ( ~ ( relation @ SV145 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SV145 ) ) @ ( relation_dom @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1571,plain,
! [SV31: $i,SV146: $i] :
( ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SV146 ) ) @ ( relation_rng @ SV146 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1572,plain,
! [SV32: $i,SV147: $i] :
( ( ( ~ ( relation @ SV147 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV147 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV147 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1573,plain,
! [SV33: $i,SV148: $i] :
( ( ( ~ ( relation @ SV148 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV148 ) )
| ( ( relation_rng @ ( relation_composition @ SV148 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1574,plain,
! [SV34: $i,SV149: $i] :
( ( ( ~ ( relation @ SV149 ) )
= $true )
| ( ( ! [SY4764: $i] :
( ~ ( function @ SY4764 )
| ~ ( relation @ SY4764 )
| ~ ( relation_isomorphism @ SV34 @ SV149 @ SY4764 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SY4764 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1575,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( function @ SV36 )
= $false )
| ( ( ~ ( one_to_one @ SV36 )
| ( one_to_one @ ( function_inverse @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1576,plain,
! [SV37: $i,SV124: $i,SV142: $i] :
( ( ( ~ ( function @ SV142 ) )
= $true )
| ( ( ~ ( relation @ SV142 ) )
= $true )
| ( ( ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1577,plain,
! [SV38: $i,SV125: $i,SV143: $i] :
( ( ( ~ ( function @ SV143 ) )
= $true )
| ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1578,plain,
! [SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( function @ SV47 )
= $false )
| ( ( ~ ( one_to_one @ SV47 )
| ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1579,plain,
! [SV130: $i,SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( relation @ SV130 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV50 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1418]) ).
thf(1580,plain,
! [SV132: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( relation @ SV132 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1581,plain,
! [SV133: $i,SV55: $i] :
( ( ( relation @ SV55 )
= $false )
| ( ( ~ ( relation @ SV133 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1582,plain,
! [SV134: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( relation @ ( set_difference @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1583,plain,
! [SV57: $i] :
( ( ( empty @ ( relation_dom @ SV57 ) )
= $false )
| ( ( empty @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1584,plain,
! [SV58: $i] :
( ( ( empty @ ( relation_rng @ SV58 ) )
= $false )
| ( ( empty @ SV58 )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1585,plain,
! [SV153: $i] :
( ( ( ~ ( function @ SV153 )
| ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
| ( one_to_one @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1586,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1587,plain,
! [SV155: $i,SV223: $i] :
( ( ~ ( function @ SV223 )
| ~ ( relation @ SV223 )
| ( function @ ( relation_rng_restriction @ SV155 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1588,plain,
! [SV156: $i,SV224: $i] :
( ( ~ ( function @ SV224 )
| ~ ( relation @ SV224 )
| ( relation @ ( relation_rng_restriction @ SV156 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1589,plain,
! [SV157: $i] :
( ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV157 )
!= empty_set )
| ( ( relation_rng @ SV157 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1590,plain,
! [SV158: $i] :
( ( ( ~ ( relation @ SV158 ) )
= $true )
| ( ( ( ( relation_rng @ SV158 )
!= empty_set )
| ( ( relation_dom @ SV158 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1591,plain,
! [SV159: $i] :
( ( ( ~ ( relation @ SV159 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
| ( reflexive @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1592,plain,
! [SV160: $i] :
( ( ( ~ ( relation @ SV160 ) )
= $true )
| ( ( ~ ( reflexive @ SV160 )
| ! [SY4769: $i] :
( ~ ( in @ SY4769 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SY4769 @ SY4769 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1593,plain,
! [SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( ~ ( one_to_one @ SV60 )
| ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1594,plain,
! [SV135: $i,SV61: $i] :
( ( ! [SY4743: $i,SY4744: $i] :
( ~ ( relation @ SY4744 )
| ~ ( in @ SV61 @ SY4743 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4744 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4743 ) @ SY4744 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1595,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) )
| ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1596,plain,
! [SV161: $i] :
( ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ~ ( is_reflexive_in @ SV161 @ ( relation_field @ SV161 ) )
| ( reflexive @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1597,plain,
! [SV162: $i] :
( ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( reflexive @ SV162 )
| ( is_reflexive_in @ SV162 @ ( relation_field @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1598,plain,
! [SV62: $i] :
( ( ( ~ ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1599,plain,
! [SV62: $i] :
( ( ( ~ ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1600,plain,
! [SV63: $i] :
( ( ( ~ ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1601,plain,
! [SV63: $i] :
( ( ( ~ ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1602,plain,
! [SV225: $i,SV64: $i] :
( ( ! [SY4831: $i] :
( ~ ( relation @ SY4831 )
| ~ ( in @ SV64 @ SY4831 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) )
| ( in @ SV64 @ ( relation_restriction @ SY4831 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1603,plain,
! [SV64: $i] :
( ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) )
| ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1604,plain,
! [SV65: $i] :
( ( ( ~ ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1605,plain,
! [SV65: $i] :
( ( ( ~ ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1606,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1607,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1608,plain,
! [SV163: $i] :
( ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 )
| ~ ( connected @ SV163 )
| ~ ( well_founded_relation @ SV163 )
| ( well_ordering @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1609,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)],[1446]) ).
thf(1610,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1611,plain,
( ( ~ ( function @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1612,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1613,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1614,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1615,plain,
! [SV164: $i] :
( ( ( ~ ( empty @ SV164 )
| ~ ( relation @ SV164 )
| ~ ( function @ SV164 ) )
= $true )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1616,plain,
! [SV165: $i] :
( ( ( ~ ( empty @ SV165 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1617,plain,
! [SV166: $i] :
( ( ( ~ ( empty @ SV166 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1618,plain,
! [SV167: $i] :
( ( ( ~ ( relation @ SV167 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV167 @ ( relation_field @ SV167 ) )
| ( transitive @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1452]) ).
thf(1619,plain,
! [SV168: $i] :
( ( ( ~ ( relation @ SV168 ) )
= $true )
| ( ( ~ ( transitive @ SV168 )
| ( is_transitive_in @ SV168 @ ( relation_field @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1620,plain,
! [SV226: $i,SV169: $i] :
( ( ~ ( empty @ SV169 )
| ~ ( relation @ SV226 )
| ( empty @ ( relation_composition @ SV226 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1621,plain,
! [SV227: $i,SV170: $i] :
( ( ~ ( empty @ SV170 )
| ~ ( relation @ SV227 )
| ( relation @ ( relation_composition @ SV227 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1622,plain,
! [SV171: $i] :
( ( ( ~ ( function @ SV171 )
| ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY4772: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY4772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1623,plain,
! [SV172: $i] :
( ( ( ~ ( function @ SV172 )
| ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY4773: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY4773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1624,plain,
! [SV173: $i] :
( ( ( ~ ( relation @ SV173 ) )
= $true )
| ( ( ~ ( well_ordering @ SV173 )
| ( well_orders @ SV173 @ ( relation_field @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1625,plain,
! [SV174: $i] :
( ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( well_orders @ SV174 @ ( relation_field @ SV174 ) )
| ( well_ordering @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1626,plain,
! [SV67: $i,SV228: $i] :
( ( ! [SY4832: $i] :
( ~ ( function @ SY4832 )
| ~ ( relation @ SY4832 )
| ( SV228
!= ( apply @ SY4832 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SY4832 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SY4832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1627,plain,
! [SV67: $i] :
( ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) )
| ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1628,plain,
! [SV229: $i,SV68: $i] :
( ( ! [SY4833: $i] :
( ~ ( relation @ SY4833 )
| ! [SY4834: $i] :
( ~ ( in @ SY4834 @ ( relation_rng @ SY4833 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4834 ) @ SY4833 )
| ~ ( in @ SY4834 @ SV229 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SY4833 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1629,plain,
! [SV230: $i,SV68: $i] :
( ( ! [SY4835: $i] :
( ~ ( relation @ SY4835 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SY4835 @ SV230 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SY4835 @ SV230 @ SV68 ) @ ( relation_rng @ SY4835 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SY4835 @ SV230 @ SV68 ) ) @ SY4835 ) )
| ~ ( in @ ( sK73_D @ SY4835 @ SV230 @ SV68 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1630,plain,
! [SV69: $i,SV175: $i] :
( ( ( ~ ( relation @ SV175 ) )
= $true )
| ( ( ~ ( ~ ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) )
| ~ ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1631,plain,
! [SV231: $i,SV70: $i] :
( ( ! [SY4836: $i] :
( ~ ( relation @ SY4836 )
| ~ ( in @ SV70 @ SV231 )
| ~ ( in @ SV70 @ ( relation_dom @ SY4836 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4836 @ SV231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1632,plain,
! [SV70: $i] :
( ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) )
| ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1633,plain,
! [SV176: $i] :
( ( ( ~ ( relation @ SV176 ) )
= $true )
| ( ( ~ ( connected @ SV176 )
| ( is_connected_in @ SV176 @ ( relation_field @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1634,plain,
! [SV177: $i] :
( ( ( ~ ( relation @ SV177 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV177 @ ( relation_field @ SV177 ) )
| ( connected @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1635,plain,
! [SV178: $i] :
( ( ( ~ ( relation @ SV178 ) )
= $true )
| ( ( ( ( relation_dom @ SV178 )
!= empty_set )
| ( SV178 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1636,plain,
! [SV179: $i] :
( ( ( ~ ( relation @ SV179 ) )
= $true )
| ( ( ( ( relation_rng @ SV179 )
!= empty_set )
| ( SV179 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1637,plain,
! [SV71: $i] :
( ( ( ~ ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1638,plain,
! [SV71: $i] :
( ( ( ~ ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1639,plain,
! [SV180: $i] :
( ( ( ~ ( relation @ SV180 ) )
= $true )
| ( ( ~ ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
| ( well_founded_relation @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1640,plain,
! [SV181: $i] :
( ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV181 )
| ! [SY4788: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SY4788 @ SV181 ) ) @ SY4788 )
| ~ ( in @ ( sK42_C @ SY4788 @ SV181 ) @ SY4788 ) )
| ( SY4788 = empty_set )
| ~ ( subset @ SY4788 @ ( relation_field @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1641,plain,
! [SV72: $i,SV182: $i] :
( ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) )
| ~ ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1642,plain,
! [SV183: $i,SV232: $i] :
( ( ~ ( function @ SV232 )
| ~ ( relation @ SV232 )
| ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 )
| ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1643,plain,
! [SV184: $i,SV233: $i] :
( ( ~ ( function @ SV233 )
| ~ ( relation @ SV233 )
| ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1644,plain,
! [SV185: $i] :
( ( ( ~ ( ~ ! [SY4799: $i,SY4800: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SY4799 @ SY4800 ) )
| ~ ( in @ ( sK50_B @ SV185 ) @ SV185 ) ) )
= $true )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1645,plain,
! [SV186: $i] :
( ( ( ~ ( relation @ SV186 ) )
= $true )
| ( ( ! [SY4801: $i] :
( ( SY4801
= ( ordered_pair @ ( sK48_C @ SY4801 @ SV186 ) @ ( sK49_SY4428 @ SY4801 @ SV186 ) ) )
| ~ ( in @ SY4801 @ SV186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1646,plain,
! [SV73: $i] :
( ( ( ~ ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1480]) ).
thf(1647,plain,
! [SV73: $i] :
( ( ( ~ ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1480]) ).
thf(1648,plain,
! [SV234: $i,SV187: $i] :
( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 )
| ~ ( relation @ SV234 )
| ~ ( function @ SV234 )
| ( function @ ( relation_composition @ SV187 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1649,plain,
! [SV235: $i,SV188: $i] :
( ( ~ ( function @ SV188 )
| ~ ( relation @ SV188 )
| ~ ( relation @ SV235 )
| ~ ( function @ SV235 )
| ( relation @ ( relation_composition @ SV188 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1650,plain,
! [SV74: $i] :
( ( ( ~ ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) ) )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1651,plain,
! [SV74: $i] :
( ( ( ~ ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1652,plain,
! [SV189: $i] :
( ( ( ~ ( relation @ SV189 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
| ( connected @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1653,plain,
! [SV190: $i] :
( ( ( ~ ( relation @ SV190 ) )
= $true )
| ( ( ~ ( connected @ SV190 )
| ! [SY4804: $i,SY4805: $i] :
( ( SY4804 = SY4805 )
| ~ ( in @ SY4804 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4805 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SY4804 @ SY4805 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4805 @ SY4804 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1654,plain,
! [SV236: $i,SV75: $i] :
( ( ! [SY4837: $i] :
( ~ ( relation @ SY4837 )
| ~ ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SY4837 )
| ( in @ SV75 @ ( relation_dom @ SY4837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1655,plain,
! [SV237: $i,SV75: $i] :
( ( ! [SY4838: $i] :
( ~ ( relation @ SY4838 )
| ~ ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SY4838 )
| ( in @ SV237 @ ( relation_rng @ SY4838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1656,plain,
! [SV191: $i] :
( ( ( ~ ( function @ SV191 )
| ~ ( relation @ SV191 ) )
= $true )
| ( ( ~ ( one_to_one @ SV191 )
| ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1657,plain,
! [SV192: $i] :
( ( ( ~ ( function @ SV192 )
| ~ ( relation @ SV192 ) )
= $true )
| ( ( ~ ( one_to_one @ SV192 )
| ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1658,plain,
! [SV193: $i] :
( ( ( ~ ( empty @ SV193 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1659,plain,
! [SV194: $i] :
( ( ( ~ ( empty @ SV194 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1660,plain,
! [SV76: $i,SV136: $i] :
( ( ( function @ SV136 )
= $false )
| ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( ~ ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1661,plain,
! [SV77: $i] :
( ( ( ~ ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1662,plain,
! [SV77: $i] :
( ( ( ~ ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1663,plain,
! [SV78: $i] :
( ( ( relation @ SV78 )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( ~ ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1664,plain,
! [SV79: $i] :
( ( ( ~ ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1665,plain,
! [SV79: $i] :
( ( ( ~ ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1666,plain,
! [SV80: $i] :
( ( ( ~ ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1667,plain,
! [SV80: $i] :
( ( ( ~ ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1668,plain,
! [SV195: $i] :
( ( ( ~ ( function @ SV195 )
| ~ ( relation @ SV195 )
| ~ ( one_to_one @ SV195 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1669,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 )
| ~ ( one_to_one @ SV196 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1670,plain,
! [SV197: $i] :
( ( ( ~ ( function @ SV197 )
| ~ ( relation @ SV197 ) )
= $true )
| ( ( function @ ( function_inverse @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1671,plain,
! [SV198: $i] :
( ( ( ~ ( function @ SV198 )
| ~ ( relation @ SV198 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1672,plain,
! [SV81: $i] :
( ( ( ~ ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1673,plain,
! [SV81: $i] :
( ( ( ~ ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1674,plain,
! [SV82: $i,SV238: $i] :
( ( ! [SY4839: $i] :
( ~ ( function @ SY4839 )
| ~ ( relation @ SY4839 )
| ~ ( in @ SV238 @ ( relation_dom @ SY4839 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SY4839 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1675,plain,
! [SV82: $i] :
( ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) )
| ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1676,plain,
! [SV83: $i,SV137: $i] :
( ( ( ~ ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
| ~ ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1677,plain,
! [SV201: $i] :
( ( ( ~ ( relation @ SV201 ) )
= $true )
| ( ( ( relation_rng @ SV201 )
= ( relation_dom @ ( relation_inverse @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1678,plain,
! [SV202: $i] :
( ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ( relation_dom @ SV202 )
= ( relation_rng @ ( relation_inverse @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1679,plain,
! [SV84: $i] :
( ( ( ~ ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1680,plain,
! [SV84: $i] :
( ( ( ~ ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1681,plain,
( ( ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1682,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1510]) ).
thf(1683,plain,
! [SV203: $i] :
( ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
| ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) )
| ( antisymmetric @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1684,plain,
! [SV204: $i] :
( ( ( ~ ( relation @ SV204 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV204 )
| ! [SY4806: $i,SY4807: $i] :
( ~ ( in @ ( ordered_pair @ SY4806 @ SY4807 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4807 @ SY4806 ) @ SV204 )
| ( SY4806 = SY4807 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1685,plain,
! [SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1686,plain,
! [SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( ~ ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1687,plain,
! [SV239: $i,SV87: $i] :
( ( ! [SY4840: $i] :
( ~ ( relation @ SY4840 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4840 @ SV239 ) ) )
| ( in @ SV87 @ ( relation_field @ SY4840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1688,plain,
! [SV240: $i,SV87: $i] :
( ( ! [SY4841: $i] :
( ~ ( relation @ SY4841 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SY4841 @ SV240 ) ) )
| ( in @ SV87 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1689,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1690,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1517]) ).
thf(1691,plain,
! [SV205: $i] :
( ( ( ~ ( relation @ SV205 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ( transitive @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1692,plain,
! [SV206: $i] :
( ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ~ ( transitive @ SV206 )
| ! [SY4808: $i,SY4809: $i,SY4810: $i] :
( ~ ( in @ ( ordered_pair @ SY4808 @ SY4809 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4809 @ SY4810 ) @ SV206 )
| ( in @ ( ordered_pair @ SY4808 @ SY4810 ) @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1693,plain,
! [SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( ~ ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1694,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)],[1521]) ).
thf(1695,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1521]) ).
thf(1696,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1697,plain,
( ( ~ ( epsilon_connected @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1522]) ).
thf(1698,plain,
! [SV89: $i,SV207: $i] :
( ( ( ~ ( relation @ SV207 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
| ~ ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1699,plain,
! [SV90: $i] :
( ( ( ~ ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1700,plain,
! [SV90: $i] :
( ( ( ~ ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1701,plain,
! [SV208: $i] :
( ( ( ~ ( relation @ SV208 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV208 @ ( relation_field @ SV208 ) )
| ( well_founded_relation @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1702,plain,
! [SV209: $i] :
( ( ( ~ ( relation @ SV209 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV209 )
| ( is_well_founded_in @ SV209 @ ( relation_field @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1703,plain,
! [SV210: $i,SV241: $i] :
( ( ~ ( relation @ SV241 )
| ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
| ( SV241
= ( identity_relation @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1704,plain,
! [SV211: $i,SV242: $i] :
( ( ~ ( relation @ SV242 )
| ( SV242
!= ( identity_relation @ SV211 ) )
| ~ ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1705,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1706,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1707,plain,
! [SV212: $i] :
( ( ( ~ ( relation @ SV212 )
| ~ ( relation_empty_yielding @ SV212 ) )
= $true )
| ( ( ! [SY4824: $i] : ( relation @ ( relation_dom_restriction @ SV212 @ SY4824 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1708,plain,
! [SV213: $i] :
( ( ( ~ ( relation @ SV213 )
| ~ ( relation_empty_yielding @ SV213 ) )
= $true )
| ( ( ! [SY4825: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SY4825 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1709,plain,
! [SV91: $i] :
( ( ( ~ ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1710,plain,
! [SV91: $i] :
( ( ( ~ ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1711,plain,
! [SV243: $i,SV92: $i] :
( ( ! [SY4848: $i] :
( ~ ( relation @ SY4848 )
| ! [SY4849: $i] :
( ~ ( in @ SY4849 @ ( relation_dom @ SY4848 ) )
| ~ ( in @ ( ordered_pair @ SY4849 @ SV92 ) @ SY4848 )
| ~ ( in @ SY4849 @ SV243 ) )
| ( in @ SV92 @ ( relation_image @ SY4848 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1712,plain,
! [SV244: $i,SV92: $i] :
( ( ! [SY4850: $i] :
( ~ ( relation @ SY4850 )
| ~ ( in @ SV92 @ ( relation_image @ SY4850 @ SV244 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SY4850 @ SV244 @ SV92 ) @ ( relation_dom @ SY4850 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SY4850 @ SV244 @ SV92 ) @ SV92 ) @ SY4850 ) )
| ~ ( in @ ( sK74_D @ SY4850 @ SV244 @ SV92 ) @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1713,plain,
! [SV214: $i] :
( ( ( ~ ( relation @ SV214 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV214 )
| ( is_antisymmetric_in @ SV214 @ ( relation_field @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1714,plain,
! [SV215: $i] :
( ( ( ~ ( relation @ SV215 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV215 @ ( relation_field @ SV215 ) )
| ( antisymmetric @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1715,plain,
! [SV93: $i,SV138: $i] :
( ( ( function @ SV138 )
= $false )
| ( ( ~ ( relation @ SV138 ) )
= $true )
| ( ( ~ ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1716,plain,
! [SV216: $i] :
( ( ( ~ ( empty @ SV216 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1717,plain,
! [SV217: $i] :
( ( ( ~ ( empty @ SV217 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1718,plain,
! [SV245: $i,SV94: $i] :
( ( ! [SY4851: $i] :
( ~ ( relation @ SY4851 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SY4851 )
| ( in @ SV94 @ ( relation_field @ SY4851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1719,plain,
! [SV246: $i,SV94: $i] :
( ( ! [SY4852: $i] :
( ~ ( relation @ SY4852 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SY4852 )
| ( in @ SV246 @ ( relation_field @ SY4852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1720,plain,
! [SV247: $i,SV95: $i] :
( ( ! [SY4853: $i] :
( ~ ( relation @ SY4853 )
| ~ ( in @ SV95 @ SV247 )
| ~ ( in @ SV95 @ ( relation_rng @ SY4853 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SY4853 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1721,plain,
! [SV95: $i] :
( ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) )
| ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1722,plain,
( ( ~ ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1723,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1544]) ).
thf(1724,plain,
! [SV218: $i,SV248: $i] :
( ( ~ ( relation @ SV248 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV248 @ SV218 ) ) @ ( relation_field @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1725,plain,
! [SV219: $i,SV249: $i] :
( ( ~ ( relation @ SV249 )
| ( subset @ ( relation_field @ ( relation_restriction @ SV249 @ SV219 ) ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1726,plain,
! [SV96: $i] :
( ( ( ~ ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1727,plain,
! [SV96: $i] :
( ( ( ~ ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1728,plain,
! [SV97: $i] :
( ( ( ~ ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1729,plain,
! [SV97: $i] :
( ( ( ~ ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1730,plain,
! [SV250: $i,SV220: $i] :
( ( ~ ( empty @ SV220 )
| ~ ( relation @ SV250 )
| ( empty @ ( relation_composition @ SV220 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1731,plain,
! [SV251: $i,SV221: $i] :
( ( ~ ( empty @ SV221 )
| ~ ( relation @ SV251 )
| ( relation @ ( relation_composition @ SV221 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1732,plain,
! [SV222: $i,SV252: $i] :
( ( ~ ( function @ SV252 )
| ~ ( relation @ SV252 )
| ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 )
| ( SV252
= ( identity_relation @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1733,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)],[1552]) ).
thf(1734,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1735,plain,
! [SV8: $i,SV105: $i] :
( ( ( relation @ SV105 )
= $false )
| ( ( function @ SV105 )
= $false )
| ( ( subset @ ( relation_image @ SV105 @ ( relation_inverse_image @ SV105 @ SV8 ) ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1736,plain,
! [SV107: $i,SV10: $i] :
( ( ( subset @ SV10 @ ( relation_dom @ SV107 ) )
= $false )
| ( ( subset @ SV10 @ ( relation_inverse_image @ SV107 @ ( relation_image @ SV107 @ SV10 ) ) )
= $true )
| ( ( relation @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1737,plain,
! [SV12: $i,SV108: $i] :
( ( ( relation @ SV108 )
= $false )
| ( ( function @ SV108 )
= $false )
| ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) )
| ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1738,plain,
! [SV13: $i,SV144: $i] :
( ( ( relation @ SV144 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV13 @ SV144 ) )
= ( relation_image @ SV144 @ ( relation_rng @ SV13 ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1739,plain,
! [SV110: $i,SV15: $i] :
( ( ( SV15 = empty_set )
= $true )
| ( ( ~ ( subset @ SV15 @ ( relation_rng @ SV110 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1740,plain,
! [SV140: $i,SV111: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV111 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV140 @ SV16 ) @ ( relation_inverse_image @ SV140 @ SV111 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1741,plain,
! [SV21: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( function @ SV115 )
= $false )
| ( ( ! [SY4739: $i] :
( ~ ( function @ SY4739 )
| ~ ( relation @ SY4739 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SY4739 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SY4739 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SY4739 @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1742,plain,
! [SV22: $i,SV116: $i] :
( ( ( reflexive @ SV116 )
= $false )
| ( ( reflexive @ ( relation_restriction @ SV116 @ SV22 ) )
= $true )
| ( ( relation @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1743,plain,
! [SV23: $i,SV117: $i] :
( ( ( relation @ SV117 )
= $false )
| ( ( function @ SV117 )
= $false )
| ( ( ! [SY4740: $i] :
( ~ ( function @ SY4740 )
| ~ ( relation @ SY4740 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SY4740 ) @ SV23 )
= ( apply @ SY4740 @ ( apply @ SV117 @ SV23 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1744,plain,
! [SV24: $i,SV118: $i] :
( ( ( connected @ SV118 )
= $false )
| ( ( connected @ ( relation_restriction @ SV118 @ SV24 ) )
= $true )
| ( ( relation @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1745,plain,
! [SV25: $i,SV119: $i] :
( ( ( transitive @ SV119 )
= $false )
| ( ( transitive @ ( relation_restriction @ SV119 @ SV25 ) )
= $true )
| ( ( relation @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1746,plain,
! [SV26: $i,SV120: $i] :
( ( ( antisymmetric @ SV120 )
= $false )
| ( ( antisymmetric @ ( relation_restriction @ SV120 @ SV26 ) )
= $true )
| ( ( relation @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1747,plain,
! [SV27: $i,SV121: $i] :
( ( ( well_founded_relation @ SV121 )
= $false )
| ( ( well_founded_relation @ ( relation_restriction @ SV121 @ SV27 ) )
= $true )
| ( ( relation @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1748,plain,
! [SV28: $i,SV122: $i] :
( ( ( well_ordering @ SV122 )
= $false )
| ( ( well_ordering @ ( relation_restriction @ SV122 @ SV28 ) )
= $true )
| ( ( relation @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1749,plain,
! [SV123: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ ( relation_field @ SV123 ) ) )
= $true )
| ( ( ~ ( well_ordering @ SV123 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1750,plain,
! [SV30: $i,SV145: $i] :
( ( ( relation @ SV145 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV30 @ SV145 ) ) @ ( relation_dom @ SV30 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1751,plain,
! [SV31: $i,SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV31 @ SV146 ) ) @ ( relation_rng @ SV146 ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1752,plain,
! [SV32: $i,SV147: $i] :
( ( ( relation @ SV147 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV147 ) )
| ( ( relation_dom @ ( relation_composition @ SV32 @ SV147 ) )
= ( relation_dom @ SV32 ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1753,plain,
! [SV33: $i,SV148: $i] :
( ( ( relation @ SV148 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV148 ) )
| ( ( relation_rng @ ( relation_composition @ SV148 @ SV33 ) )
= ( relation_rng @ SV33 ) ) )
= $true )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1754,plain,
! [SV34: $i,SV149: $i] :
( ( ( relation @ SV149 )
= $false )
| ( ( ! [SY4764: $i] :
( ~ ( function @ SY4764 )
| ~ ( relation @ SY4764 )
| ~ ( relation_isomorphism @ SV34 @ SV149 @ SY4764 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SY4764 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1755,plain,
! [SV36: $i] :
( ( ( ~ ( one_to_one @ SV36 ) )
= $true )
| ( ( one_to_one @ ( function_inverse @ SV36 ) )
= $true )
| ( ( function @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1756,plain,
! [SV37: $i,SV124: $i,SV142: $i] :
( ( ( function @ SV142 )
= $false )
| ( ( ~ ( relation @ SV142 ) )
= $true )
| ( ( ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1757,plain,
! [SV38: $i,SV125: $i,SV143: $i] :
( ( ( function @ SV143 )
= $false )
| ( ( ~ ( relation @ SV143 ) )
= $true )
| ( ( ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1758,plain,
! [SV47: $i] :
( ( ( ~ ( one_to_one @ SV47 ) )
= $true )
| ( ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) )
= $true )
| ( ( function @ SV47 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1759,plain,
! [SV50: $i,SV130: $i] :
( ( ( relation @ SV130 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( relation @ ( relation_composition @ SV50 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1760,plain,
! [SV54: $i,SV132: $i] :
( ( ( relation @ SV132 )
= $false )
| ( ( relation @ SV54 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV54 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1761,plain,
! [SV55: $i,SV133: $i] :
( ( ( relation @ SV133 )
= $false )
| ( ( relation @ SV55 )
= $false )
| ( ( relation @ ( set_union2 @ SV55 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1762,plain,
! [SV56: $i,SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( relation @ ( set_difference @ SV56 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1763,plain,
! [SV153: $i] :
( ( ( ~ ( function @ SV153 ) )
= $true )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
| ( one_to_one @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1764,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 ) )
= $true )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1765,plain,
! [SV155: $i,SV223: $i] :
( ( ( ~ ( function @ SV223 )
| ~ ( relation @ SV223 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV155 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1766,plain,
! [SV156: $i,SV224: $i] :
( ( ( ~ ( function @ SV224 )
| ~ ( relation @ SV224 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV156 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1767,plain,
! [SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( ( ( relation_dom @ SV157 )
!= empty_set )
| ( ( relation_rng @ SV157 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1768,plain,
! [SV158: $i] :
( ( ( relation @ SV158 )
= $false )
| ( ( ( ( relation_rng @ SV158 )
!= empty_set )
| ( ( relation_dom @ SV158 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1769,plain,
! [SV159: $i] :
( ( ( relation @ SV159 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
| ( reflexive @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1770,plain,
! [SV160: $i] :
( ( ( relation @ SV160 )
= $false )
| ( ( ~ ( reflexive @ SV160 )
| ! [SY4769: $i] :
( ~ ( in @ SY4769 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SY4769 @ SY4769 ) @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1771,plain,
! [SV60: $i] :
( ( ( ~ ( one_to_one @ SV60 ) )
= $true )
| ( ( ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1772,plain,
! [SV135: $i,SV253: $i,SV61: $i] :
( ( ! [SY4854: $i] :
( ~ ( relation @ SY4854 )
| ~ ( in @ SV61 @ SV253 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4854 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SY4854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1773,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) )
| ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1774,plain,
! [SV161: $i] :
( ( ( relation @ SV161 )
= $false )
| ( ( ~ ( is_reflexive_in @ SV161 @ ( relation_field @ SV161 ) )
| ( reflexive @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1775,plain,
! [SV162: $i] :
( ( ( relation @ SV162 )
= $false )
| ( ( ~ ( reflexive @ SV162 )
| ( is_reflexive_in @ SV162 @ ( relation_field @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1776,plain,
! [SV62: $i] :
( ( ( ! [SY4519: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SY4519 @ SV62 ) @ SY4519 )
| ~ ( in @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ SY4519 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SY4519 @ SV62 ) @ ( sK34_SY4421 @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SY4519 @ SV62 ) @ ( sK33_C @ SY4519 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SY4519 @ SV62 )
!= ( sK34_SY4421 @ SY4519 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SY4519 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1598]) ).
thf(1777,plain,
! [SV62: $i] :
( ( ( ! [SY4520: $i] :
( ~ ( is_antisymmetric_in @ SV62 @ SY4520 )
| ! [SY4521: $i,SY4522: $i] :
( ~ ( in @ SY4521 @ SY4520 )
| ~ ( in @ SY4522 @ SY4520 )
| ~ ( in @ ( ordered_pair @ SY4521 @ SY4522 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4522 @ SY4521 ) @ SV62 )
| ( SY4521 = SY4522 ) ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1778,plain,
! [SV63: $i] :
( ( ( ! [SY4523: $i,SY4524: $i] :
( ~ ( ~ ( ! [SY4525: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4525 ) @ SV63 )
| ~ ( in @ SY4525 @ SY4523 ) )
| ~ ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4524 @ SY4523 @ SV63 ) @ SY4523 ) )
| ( in @ ( sK52_D @ SY4524 @ SY4523 @ SV63 ) @ SY4524 ) ) )
| ( SY4524
= ( relation_inverse_image @ SV63 @ SY4523 ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1779,plain,
! [SV63: $i] :
( ( ( ! [SY4526: $i,SY4527: $i] :
( ( SY4527
!= ( relation_inverse_image @ SV63 @ SY4526 ) )
| ~ ( ~ ! [SY4528: $i] :
( ! [SY4529: $i] :
( ~ ( in @ ( ordered_pair @ SY4528 @ SY4529 ) @ SV63 )
| ~ ( in @ SY4529 @ SY4526 ) )
| ( in @ SY4528 @ SY4527 ) )
| ~ ! [SY4530: $i] :
( ~ ( in @ SY4530 @ SY4527 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4530 @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4530 @ SY4527 @ SY4526 @ SV63 ) @ SY4526 ) ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1780,plain,
! [SV225: $i,SV64: $i,SV254: $i] :
( ( ~ ( relation @ SV254 )
| ~ ( in @ SV64 @ SV254 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) )
| ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1781,plain,
! [SV64: $i] :
( ( ~ ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1782,plain,
! [SV64: $i] :
( ( ~ ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1783,plain,
! [SV65: $i] :
( ( ( ! [SY4537: $i] :
( ~ ( relation @ SY4537 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SY4537 @ SV65 ) @ ( sK41_SY4425 @ SY4537 @ SV65 ) ) @ SY4537 ) )
| ( subset @ SV65 @ SY4537 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1784,plain,
! [SV65: $i] :
( ( ( ! [SY4538: $i] :
( ~ ( relation @ SY4538 )
| ~ ( subset @ SV65 @ SY4538 )
| ! [SY4539: $i,SY4540: $i] :
( ~ ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4539 @ SY4540 ) @ SY4538 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1785,plain,
! [SV66: $i] :
( ( ( ! [SY4541: $i] :
( ~ ( is_reflexive_in @ SV66 @ SY4541 )
| ~ ( is_transitive_in @ SV66 @ SY4541 )
| ~ ( is_antisymmetric_in @ SV66 @ SY4541 )
| ~ ( is_connected_in @ SV66 @ SY4541 )
| ~ ( is_well_founded_in @ SV66 @ SY4541 )
| ( well_orders @ SV66 @ SY4541 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1786,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1787,plain,
! [SV163: $i] :
( ( ( relation @ SV163 )
= $false )
| ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 )
| ~ ( connected @ SV163 )
| ~ ( well_founded_relation @ SV163 )
| ( well_ordering @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1788,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)],[1609]) ).
thf(1789,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( well_founded_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1790,plain,
( ( function @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1791,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1792,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1793,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1794,plain,
! [SV164: $i] :
( ( ( ~ ( empty @ SV164 )
| ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1795,plain,
! [SV165: $i] :
( ( ( empty @ SV165 )
= $false )
| ( ( empty @ ( relation_rng @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1796,plain,
! [SV166: $i] :
( ( ( empty @ SV166 )
= $false )
| ( ( relation @ ( relation_rng @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1797,plain,
! [SV167: $i] :
( ( ( relation @ SV167 )
= $false )
| ( ( ~ ( is_transitive_in @ SV167 @ ( relation_field @ SV167 ) )
| ( transitive @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1798,plain,
! [SV168: $i] :
( ( ( relation @ SV168 )
= $false )
| ( ( ~ ( transitive @ SV168 )
| ( is_transitive_in @ SV168 @ ( relation_field @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1799,plain,
! [SV226: $i,SV169: $i] :
( ( ( ~ ( empty @ SV169 )
| ~ ( relation @ SV226 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV226 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1800,plain,
! [SV227: $i,SV170: $i] :
( ( ( ~ ( empty @ SV170 )
| ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV227 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1801,plain,
! [SV171: $i] :
( ( ( ~ ( function @ SV171 ) )
= $true )
| ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY4772: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY4772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1802,plain,
! [SV172: $i] :
( ( ( ~ ( function @ SV172 ) )
= $true )
| ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY4773: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY4773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1803,plain,
! [SV173: $i] :
( ( ( relation @ SV173 )
= $false )
| ( ( ~ ( well_ordering @ SV173 )
| ( well_orders @ SV173 @ ( relation_field @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1804,plain,
! [SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( ~ ( well_orders @ SV174 @ ( relation_field @ SV174 ) )
| ( well_ordering @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1805,plain,
! [SV67: $i,SV228: $i,SV255: $i] :
( ( ~ ( function @ SV255 )
| ~ ( relation @ SV255 )
| ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1806,plain,
! [SV67: $i] :
( ( ~ ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1807,plain,
! [SV67: $i] :
( ( ~ ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1627]) ).
thf(1808,plain,
! [SV229: $i,SV68: $i,SV256: $i] :
( ( ~ ( relation @ SV256 )
| ! [SY4855: $i] :
( ~ ( in @ SY4855 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4855 ) @ SV256 )
| ~ ( in @ SY4855 @ SV229 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1809,plain,
! [SV230: $i,SV68: $i,SV257: $i] :
( ( ~ ( relation @ SV257 )
| ~ ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1810,plain,
! [SV69: $i,SV175: $i] :
( ( ( relation @ SV175 )
= $false )
| ( ( ~ ( ~ ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) )
| ~ ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) ) )
= $true )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1811,plain,
! [SV231: $i,SV70: $i,SV258: $i] :
( ( ~ ( relation @ SV258 )
| ~ ( in @ SV70 @ SV231 )
| ~ ( in @ SV70 @ ( relation_dom @ SV258 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1812,plain,
! [SV70: $i] :
( ( ~ ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1813,plain,
! [SV70: $i] :
( ( ~ ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1632]) ).
thf(1814,plain,
! [SV176: $i] :
( ( ( relation @ SV176 )
= $false )
| ( ( ~ ( connected @ SV176 )
| ( is_connected_in @ SV176 @ ( relation_field @ SV176 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1815,plain,
! [SV177: $i] :
( ( ( relation @ SV177 )
= $false )
| ( ( ~ ( is_connected_in @ SV177 @ ( relation_field @ SV177 ) )
| ( connected @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1816,plain,
! [SV178: $i] :
( ( ( relation @ SV178 )
= $false )
| ( ( ( ( relation_dom @ SV178 )
!= empty_set )
| ( SV178 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1817,plain,
! [SV179: $i] :
( ( ( relation @ SV179 )
= $false )
| ( ( ( ( relation_rng @ SV179 )
!= empty_set )
| ( SV179 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1818,plain,
! [SV71: $i] :
( ( ( ! [SY4578: $i] :
( ~ ( relation @ SY4578 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SY4578 @ SV71 ) @ ( sK24_SY4415 @ SY4578 @ SV71 ) ) @ SY4578 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SY4578 @ SV71 ) @ ( sK23_C @ SY4578 @ SV71 ) ) @ SV71 ) ) )
| ( SY4578
= ( relation_inverse @ SV71 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1819,plain,
! [SV71: $i] :
( ( ( ! [SY4579: $i] :
( ~ ( relation @ SY4579 )
| ( SY4579
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4580: $i,SY4581: $i] :
( ~ ( in @ ( ordered_pair @ SY4580 @ SY4581 ) @ SY4579 )
| ( in @ ( ordered_pair @ SY4581 @ SY4580 ) @ SV71 ) )
| ~ ! [SY4582: $i,SY4583: $i] :
( ~ ( in @ ( ordered_pair @ SY4583 @ SY4582 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4582 @ SY4583 ) @ SY4579 ) ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1820,plain,
! [SV180: $i] :
( ( ( relation @ SV180 )
= $false )
| ( ( ~ ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
| ( well_founded_relation @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1821,plain,
! [SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( ~ ( well_founded_relation @ SV181 )
| ! [SY4788: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SY4788 @ SV181 ) ) @ SY4788 )
| ~ ( in @ ( sK42_C @ SY4788 @ SV181 ) @ SY4788 ) )
| ( SY4788 = empty_set )
| ~ ( subset @ SY4788 @ ( relation_field @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1822,plain,
! [SV72: $i,SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( ~ ( ~ ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) )
| ~ ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1823,plain,
! [SV183: $i,SV232: $i] :
( ( ( ~ ( function @ SV232 )
| ~ ( relation @ SV232 ) )
= $true )
| ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 )
| ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1824,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( function @ SV233 )
| ~ ( relation @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1825,plain,
! [SV185: $i] :
( ( ( ~ ! [SY4799: $i,SY4800: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SY4799 @ SY4800 ) )
| ~ ( in @ ( sK50_B @ SV185 ) @ SV185 ) )
= $false )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1826,plain,
! [SV186: $i] :
( ( ( relation @ SV186 )
= $false )
| ( ( ! [SY4801: $i] :
( ( SY4801
= ( ordered_pair @ ( sK48_C @ SY4801 @ SV186 ) @ ( sK49_SY4428 @ SY4801 @ SV186 ) ) )
| ~ ( in @ SY4801 @ SV186 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1827,plain,
! [SV73: $i] :
( ( ( ! [SY4593: $i] :
( ~ ( ~ ( ! [SY4594: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ SY4594 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SY4593 @ SV73 ) @ ( sK37_SY4423 @ SY4593 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SY4593 @ SV73 ) @ SY4593 ) ) )
| ( SY4593
= ( relation_dom @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1828,plain,
! [SV73: $i] :
( ( ( ! [SY4595: $i] :
( ( SY4595
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4596: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4596 @ SY4597 ) @ SV73 )
| ( in @ SY4596 @ SY4595 ) )
| ~ ! [SY4598: $i] :
( ~ ( in @ SY4598 @ SY4595 )
| ( in @ ( ordered_pair @ SY4598 @ ( sK35_D @ SY4598 @ SY4595 @ SV73 ) ) @ SV73 ) ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1829,plain,
! [SV234: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 )
| ~ ( relation @ SV234 )
| ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1830,plain,
! [SV235: $i,SV188: $i] :
( ( ( ~ ( function @ SV188 )
| ~ ( relation @ SV188 )
| ~ ( relation @ SV235 )
| ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1831,plain,
! [SV74: $i] :
( ( ( ! [SY4599: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SY4599 @ SV74 )
!= ( sK26_SY4416 @ SY4599 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SY4599 @ SV74 ) @ SY4599 )
| ~ ( in @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ SY4599 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SY4599 @ SV74 ) @ ( sK26_SY4416 @ SY4599 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SY4599 @ SV74 ) @ ( sK25_C @ SY4599 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SY4599 ) ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1832,plain,
! [SV74: $i] :
( ( ( ! [SY4600: $i] :
( ~ ( is_connected_in @ SV74 @ SY4600 )
| ! [SY4601: $i,SY4602: $i] :
( ( SY4601 = SY4602 )
| ~ ( in @ SY4601 @ SY4600 )
| ~ ( in @ SY4602 @ SY4600 )
| ( in @ ( ordered_pair @ SY4601 @ SY4602 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4602 @ SY4601 ) @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1833,plain,
! [SV189: $i] :
( ( ( relation @ SV189 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
| ( connected @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1834,plain,
! [SV190: $i] :
( ( ( relation @ SV190 )
= $false )
| ( ( ~ ( connected @ SV190 )
| ! [SY4804: $i,SY4805: $i] :
( ( SY4804 = SY4805 )
| ~ ( in @ SY4804 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4805 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SY4804 @ SY4805 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4805 @ SY4804 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1835,plain,
! [SV236: $i,SV75: $i,SV259: $i] :
( ( ~ ( relation @ SV259 )
| ~ ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SV259 )
| ( in @ SV75 @ ( relation_dom @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1836,plain,
! [SV237: $i,SV75: $i,SV260: $i] :
( ( ~ ( relation @ SV260 )
| ~ ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SV260 )
| ( in @ SV237 @ ( relation_rng @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1837,plain,
! [SV191: $i] :
( ( ( ~ ( function @ SV191 ) )
= $true )
| ( ( ~ ( relation @ SV191 ) )
= $true )
| ( ( ~ ( one_to_one @ SV191 )
| ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1838,plain,
! [SV192: $i] :
( ( ( ~ ( function @ SV192 ) )
= $true )
| ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ~ ( one_to_one @ SV192 )
| ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1839,plain,
! [SV193: $i] :
( ( ( empty @ SV193 )
= $false )
| ( ( empty @ ( relation_dom @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1840,plain,
! [SV194: $i] :
( ( ( empty @ SV194 )
= $false )
| ( ( relation @ ( relation_dom @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1841,plain,
! [SV76: $i,SV136: $i] :
( ( ( relation @ SV136 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( ~ ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1842,plain,
! [SV77: $i] :
( ( ( ! [SY4611: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SY4611 @ SV77 ) @ SY4611 )
| ~ ( in @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( sK14_SY4407 @ SY4611 @ SV77 ) @ SY4611 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK13_SY4405 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SY4611 @ SV77 ) @ ( sK14_SY4407 @ SY4611 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SY4611 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1843,plain,
! [SV77: $i] :
( ( ( ! [SY4612: $i] :
( ~ ( is_transitive_in @ SV77 @ SY4612 )
| ! [SY4613: $i,SY4614: $i,SY4615: $i] :
( ~ ( in @ SY4613 @ SY4612 )
| ~ ( in @ SY4614 @ SY4612 )
| ~ ( in @ SY4615 @ SY4612 )
| ~ ( in @ ( ordered_pair @ SY4613 @ SY4614 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4614 @ SY4615 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4613 @ SY4615 ) @ SV77 ) ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1844,plain,
! [SV78: $i] :
( ( ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) )
| ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1845,plain,
! [SV79: $i] :
( ( ( ! [SY4624: $i,SY4625: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
= SY4624 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4625 @ SY4624 @ SV79 )
!= SY4624 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4624 ) @ SV79 )
| ( in @ ( sK46_D @ SY4625 @ SY4624 @ SV79 ) @ SY4625 ) ) ) )
| ( SY4625
= ( fiber @ SV79 @ SY4624 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1846,plain,
! [SV79: $i] :
( ( ( ! [SY4626: $i,SY4627: $i] :
( ( SY4627
!= ( fiber @ SV79 @ SY4626 ) )
| ~ ( ~ ! [SY4628: $i] :
( ( SY4628 = SY4626 )
| ~ ( in @ ( ordered_pair @ SY4628 @ SY4626 ) @ SV79 )
| ( in @ SY4628 @ SY4627 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY4627 )
| ( SX3 != SY4626 ) )
| ~ ! [SY4630: $i] :
( ~ ( in @ SY4630 @ SY4627 )
| ( in @ ( ordered_pair @ SY4630 @ SY4626 ) @ SV79 ) ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1847,plain,
! [SV80: $i] :
( ( ( ! [SY4631: $i] :
( ~ ( relation @ SY4631 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SY4631 @ SV80 ) @ ( sK45_SY4427 @ SY4631 @ SV80 ) ) @ SY4631 ) ) )
| ( SV80 = SY4631 ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1848,plain,
! [SV80: $i] :
( ( ( ! [SY4632: $i] :
( ~ ( relation @ SY4632 )
| ( SV80 != SY4632 )
| ~ ( ~ ! [SY4633: $i,SY4634: $i] :
( ~ ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4633 @ SY4634 ) @ SY4632 ) )
| ~ ! [SY4635: $i,SY4636: $i] :
( ~ ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SY4632 )
| ( in @ ( ordered_pair @ SY4635 @ SY4636 ) @ SV80 ) ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1849,plain,
! [SV195: $i] :
( ( ( ~ ( function @ SV195 )
| ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( one_to_one @ SV195 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1850,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 )
| ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( one_to_one @ SV196 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1851,plain,
! [SV197: $i] :
( ( ( ~ ( function @ SV197 ) )
= $true )
| ( ( ~ ( relation @ SV197 ) )
= $true )
| ( ( function @ ( function_inverse @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1852,plain,
! [SV198: $i] :
( ( ( ~ ( function @ SV198 ) )
= $true )
| ( ( ~ ( relation @ SV198 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1853,plain,
! [SV81: $i] :
( ( ( ! [SY4637: $i] :
( ~ ( ~ ( in @ ( sK47_C @ SY4637 @ SV81 ) @ SY4637 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SY4637 @ SV81 ) @ ( sK47_C @ SY4637 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SY4637 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1854,plain,
! [SV81: $i] :
( ( ( ! [SY4638: $i] :
( ~ ( is_reflexive_in @ SV81 @ SY4638 )
| ! [SY4639: $i] :
( ~ ( in @ SY4639 @ SY4638 )
| ( in @ ( ordered_pair @ SY4639 @ SY4639 ) @ SV81 ) ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1855,plain,
! [SV82: $i,SV238: $i,SV261: $i] :
( ( ~ ( function @ SV261 )
| ~ ( relation @ SV261 )
| ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1856,plain,
! [SV82: $i] :
( ( ~ ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1857,plain,
! [SV82: $i] :
( ( ~ ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1675]) ).
thf(1858,plain,
! [SV83: $i,SV137: $i] :
( ( ( ~ ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1859,plain,
! [SV137: $i,SV83: $i] :
( ( ( ~ ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1676]) ).
thf(1860,plain,
! [SV201: $i] :
( ( ( relation @ SV201 )
= $false )
| ( ( ( relation_rng @ SV201 )
= ( relation_dom @ ( relation_inverse @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1861,plain,
! [SV202: $i] :
( ( ( relation @ SV202 )
= $false )
| ( ( ( relation_dom @ SV202 )
= ( relation_rng @ ( relation_inverse @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1862,plain,
! [SV84: $i] :
( ( ( ! [SY4655: $i] :
( ~ ( ~ ! [SY4656: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4656 ) @ ( sK39_C @ SY4655 @ SV84 ) )
| ~ ( in @ SY4656 @ ( sK39_C @ SY4655 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SY4655 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SY4655 @ SV84 ) @ SY4655 ) ) )
| ( is_well_founded_in @ SV84 @ SY4655 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1863,plain,
! [SV84: $i] :
( ( ( ! [SY4657: $i] :
( ~ ( is_well_founded_in @ SV84 @ SY4657 )
| ! [SY4658: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) ) @ SY4658 )
| ~ ( in @ ( sK38_D @ SY4658 @ SY4657 @ SV84 ) @ SY4658 ) )
| ( SY4658 = empty_set )
| ~ ( subset @ SY4658 @ SY4657 ) ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1864,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1865,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1866,plain,
! [SV203: $i] :
( ( ( relation @ SV203 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
| ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) )
| ( antisymmetric @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1867,plain,
! [SV204: $i] :
( ( ( relation @ SV204 )
= $false )
| ( ( ~ ( antisymmetric @ SV204 )
| ! [SY4806: $i,SY4807: $i] :
( ~ ( in @ ( ordered_pair @ SY4806 @ SY4807 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4807 @ SY4806 ) @ SV204 )
| ( SY4806 = SY4807 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1868,plain,
! [SV85: $i] :
( ( ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
| ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1869,plain,
! [SV86: $i] :
( ( ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) )
| ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1870,plain,
! [SV239: $i,SV87: $i,SV262: $i] :
( ( ~ ( relation @ SV262 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV262 @ SV239 ) ) )
| ( in @ SV87 @ ( relation_field @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1871,plain,
! [SV240: $i,SV87: $i,SV263: $i] :
( ( ~ ( relation @ SV263 )
| ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV263 @ SV240 ) ) )
| ( in @ SV87 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1872,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1873,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1874,plain,
! [SV205: $i] :
( ( ( relation @ SV205 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ( transitive @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1875,plain,
! [SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( ~ ( transitive @ SV206 )
| ! [SY4808: $i,SY4809: $i,SY4810: $i] :
( ~ ( in @ ( ordered_pair @ SY4808 @ SY4809 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4809 @ SY4810 ) @ SV206 )
| ( in @ ( ordered_pair @ SY4808 @ SY4810 ) @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1876,plain,
! [SV88: $i] :
( ( ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) )
| ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1877,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)],[1694]) ).
thf(1878,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1879,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1880,plain,
( ( epsilon_connected @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1881,plain,
! [SV89: $i,SV207: $i] :
( ( ( relation @ SV207 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
| ~ ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1882,plain,
! [SV90: $i] :
( ( ( ! [SY4690: $i] :
( ~ ( relation @ SY4690 )
| ~ ( subset @ SV90 @ SY4690 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SY4690 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1883,plain,
! [SV90: $i] :
( ( ( ! [SY4691: $i] :
( ~ ( relation @ SY4691 )
| ~ ( subset @ SV90 @ SY4691 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SY4691 ) ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1884,plain,
! [SV208: $i] :
( ( ( relation @ SV208 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV208 @ ( relation_field @ SV208 ) )
| ( well_founded_relation @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1885,plain,
! [SV209: $i] :
( ( ( relation @ SV209 )
= $false )
| ( ( ~ ( well_founded_relation @ SV209 )
| ( is_well_founded_in @ SV209 @ ( relation_field @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1886,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( relation @ SV241 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
| ( SV241
= ( identity_relation @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1887,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ( relation @ SV242 ) )
= $true )
| ( ( ( SV242
!= ( identity_relation @ SV211 ) )
| ~ ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1888,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1889,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1890,plain,
! [SV212: $i] :
( ( ( ~ ( relation @ SV212 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV212 ) )
= $true )
| ( ( ! [SY4824: $i] : ( relation @ ( relation_dom_restriction @ SV212 @ SY4824 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1891,plain,
! [SV213: $i] :
( ( ( ~ ( relation @ SV213 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV213 ) )
= $true )
| ( ( ! [SY4825: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SY4825 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1892,plain,
! [SV91: $i] :
( ( ( ! [SY4692: $i] :
( ~ ( ~ ( ! [SY4693: $i] :
~ ( in @ ( ordered_pair @ SY4693 @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SY4692 @ SV91 ) @ ( sK28_C @ SY4692 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SY4692 @ SV91 ) @ SY4692 ) ) )
| ( SY4692
= ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1893,plain,
! [SV91: $i] :
( ( ( ! [SY4694: $i] :
( ( SY4694
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4695: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4695 ) @ SV91 )
| ( in @ SY4695 @ SY4694 ) )
| ~ ! [SY4697: $i] :
( ~ ( in @ SY4697 @ SY4694 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4697 @ SY4694 @ SV91 ) @ SY4697 ) @ SV91 ) ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1894,plain,
! [SV243: $i,SV92: $i,SV264: $i] :
( ( ~ ( relation @ SV264 )
| ! [SY4856: $i] :
( ~ ( in @ SY4856 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SY4856 @ SV92 ) @ SV264 )
| ~ ( in @ SY4856 @ SV243 ) )
| ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1895,plain,
! [SV244: $i,SV92: $i,SV265: $i] :
( ( ~ ( relation @ SV265 )
| ~ ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1896,plain,
! [SV214: $i] :
( ( ( relation @ SV214 )
= $false )
| ( ( ~ ( antisymmetric @ SV214 )
| ( is_antisymmetric_in @ SV214 @ ( relation_field @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1897,plain,
! [SV215: $i] :
( ( ( relation @ SV215 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV215 @ ( relation_field @ SV215 ) )
| ( antisymmetric @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1898,plain,
! [SV93: $i,SV138: $i] :
( ( ( relation @ SV138 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( ~ ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1899,plain,
! [SV216: $i] :
( ( ( empty @ SV216 )
= $false )
| ( ( empty @ ( relation_inverse @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1900,plain,
! [SV217: $i] :
( ( ( empty @ SV217 )
= $false )
| ( ( relation @ ( relation_inverse @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1901,plain,
! [SV245: $i,SV94: $i,SV266: $i] :
( ( ~ ( relation @ SV266 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SV266 )
| ( in @ SV94 @ ( relation_field @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1902,plain,
! [SV246: $i,SV94: $i,SV267: $i] :
( ( ~ ( relation @ SV267 )
| ~ ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SV267 )
| ( in @ SV246 @ ( relation_field @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(1903,plain,
! [SV247: $i,SV95: $i,SV268: $i] :
( ( ~ ( relation @ SV268 )
| ~ ( in @ SV95 @ SV247 )
| ~ ( in @ SV95 @ ( relation_rng @ SV268 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1904,plain,
! [SV95: $i] :
( ( ~ ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1905,plain,
! [SV95: $i] :
( ( ~ ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1906,plain,
( ( ~ ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1907,plain,
( ( ~ ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1908,plain,
! [SV218: $i,SV248: $i] :
( ( ( ~ ( relation @ SV248 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV248 @ SV218 ) ) @ ( relation_field @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1909,plain,
! [SV219: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV249 @ SV219 ) ) @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1910,plain,
! [SV96: $i] :
( ( ( ! [SY4718: $i,SY4719: $i] :
( ~ ( relation @ SY4719 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ SY4718 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4719 @ SY4718 @ SV96 ) @ ( sK64_SY4438 @ SY4719 @ SY4718 @ SV96 ) ) @ SY4719 ) ) ) )
| ( SY4719
= ( relation_dom_restriction @ SV96 @ SY4718 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1911,plain,
! [SV96: $i] :
( ( ( ! [SY4720: $i,SY4721: $i] :
( ~ ( relation @ SY4721 )
| ( SY4721
!= ( relation_dom_restriction @ SV96 @ SY4720 ) )
| ~ ( ~ ! [SY4722: $i,SY4723: $i] :
( ~ ( in @ SY4722 @ SY4720 )
| ~ ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4722 @ SY4723 ) @ SY4721 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY4721 )
| ( in @ SX3 @ SY4720 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4721 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1912,plain,
! [SV97: $i] :
( ( ( ! [SY4728: $i,SY4729: $i] :
( ~ ( ~ ( ! [SY4730: $i] :
( ~ ( in @ ( ordered_pair @ SY4730 @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4730 @ SY4728 ) )
| ~ ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4729 @ SY4728 @ SV97 ) @ SY4728 ) )
| ( in @ ( sK55_D @ SY4729 @ SY4728 @ SV97 ) @ SY4729 ) ) )
| ( SY4729
= ( relation_image @ SV97 @ SY4728 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1913,plain,
! [SV97: $i] :
( ( ( ! [SY4731: $i,SY4732: $i] :
( ( SY4732
!= ( relation_image @ SV97 @ SY4731 ) )
| ~ ( ~ ! [SY4733: $i] :
( ! [SY4734: $i] :
( ~ ( in @ ( ordered_pair @ SY4734 @ SY4733 ) @ SV97 )
| ~ ( in @ SY4734 @ SY4731 ) )
| ( in @ SY4733 @ SY4732 ) )
| ~ ! [SY4735: $i] :
( ~ ( in @ SY4735 @ SY4732 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4735 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4735 @ SY4732 @ SY4731 @ SV97 ) @ SY4731 ) ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1914,plain,
! [SV250: $i,SV220: $i] :
( ( ( ~ ( empty @ SV220 )
| ~ ( relation @ SV250 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV220 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1915,plain,
! [SV251: $i,SV221: $i] :
( ( ( ~ ( empty @ SV221 )
| ~ ( relation @ SV251 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV221 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1916,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( function @ SV252 )
| ~ ( relation @ SV252 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 )
| ( SV252
= ( identity_relation @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1917,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)],[1733]) ).
thf(1918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1919,plain,
! [SV108: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ ( relation_rng @ SV108 ) ) )
= $true )
| ( ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 )
= $true )
| ( ( function @ SV108 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(1920,plain,
! [SV110: $i,SV15: $i] :
( ( ( subset @ SV15 @ ( relation_rng @ SV110 ) )
= $false )
| ( ( SV15 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV110 @ SV15 )
!= empty_set ) )
= $true )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1921,plain,
! [SV140: $i,SV111: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV111 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV140 @ SV16 ) @ ( relation_inverse_image @ SV140 @ SV111 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1922,plain,
! [SV115: $i,SV21: $i,SV269: $i] :
( ( ( ~ ( function @ SV269 )
| ~ ( relation @ SV269 )
| ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) ) )
= $true )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1923,plain,
! [SV117: $i,SV23: $i,SV270: $i] :
( ( ( ~ ( function @ SV270 )
| ~ ( relation @ SV270 )
| ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) ) )
= $true )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(1924,plain,
! [SV123: $i,SV29: $i] :
( ( ( subset @ SV29 @ ( relation_field @ SV123 ) )
= $false )
| ( ( ~ ( well_ordering @ SV123 ) )
= $true )
| ( ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1925,plain,
! [SV147: $i,SV32: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV147 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV147 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV147 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1752]) ).
thf(1926,plain,
! [SV148: $i,SV33: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV148 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV148 @ SV33 ) )
= ( relation_rng @ SV33 ) )
= $true )
| ( ( relation @ SV148 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1927,plain,
! [SV149: $i,SV34: $i,SV271: $i] :
( ( ( ~ ( function @ SV271 )
| ~ ( relation @ SV271 )
| ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1928,plain,
! [SV36: $i] :
( ( ( one_to_one @ SV36 )
= $false )
| ( ( one_to_one @ ( function_inverse @ SV36 ) )
= $true )
| ( ( function @ SV36 )
= $false )
| ( ( relation @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1929,plain,
! [SV37: $i,SV124: $i,SV142: $i] :
( ( ( relation @ SV142 )
= $false )
| ( ( function @ SV142 )
= $false )
| ( ( ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1930,plain,
! [SV38: $i,SV125: $i,SV143: $i] :
( ( ( relation @ SV143 )
= $false )
| ( ( function @ SV143 )
= $false )
| ( ( ~ ( in @ SV125 @ SV38 )
| ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1931,plain,
! [SV47: $i] :
( ( ( one_to_one @ SV47 )
= $false )
| ( ( ( function_inverse @ SV47 )
= ( relation_inverse @ SV47 ) )
= $true )
| ( ( function @ SV47 )
= $false )
| ( ( relation @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1932,plain,
! [SV153: $i] :
( ( ( function @ SV153 )
= $false )
| ( ( ~ ( relation @ SV153 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
| ( one_to_one @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1933,plain,
! [SV154: $i] :
( ( ( function @ SV154 )
= $false )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( one_to_one @ SV154 )
| ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1934,plain,
! [SV155: $i,SV223: $i] :
( ( ( ~ ( function @ SV223 ) )
= $true )
| ( ( ~ ( relation @ SV223 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV155 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1935,plain,
! [SV156: $i,SV224: $i] :
( ( ( ~ ( function @ SV224 ) )
= $true )
| ( ( ~ ( relation @ SV224 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV156 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1936,plain,
! [SV157: $i] :
( ( ( ( ( relation_dom @ SV157 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV157 )
= empty_set )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(1937,plain,
! [SV158: $i] :
( ( ( ( ( relation_rng @ SV158 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV158 )
= empty_set )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1938,plain,
! [SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) ) )
= $true )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1939,plain,
! [SV160: $i] :
( ( ( ~ ( reflexive @ SV160 ) )
= $true )
| ( ( ! [SY4769: $i] :
( ~ ( in @ SY4769 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SY4769 @ SY4769 ) @ SV160 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1940,plain,
! [SV60: $i] :
( ( ( one_to_one @ SV60 )
= $false )
| ( ( ~ ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1941,plain,
! [SV135: $i,SV253: $i,SV61: $i,SV272: $i] :
( ( ~ ( relation @ SV272 )
| ~ ( in @ SV61 @ SV253 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1942,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1943,plain,
! [SV135: $i,SV61: $i] :
( ( ~ ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1773]) ).
thf(1944,plain,
! [SV161: $i] :
( ( ( ~ ( is_reflexive_in @ SV161 @ ( relation_field @ SV161 ) ) )
= $true )
| ( ( reflexive @ SV161 )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1945,plain,
! [SV162: $i] :
( ( ( ~ ( reflexive @ SV162 ) )
= $true )
| ( ( is_reflexive_in @ SV162 @ ( relation_field @ SV162 ) )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1946,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SV273 @ SV62 )
!= ( sK34_SY4421 @ SV273 @ SV62 ) ) ) )
| ( is_antisymmetric_in @ SV62 @ SV273 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(1947,plain,
! [SV274: $i,SV62: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV62 @ SV274 )
| ! [SY4857: $i,SY4858: $i] :
( ~ ( in @ SY4857 @ SV274 )
| ~ ( in @ SY4858 @ SV274 )
| ~ ( in @ ( ordered_pair @ SY4857 @ SY4858 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4858 @ SY4857 ) @ SV62 )
| ( SY4857 = SY4858 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(1948,plain,
! [SV63: $i,SV275: $i] :
( ( ( ! [SY4859: $i] :
( ~ ( ~ ( ! [SY4860: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4859 @ SV275 @ SV63 ) @ SY4860 ) @ SV63 )
| ~ ( in @ SY4860 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SY4859 @ SV275 @ SV63 ) @ SY4859 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SY4859 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SY4859 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SY4859 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SY4859 @ SV275 @ SV63 ) @ SY4859 ) ) )
| ( SY4859
= ( relation_inverse_image @ SV63 @ SV275 ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1949,plain,
! [SV276: $i,SV63: $i] :
( ( ( ! [SY4861: $i] :
( ( SY4861
!= ( relation_inverse_image @ SV63 @ SV276 ) )
| ~ ( ~ ! [SY4862: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4862 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4862 @ SY4861 ) )
| ~ ! [SY4864: $i] :
( ~ ( in @ SY4864 @ SY4861 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4864 @ ( sK51_E @ SY4864 @ SY4861 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4864 @ SY4861 @ SV276 @ SV63 ) @ SV276 ) ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1950,plain,
! [SV225: $i,SV64: $i,SV254: $i] :
( ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( in @ SV64 @ SV254 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) )
| ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1951,plain,
! [SV64: $i] :
( ( ! [SY4533: $i,SY4534: $i] :
( ~ ( relation @ SY4534 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4534 @ SY4533 ) )
| ( in @ SV64 @ SY4534 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1952,plain,
! [SV64: $i] :
( ( ! [SY4535: $i,SY4536: $i] :
( ~ ( relation @ SY4536 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4536 @ SY4535 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SY4535 @ SY4535 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1953,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( relation @ SV277 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
| ( subset @ SV65 @ SV277 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1954,plain,
! [SV65: $i,SV278: $i] :
( ( ( ~ ( relation @ SV278 )
| ~ ( subset @ SV65 @ SV278 )
| ! [SY4865: $i,SY4866: $i] :
( ~ ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV278 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1955,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 )
| ~ ( is_transitive_in @ SV66 @ SV279 )
| ~ ( is_antisymmetric_in @ SV66 @ SV279 )
| ~ ( is_connected_in @ SV66 @ SV279 )
| ~ ( is_well_founded_in @ SV66 @ SV279 )
| ( well_orders @ SV66 @ SV279 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1956,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
| ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1957,plain,
! [SV163: $i] :
( ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 )
| ~ ( connected @ SV163 )
| ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1958,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)],[1788]) ).
thf(1959,plain,
! [SV280: $i] :
( ( ~ ( relation @ SV280 )
| ~ ( well_ordering @ SV280 )
| ( well_founded_relation @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1960,plain,
! [SV281: $i] :
( ( ~ ( empty @ SV281 )
| ~ ( relation @ SV281 )
| ~ ( function @ SV281 )
| ( function @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(1961,plain,
! [SV282: $i] :
( ( ~ ( empty @ SV282 )
| ~ ( relation @ SV282 )
| ~ ( function @ SV282 )
| ( relation @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1962,plain,
! [SV164: $i] :
( ( ( ~ ( empty @ SV164 ) )
= $true )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1963,plain,
! [SV167: $i] :
( ( ( ~ ( is_transitive_in @ SV167 @ ( relation_field @ SV167 ) ) )
= $true )
| ( ( transitive @ SV167 )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1797]) ).
thf(1964,plain,
! [SV168: $i] :
( ( ( ~ ( transitive @ SV168 ) )
= $true )
| ( ( is_transitive_in @ SV168 @ ( relation_field @ SV168 ) )
= $true )
| ( ( relation @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(1965,plain,
! [SV226: $i,SV169: $i] :
( ( ( ~ ( empty @ SV169 ) )
= $true )
| ( ( ~ ( relation @ SV226 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV226 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1966,plain,
! [SV227: $i,SV170: $i] :
( ( ( ~ ( empty @ SV170 ) )
= $true )
| ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV227 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(1967,plain,
! [SV171: $i] :
( ( ( function @ SV171 )
= $false )
| ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ! [SY4772: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY4772 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1968,plain,
! [SV172: $i] :
( ( ( function @ SV172 )
= $false )
| ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY4773: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY4773 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1802]) ).
thf(1969,plain,
! [SV173: $i] :
( ( ( ~ ( well_ordering @ SV173 ) )
= $true )
| ( ( well_orders @ SV173 @ ( relation_field @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(1970,plain,
! [SV174: $i] :
( ( ( ~ ( well_orders @ SV174 @ ( relation_field @ SV174 ) ) )
= $true )
| ( ( well_ordering @ SV174 )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(1971,plain,
! [SV67: $i,SV228: $i,SV255: $i] :
( ( ( ~ ( function @ SV255 )
| ~ ( relation @ SV255 ) )
= $true )
| ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(1972,plain,
! [SV67: $i] :
( ( ! [SY4549: $i,SY4550: $i] :
( ~ ( function @ SY4550 )
| ~ ( relation @ SY4550 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4549 ) @ SY4550 )
| ( SY4549
= ( apply @ SY4550 @ SV67 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1973,plain,
! [SV67: $i] :
( ( ! [SY4551: $i,SY4552: $i] :
( ~ ( function @ SY4552 )
| ~ ( relation @ SY4552 )
| ~ ( in @ ( ordered_pair @ SV67 @ SY4551 ) @ SY4552 )
| ( in @ SV67 @ ( relation_dom @ SY4552 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1974,plain,
! [SV229: $i,SV68: $i,SV256: $i] :
( ( ( ~ ( relation @ SV256 ) )
= $true )
| ( ( ! [SY4855: $i] :
( ~ ( in @ SY4855 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4855 ) @ SV256 )
| ~ ( in @ SY4855 @ SV229 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1975,plain,
! [SV230: $i,SV68: $i,SV257: $i] :
( ( ( ~ ( relation @ SV257 ) )
= $true )
| ( ( ~ ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1809]) ).
thf(1976,plain,
! [SV69: $i,SV175: $i] :
( ( ( ~ ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) )
| ~ ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1977,plain,
! [SV231: $i,SV70: $i,SV258: $i] :
( ( ( ~ ( relation @ SV258 ) )
= $true )
| ( ( ~ ( in @ SV70 @ SV231 )
| ~ ( in @ SV70 @ ( relation_dom @ SV258 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(1978,plain,
! [SV70: $i] :
( ( ! [SY4574: $i,SY4575: $i] :
( ~ ( relation @ SY4575 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4575 @ SY4574 ) ) )
| ( in @ SV70 @ SY4574 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1979,plain,
! [SV70: $i] :
( ( ! [SY4576: $i,SY4577: $i] :
( ~ ( relation @ SY4577 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4577 @ SY4576 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4577 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1980,plain,
! [SV176: $i] :
( ( ( ~ ( connected @ SV176 ) )
= $true )
| ( ( is_connected_in @ SV176 @ ( relation_field @ SV176 ) )
= $true )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1981,plain,
! [SV177: $i] :
( ( ( ~ ( is_connected_in @ SV177 @ ( relation_field @ SV177 ) ) )
= $true )
| ( ( connected @ SV177 )
= $true )
| ( ( relation @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1982,plain,
! [SV178: $i] :
( ( ( ( ( relation_dom @ SV178 )
!= empty_set ) )
= $true )
| ( ( SV178 = empty_set )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1983,plain,
! [SV179: $i] :
( ( ( ( ( relation_rng @ SV179 )
!= empty_set ) )
= $true )
| ( ( SV179 = empty_set )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(1984,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( relation @ SV283 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
| ( SV283
= ( relation_inverse @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(1985,plain,
! [SV71: $i,SV284: $i] :
( ( ( ~ ( relation @ SV284 )
| ( SV284
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(1986,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1987,plain,
! [SV181: $i] :
( ( ( ~ ( well_founded_relation @ SV181 ) )
= $true )
| ( ( ! [SY4788: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SY4788 @ SV181 ) ) @ SY4788 )
| ~ ( in @ ( sK42_C @ SY4788 @ SV181 ) @ SY4788 ) )
| ( SY4788 = empty_set )
| ~ ( subset @ SY4788 @ ( relation_field @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1988,plain,
! [SV72: $i,SV182: $i] :
( ( ( ~ ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) )
| ~ ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1989,plain,
! [SV183: $i,SV232: $i] :
( ( ( ~ ( function @ SV232 ) )
= $true )
| ( ( ~ ( relation @ SV232 ) )
= $true )
| ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 )
| ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1990,plain,
! [SV184: $i,SV233: $i] :
( ( ( ~ ( function @ SV233 ) )
= $true )
| ( ( ~ ( relation @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1991,plain,
! [SV185: $i] :
( ( ( ~ ! [SY4799: $i,SY4800: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SY4799 @ SY4800 ) ) )
= $false )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1992,plain,
! [SV185: $i] :
( ( ( ~ ( in @ ( sK50_B @ SV185 ) @ SV185 ) )
= $false )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1993,plain,
! [SV186: $i,SV285: $i] :
( ( ( ( SV285
= ( ordered_pair @ ( sK48_C @ SV285 @ SV186 ) @ ( sK49_SY4428 @ SV285 @ SV186 ) ) )
| ~ ( in @ SV285 @ SV186 ) )
= $true )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(1994,plain,
! [SV73: $i,SV286: $i] :
( ( ( ~ ( ~ ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) ) )
| ( SV286
= ( relation_dom @ SV73 ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1995,plain,
! [SV73: $i,SV287: $i] :
( ( ( ( SV287
!= ( relation_dom @ SV73 ) )
| ~ ( ~ ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) )
| ~ ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1996,plain,
! [SV234: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 )
| ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1997,plain,
! [SV235: $i,SV188: $i] :
( ( ( ~ ( function @ SV188 )
| ~ ( relation @ SV188 )
| ~ ( relation @ SV235 ) )
= $true )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1998,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 ) )
| ( is_connected_in @ SV74 @ SV288 ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(1999,plain,
! [SV289: $i,SV74: $i] :
( ( ( ~ ( is_connected_in @ SV74 @ SV289 )
| ! [SY4875: $i,SY4876: $i] :
( ( SY4875 = SY4876 )
| ~ ( in @ SY4875 @ SV289 )
| ~ ( in @ SY4876 @ SV289 )
| ( in @ ( ordered_pair @ SY4875 @ SY4876 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4876 @ SY4875 ) @ SV74 ) ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2000,plain,
! [SV189: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2001,plain,
! [SV190: $i] :
( ( ( ~ ( connected @ SV190 ) )
= $true )
| ( ( ! [SY4804: $i,SY4805: $i] :
( ( SY4804 = SY4805 )
| ~ ( in @ SY4804 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4805 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SY4804 @ SY4805 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4805 @ SY4804 ) @ SV190 ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2002,plain,
! [SV236: $i,SV75: $i,SV259: $i] :
( ( ( ~ ( relation @ SV259 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SV259 )
| ( in @ SV75 @ ( relation_dom @ SV259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2003,plain,
! [SV237: $i,SV75: $i,SV260: $i] :
( ( ( ~ ( relation @ SV260 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SV260 )
| ( in @ SV237 @ ( relation_rng @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2004,plain,
! [SV191: $i] :
( ( ( function @ SV191 )
= $false )
| ( ( ~ ( relation @ SV191 ) )
= $true )
| ( ( ~ ( one_to_one @ SV191 )
| ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2005,plain,
! [SV192: $i] :
( ( ( function @ SV192 )
= $false )
| ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ~ ( one_to_one @ SV192 )
| ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2006,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) )
| ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(2007,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
| ( is_transitive_in @ SV77 @ SV290 ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2008,plain,
! [SV291: $i,SV77: $i] :
( ( ( ~ ( is_transitive_in @ SV77 @ SV291 )
| ! [SY4877: $i,SY4878: $i,SY4879: $i] :
( ~ ( in @ SY4877 @ SV291 )
| ~ ( in @ SY4878 @ SV291 )
| ~ ( in @ SY4879 @ SV291 )
| ~ ( in @ ( ordered_pair @ SY4877 @ SY4878 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4878 @ SY4879 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4877 @ SY4879 ) @ SV77 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2009,plain,
! [SV78: $i] :
( ( ( ~ ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(2010,plain,
! [SV78: $i] :
( ( ( ~ ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1844]) ).
thf(2011,plain,
! [SV79: $i,SV292: $i] :
( ( ( ! [SY4880: $i] :
( ~ ( ~ ( ( ( sK46_D @ SY4880 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SY4880 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SY4880 @ SV292 @ SV79 ) @ SY4880 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SY4880 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SY4880 @ SV292 @ SV79 ) @ SY4880 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SY4880 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SY4880 @ SV292 @ SV79 ) @ SY4880 ) ) ) )
| ( SY4880
= ( fiber @ SV79 @ SV292 ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2012,plain,
! [SV293: $i,SV79: $i] :
( ( ( ! [SY4881: $i] :
( ( SY4881
!= ( fiber @ SV79 @ SV293 ) )
| ~ ( ~ ! [SY4882: $i] :
( ( SY4882 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4882 @ SV293 ) @ SV79 )
| ( in @ SY4882 @ SY4881 ) )
| ~ ~ ( ~ ! [SY4883: $i] :
( ~ ( in @ SY4883 @ SY4881 )
| ( SY4883 != SV293 ) )
| ~ ! [SY4884: $i] :
( ~ ( in @ SY4884 @ SY4881 )
| ( in @ ( ordered_pair @ SY4884 @ SV293 ) @ SV79 ) ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2013,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( relation @ SV294 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
| ( SV80 = SV294 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2014,plain,
! [SV80: $i,SV295: $i] :
( ( ( ~ ( relation @ SV295 )
| ( SV80 != SV295 )
| ~ ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2015,plain,
! [SV195: $i] :
( ( ( ~ ( function @ SV195 ) )
= $true )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( one_to_one @ SV195 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2016,plain,
! [SV196: $i] :
( ( ( ~ ( function @ SV196 ) )
= $true )
| ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( one_to_one @ SV196 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2017,plain,
! [SV197: $i] :
( ( ( function @ SV197 )
= $false )
| ( ( ~ ( relation @ SV197 ) )
= $true )
| ( ( function @ ( function_inverse @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2018,plain,
! [SV198: $i] :
( ( ( function @ SV198 )
= $false )
| ( ( ~ ( relation @ SV198 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2019,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_C @ SV296 @ SV81 ) @ SV296 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 ) )
| ( is_reflexive_in @ SV81 @ SV296 ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2020,plain,
! [SV297: $i,SV81: $i] :
( ( ( ~ ( is_reflexive_in @ SV81 @ SV297 )
| ! [SY4889: $i] :
( ~ ( in @ SY4889 @ SV297 )
| ( in @ ( ordered_pair @ SY4889 @ SY4889 ) @ SV81 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2021,plain,
! [SV82: $i,SV238: $i,SV261: $i] :
( ( ( ~ ( function @ SV261 )
| ~ ( relation @ SV261 ) )
= $true )
| ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2022,plain,
! [SV82: $i] :
( ( ! [SY4642: $i,SY4643: $i] :
( ~ ( function @ SY4643 )
| ~ ( relation @ SY4643 )
| ~ ( in @ SY4642 @ ( relation_dom @ ( relation_dom_restriction @ SY4643 @ SV82 ) ) )
| ( in @ SY4642 @ ( relation_dom @ SY4643 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(2023,plain,
! [SV82: $i] :
( ( ! [SY4644: $i,SY4645: $i] :
( ~ ( function @ SY4645 )
| ~ ( relation @ SY4645 )
| ~ ( in @ SY4644 @ ( relation_dom @ ( relation_dom_restriction @ SY4645 @ SV82 ) ) )
| ( in @ SY4644 @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2024,plain,
! [SV83: $i,SV137: $i] :
( ( ( ! [SY4752: $i] :
( ~ ( relation @ SY4752 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SY4752 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SY4752 @ SV137 @ SV83 ) ) @ SY4752 ) ) ) )
| ( SY4752
= ( relation_rng_restriction @ SV83 @ SV137 ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1858]) ).
thf(2025,plain,
! [SV137: $i,SV83: $i] :
( ( ( ! [SY4753: $i] :
( ~ ( relation @ SY4753 )
| ( SY4753
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4754: $i,SY4755: $i] :
( ~ ( in @ SY4755 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4754 @ SY4755 ) @ SY4753 ) )
| ~ ~ ( ~ ! [SY4651: $i,SY4652: $i] :
( ~ ( in @ ( ordered_pair @ SY4651 @ SY4652 ) @ SY4753 )
| ( in @ SY4652 @ SV83 ) )
| ~ ! [SY4758: $i,SY4759: $i] :
( ~ ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SY4753 )
| ( in @ ( ordered_pair @ SY4758 @ SY4759 ) @ SV137 ) ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(2026,plain,
! [SV298: $i,SV84: $i] :
( ( ( ~ ( ~ ! [SY4890: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4890 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SY4890 @ ( sK39_C @ SV298 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) ) )
| ( is_well_founded_in @ SV84 @ SV298 ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2027,plain,
! [SV299: $i,SV84: $i] :
( ( ( ~ ( is_well_founded_in @ SV84 @ SV299 )
| ! [SY4891: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) ) @ SY4891 )
| ~ ( in @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) @ SY4891 ) )
| ( SY4891 = empty_set )
| ~ ( subset @ SY4891 @ SV299 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2028,plain,
! [SV203: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
| ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2029,plain,
! [SV204: $i] :
( ( ( ~ ( antisymmetric @ SV204 ) )
= $true )
| ( ( ! [SY4806: $i,SY4807: $i] :
( ~ ( in @ ( ordered_pair @ SY4806 @ SY4807 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4807 @ SY4806 ) @ SV204 )
| ( SY4806 = SY4807 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2030,plain,
! [SV85: $i] :
( ( ( ~ ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(2031,plain,
! [SV85: $i] :
( ( ( ~ ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(2032,plain,
! [SV86: $i] :
( ( ( ~ ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(2033,plain,
! [SV86: $i] :
( ( ( ~ ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(2034,plain,
! [SV239: $i,SV87: $i,SV262: $i] :
( ( ( ~ ( relation @ SV262 ) )
= $true )
| ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV262 @ SV239 ) ) )
| ( in @ SV87 @ ( relation_field @ SV262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(2035,plain,
! [SV240: $i,SV87: $i,SV263: $i] :
( ( ( ~ ( relation @ SV263 ) )
= $true )
| ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV263 @ SV240 ) ) )
| ( in @ SV87 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2036,plain,
! [SV205: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) ) )
= $true )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2037,plain,
! [SV206: $i] :
( ( ( ~ ( transitive @ SV206 ) )
= $true )
| ( ( ! [SY4808: $i,SY4809: $i,SY4810: $i] :
( ~ ( in @ ( ordered_pair @ SY4808 @ SY4809 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4809 @ SY4810 ) @ SV206 )
| ( in @ ( ordered_pair @ SY4808 @ SY4810 ) @ SV206 ) ) )
= $true )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2038,plain,
! [SV88: $i] :
( ( ( ~ ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2039,plain,
! [SV88: $i] :
( ( ( ~ ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1876]) ).
thf(2040,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)],[1877]) ).
thf(2041,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
| ~ ( epsilon_transitive @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2042,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
| ~ ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2043,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( relation @ SV300 )
| ~ ( subset @ SV90 @ SV300 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SV300 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2044,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ( relation @ SV301 )
| ~ ( subset @ SV90 @ SV301 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SV301 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2045,plain,
! [SV208: $i] :
( ( ( ~ ( is_well_founded_in @ SV208 @ ( relation_field @ SV208 ) ) )
= $true )
| ( ( well_founded_relation @ SV208 )
= $true )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2046,plain,
! [SV209: $i] :
( ( ( ~ ( well_founded_relation @ SV209 ) )
= $true )
| ( ( is_well_founded_in @ SV209 @ ( relation_field @ SV209 ) )
= $true )
| ( ( relation @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2047,plain,
! [SV210: $i,SV241: $i] :
( ( ( relation @ SV241 )
= $false )
| ( ( ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
| ( SV241
= ( identity_relation @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2048,plain,
! [SV211: $i,SV242: $i] :
( ( ( relation @ SV242 )
= $false )
| ( ( ( SV242
!= ( identity_relation @ SV211 ) )
| ~ ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2049,plain,
! [SV212: $i] :
( ( ( relation @ SV212 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV212 ) )
= $true )
| ( ( ! [SY4824: $i] : ( relation @ ( relation_dom_restriction @ SV212 @ SY4824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2050,plain,
! [SV213: $i] :
( ( ( relation @ SV213 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV213 ) )
= $true )
| ( ( ! [SY4825: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SY4825 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2051,plain,
! [SV91: $i,SV302: $i] :
( ( ( ~ ( ~ ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) ) )
| ( SV302
= ( relation_rng @ SV91 ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2052,plain,
! [SV91: $i,SV303: $i] :
( ( ( ( SV303
!= ( relation_rng @ SV91 ) )
| ~ ( ~ ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) )
| ~ ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2053,plain,
! [SV243: $i,SV92: $i,SV264: $i] :
( ( ( ~ ( relation @ SV264 ) )
= $true )
| ( ( ! [SY4856: $i] :
( ~ ( in @ SY4856 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SY4856 @ SV92 ) @ SV264 )
| ~ ( in @ SY4856 @ SV243 ) )
| ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2054,plain,
! [SV244: $i,SV92: $i,SV265: $i] :
( ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2055,plain,
! [SV214: $i] :
( ( ( ~ ( antisymmetric @ SV214 ) )
= $true )
| ( ( is_antisymmetric_in @ SV214 @ ( relation_field @ SV214 ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(2056,plain,
! [SV215: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV215 @ ( relation_field @ SV215 ) ) )
= $true )
| ( ( antisymmetric @ SV215 )
= $true )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2057,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) )
| ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2058,plain,
! [SV245: $i,SV94: $i,SV266: $i] :
( ( ( ~ ( relation @ SV266 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SV266 )
| ( in @ SV94 @ ( relation_field @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2059,plain,
! [SV246: $i,SV94: $i,SV267: $i] :
( ( ( ~ ( relation @ SV267 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SV267 )
| ( in @ SV246 @ ( relation_field @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2060,plain,
! [SV247: $i,SV95: $i,SV268: $i] :
( ( ( ~ ( relation @ SV268 ) )
= $true )
| ( ( ~ ( in @ SV95 @ SV247 )
| ~ ( in @ SV95 @ ( relation_rng @ SV268 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2061,plain,
! [SV95: $i] :
( ( ! [SY4714: $i,SY4715: $i] :
( ~ ( relation @ SY4715 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4714 @ SY4715 ) ) )
| ( in @ SV95 @ SY4714 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2062,plain,
! [SV95: $i] :
( ( ! [SY4716: $i,SY4717: $i] :
( ~ ( relation @ SY4717 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SY4716 @ SY4717 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4717 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(2063,plain,
( ( ~ ( function @ sK3_SY4404 )
| ~ ( relation @ sK3_SY4404 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(2064,plain,
( ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
| ~ ~ ( well_ordering @ sK2_SY4402 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2065,plain,
! [SV218: $i,SV248: $i] :
( ( ( relation @ SV248 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV248 @ SV218 ) ) @ ( relation_field @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2066,plain,
! [SV219: $i,SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( subset @ ( relation_field @ ( relation_restriction @ SV249 @ SV219 ) ) @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2067,plain,
! [SV96: $i,SV304: $i] :
( ( ( ! [SY4896: $i] :
( ~ ( relation @ SY4896 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SY4896 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SY4896 @ SV304 @ SV96 ) ) @ SY4896 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SY4896 @ SV304 @ SV96 ) ) @ SY4896 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SY4896 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SY4896 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SY4896 @ SV304 @ SV96 ) ) @ SY4896 ) ) ) )
| ( SY4896
= ( relation_dom_restriction @ SV96 @ SV304 ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2068,plain,
! [SV305: $i,SV96: $i] :
( ( ( ! [SY4897: $i] :
( ~ ( relation @ SY4897 )
| ( SY4897
!= ( relation_dom_restriction @ SV96 @ SV305 ) )
| ~ ( ~ ! [SY4898: $i,SY4899: $i] :
( ~ ( in @ SY4898 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4898 @ SY4899 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4898 @ SY4899 ) @ SY4897 ) )
| ~ ~ ( ~ ! [SY4900: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY4900 @ SX4 ) @ SY4897 )
| ( in @ SY4900 @ SV305 ) )
| ~ ! [SY4726: $i,SY4727: $i] :
( ~ ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SY4897 )
| ( in @ ( ordered_pair @ SY4726 @ SY4727 ) @ SV96 ) ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2069,plain,
! [SV97: $i,SV306: $i] :
( ( ( ! [SY4904: $i] :
( ~ ( ~ ( ! [SY4905: $i] :
( ~ ( in @ ( ordered_pair @ SY4905 @ ( sK55_D @ SY4904 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4905 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SY4904 @ SV306 @ SV97 ) @ SY4904 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SY4904 @ SV306 @ SV97 ) @ ( sK55_D @ SY4904 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SY4904 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SY4904 @ SV306 @ SV97 ) @ SY4904 ) ) )
| ( SY4904
= ( relation_image @ SV97 @ SV306 ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2070,plain,
! [SV307: $i,SV97: $i] :
( ( ( ! [SY4906: $i] :
( ( SY4906
!= ( relation_image @ SV97 @ SV307 ) )
| ~ ( ~ ! [SY4907: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4907 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4907 @ SY4906 ) )
| ~ ! [SY4909: $i] :
( ~ ( in @ SY4909 @ SY4906 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4909 @ SY4906 @ SV307 @ SV97 ) @ SY4909 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4909 @ SY4906 @ SV307 @ SV97 ) @ SV307 ) ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2071,plain,
! [SV250: $i,SV220: $i] :
( ( ( ~ ( empty @ SV220 ) )
= $true )
| ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV220 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2072,plain,
! [SV251: $i,SV221: $i] :
( ( ( ~ ( empty @ SV221 ) )
= $true )
| ( ( ~ ( relation @ SV251 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV221 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2073,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( function @ SV252 ) )
= $true )
| ( ( ~ ( relation @ SV252 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 )
| ( SV252
= ( identity_relation @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2074,plain,
! [SV308: $i] :
( ( ! [SY4910: $i] :
( ~ ( function @ SY4910 )
| ~ ( relation @ SY4910 )
| ( SY4910
!= ( identity_relation @ SV308 ) )
| ! [SY4911: $i] :
( ~ ( in @ SY4911 @ SV308 )
| ( ( apply @ SY4910 @ SY4911 )
= SY4911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2075,plain,
! [SV309: $i] :
( ( ! [SY4912: $i] :
( ~ ( function @ SY4912 )
| ~ ( relation @ SY4912 )
| ( SY4912
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SY4912 )
= SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2076,plain,
! [SV108: $i,SV12: $i] :
( ( ( subset @ SV12 @ ( relation_rng @ SV108 ) )
= $false )
| ( ( ( relation_image @ SV108 @ ( relation_inverse_image @ SV108 @ SV12 ) )
= SV12 )
= $true )
| ( ( function @ SV108 )
= $false )
| ( ( relation @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2077,plain,
! [SV15: $i,SV110: $i] :
( ( ( ( relation_inverse_image @ SV110 @ SV15 )
= empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true )
| ( ( subset @ SV15 @ ( relation_rng @ SV110 ) )
= $false )
| ( ( relation @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2078,plain,
! [SV115: $i,SV21: $i,SV269: $i] :
( ( ( ~ ( function @ SV269 )
| ~ ( relation @ SV269 ) )
= $true )
| ( ( ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) ) )
= $true )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2079,plain,
! [SV117: $i,SV23: $i,SV270: $i] :
( ( ( ~ ( function @ SV270 )
| ~ ( relation @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) ) )
= $true )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2080,plain,
! [SV29: $i,SV123: $i] :
( ( ( well_ordering @ SV123 )
= $false )
| ( ( subset @ SV29 @ ( relation_field @ SV123 ) )
= $false )
| ( ( ( relation_field @ ( relation_restriction @ SV123 @ SV29 ) )
= SV29 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2081,plain,
! [SV147: $i,SV32: $i] :
( ( ( subset @ ( relation_rng @ SV32 ) @ ( relation_dom @ SV147 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV32 @ SV147 ) )
= ( relation_dom @ SV32 ) )
= $true )
| ( ( relation @ SV147 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2082,plain,
! [SV148: $i,SV33: $i] :
( ( ( subset @ ( relation_dom @ SV33 ) @ ( relation_rng @ SV148 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV148 @ SV33 ) )
= ( relation_rng @ SV33 ) )
= $true )
| ( ( relation @ SV148 )
= $false )
| ( ( relation @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2083,plain,
! [SV149: $i,SV34: $i,SV271: $i] :
( ( ( ~ ( function @ SV271 )
| ~ ( relation @ SV271 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2084,plain,
! [SV37: $i,SV142: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) )
= $true )
| ( ( function @ SV142 )
= $false )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2085,plain,
! [SV143: $i,SV38: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV38 ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) )
= $true )
| ( ( function @ SV143 )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2086,plain,
! [SV153: $i] :
( ( ( relation @ SV153 )
= $false )
| ( ( function @ SV153 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
| ( one_to_one @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2087,plain,
! [SV154: $i] :
( ( ( relation @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( ~ ( one_to_one @ SV154 )
| ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2088,plain,
! [SV155: $i,SV223: $i] :
( ( ( function @ SV223 )
= $false )
| ( ( ~ ( relation @ SV223 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV155 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2089,plain,
! [SV156: $i,SV224: $i] :
( ( ( function @ SV224 )
= $false )
| ( ( ~ ( relation @ SV224 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV156 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2090,plain,
! [SV157: $i] :
( ( ( ( relation_dom @ SV157 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV157 )
= empty_set )
= $true )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2091,plain,
! [SV158: $i] :
( ( ( ( relation_rng @ SV158 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV158 )
= empty_set )
= $true )
| ( ( relation @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2092,plain,
! [SV159: $i] :
( ( ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
= $false )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2093,plain,
! [SV160: $i] :
( ( ( reflexive @ SV160 )
= $false )
| ( ( ! [SY4769: $i] :
( ~ ( in @ SY4769 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SY4769 @ SY4769 ) @ SV160 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2094,plain,
! [SV60: $i] :
( ( ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) )
| ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2095,plain,
! [SV135: $i,SV253: $i,SV61: $i,SV272: $i] :
( ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ~ ( in @ SV61 @ SV253 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2096,plain,
! [SV135: $i,SV61: $i] :
( ( ! [SY4745: $i,SY4746: $i] :
( ~ ( relation @ SY4746 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4745 ) @ SY4746 ) )
| ( in @ SV61 @ SY4745 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2097,plain,
! [SV135: $i,SV61: $i] :
( ( ! [SY4747: $i,SY4748: $i] :
( ~ ( relation @ SY4748 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SY4747 ) @ SY4748 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4748 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2098,plain,
! [SV161: $i] :
( ( ( is_reflexive_in @ SV161 @ ( relation_field @ SV161 ) )
= $false )
| ( ( reflexive @ SV161 )
= $true )
| ( ( relation @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2099,plain,
! [SV162: $i] :
( ( ( reflexive @ SV162 )
= $false )
| ( ( is_reflexive_in @ SV162 @ ( relation_field @ SV162 ) )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2100,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SV273 @ SV62 )
!= ( sK34_SY4421 @ SV273 @ SV62 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2101,plain,
! [SV274: $i,SV62: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV62 @ SV274 ) )
= $true )
| ( ( ! [SY4857: $i,SY4858: $i] :
( ~ ( in @ SY4857 @ SV274 )
| ~ ( in @ SY4858 @ SV274 )
| ~ ( in @ ( ordered_pair @ SY4857 @ SY4858 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4858 @ SY4857 ) @ SV62 )
| ( SY4857 = SY4858 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2102,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ~ ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) ) )
| ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2103,plain,
! [SV276: $i,SV63: $i,SV311: $i] :
( ( ( ( SV311
!= ( relation_inverse_image @ SV63 @ SV276 ) )
| ~ ( ~ ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) )
| ~ ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2104,plain,
! [SV225: $i,SV64: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( ~ ( in @ SV64 @ SV254 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) )
| ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2105,plain,
! [SV312: $i,SV64: $i] :
( ( ! [SY4917: $i] :
( ~ ( relation @ SY4917 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4917 @ SV312 ) )
| ( in @ SV64 @ SY4917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2106,plain,
! [SV313: $i,SV64: $i] :
( ( ! [SY4918: $i] :
( ~ ( relation @ SY4918 )
| ~ ( in @ SV64 @ ( relation_restriction @ SY4918 @ SV313 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2107,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( relation @ SV277 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
| ( subset @ SV65 @ SV277 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2108,plain,
! [SV65: $i,SV278: $i] :
( ( ( ~ ( relation @ SV278 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV278 )
| ! [SY4865: $i,SY4866: $i] :
( ~ ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV278 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2109,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 )
| ~ ( is_transitive_in @ SV66 @ SV279 )
| ~ ( is_antisymmetric_in @ SV66 @ SV279 )
| ~ ( is_connected_in @ SV66 @ SV279 )
| ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2110,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2111,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1956]) ).
thf(2112,plain,
! [SV163: $i] :
( ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 )
| ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2113,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)],[1958]) ).
thf(2114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1958]) ).
thf(2115,plain,
! [SV280: $i] :
( ( ( ~ ( relation @ SV280 ) )
= $true )
| ( ( ~ ( well_ordering @ SV280 )
| ( well_founded_relation @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2116,plain,
! [SV281: $i] :
( ( ( ~ ( empty @ SV281 )
| ~ ( relation @ SV281 )
| ~ ( function @ SV281 ) )
= $true )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2117,plain,
! [SV282: $i] :
( ( ( ~ ( empty @ SV282 )
| ~ ( relation @ SV282 )
| ~ ( function @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2118,plain,
! [SV164: $i] :
( ( ( empty @ SV164 )
= $false )
| ( ( ~ ( relation @ SV164 ) )
= $true )
| ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2119,plain,
! [SV167: $i] :
( ( ( is_transitive_in @ SV167 @ ( relation_field @ SV167 ) )
= $false )
| ( ( transitive @ SV167 )
= $true )
| ( ( relation @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2120,plain,
! [SV168: $i] :
( ( ( transitive @ SV168 )
= $false )
| ( ( is_transitive_in @ SV168 @ ( relation_field @ SV168 ) )
= $true )
| ( ( relation @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2121,plain,
! [SV226: $i,SV169: $i] :
( ( ( empty @ SV169 )
= $false )
| ( ( ~ ( relation @ SV226 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV226 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2122,plain,
! [SV227: $i,SV170: $i] :
( ( ( empty @ SV170 )
= $false )
| ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV227 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2123,plain,
! [SV171: $i] :
( ( ( relation @ SV171 )
= $false )
| ( ( function @ SV171 )
= $false )
| ( ( ! [SY4772: $i] : ( function @ ( relation_dom_restriction @ SV171 @ SY4772 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2124,plain,
! [SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( function @ SV172 )
= $false )
| ( ( ! [SY4773: $i] : ( relation @ ( relation_dom_restriction @ SV172 @ SY4773 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2125,plain,
! [SV173: $i] :
( ( ( well_ordering @ SV173 )
= $false )
| ( ( well_orders @ SV173 @ ( relation_field @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2126,plain,
! [SV174: $i] :
( ( ( well_orders @ SV174 @ ( relation_field @ SV174 ) )
= $false )
| ( ( well_ordering @ SV174 )
= $true )
| ( ( relation @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2127,plain,
! [SV67: $i,SV228: $i,SV255: $i] :
( ( ( ~ ( function @ SV255 ) )
= $true )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2128,plain,
! [SV314: $i,SV67: $i] :
( ( ! [SY4919: $i] :
( ~ ( function @ SY4919 )
| ~ ( relation @ SY4919 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SY4919 )
| ( SV314
= ( apply @ SY4919 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2129,plain,
! [SV315: $i,SV67: $i] :
( ( ! [SY4920: $i] :
( ~ ( function @ SY4920 )
| ~ ( relation @ SY4920 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SY4920 )
| ( in @ SV67 @ ( relation_dom @ SY4920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2130,plain,
! [SV229: $i,SV68: $i,SV256: $i] :
( ( ( relation @ SV256 )
= $false )
| ( ( ! [SY4855: $i] :
( ~ ( in @ SY4855 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4855 ) @ SV256 )
| ~ ( in @ SY4855 @ SV229 ) )
| ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2131,plain,
! [SV230: $i,SV68: $i,SV257: $i] :
( ( ( relation @ SV257 )
= $false )
| ( ( ~ ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2132,plain,
! [SV69: $i,SV175: $i] :
( ( ( ~ ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2133,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2134,plain,
! [SV231: $i,SV70: $i,SV258: $i] :
( ( ( relation @ SV258 )
= $false )
| ( ( ~ ( in @ SV70 @ SV231 )
| ~ ( in @ SV70 @ ( relation_dom @ SV258 ) )
| ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2135,plain,
! [SV316: $i,SV70: $i] :
( ( ! [SY4921: $i] :
( ~ ( relation @ SY4921 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4921 @ SV316 ) ) )
| ( in @ SV70 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2136,plain,
! [SV317: $i,SV70: $i] :
( ( ! [SY4922: $i] :
( ~ ( relation @ SY4922 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SY4922 @ SV317 ) ) )
| ( in @ SV70 @ ( relation_dom @ SY4922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2137,plain,
! [SV176: $i] :
( ( ( connected @ SV176 )
= $false )
| ( ( is_connected_in @ SV176 @ ( relation_field @ SV176 ) )
= $true )
| ( ( relation @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2138,plain,
! [SV177: $i] :
( ( ( is_connected_in @ SV177 @ ( relation_field @ SV177 ) )
= $false )
| ( ( connected @ SV177 )
= $true )
| ( ( relation @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2139,plain,
! [SV178: $i] :
( ( ( ( relation_dom @ SV178 )
= empty_set )
= $false )
| ( ( SV178 = empty_set )
= $true )
| ( ( relation @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2140,plain,
! [SV179: $i] :
( ( ( ( relation_rng @ SV179 )
= empty_set )
= $false )
| ( ( SV179 = empty_set )
= $true )
| ( ( relation @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2141,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( relation @ SV283 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
| ( SV283
= ( relation_inverse @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2142,plain,
! [SV71: $i,SV284: $i] :
( ( ( ~ ( relation @ SV284 ) )
= $true )
| ( ( ( SV284
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2143,plain,
! [SV180: $i] :
( ( ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) )
| ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2144,plain,
! [SV181: $i] :
( ( ( well_founded_relation @ SV181 )
= $false )
| ( ( ! [SY4788: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SY4788 @ SV181 ) ) @ SY4788 )
| ~ ( in @ ( sK42_C @ SY4788 @ SV181 ) @ SY4788 ) )
| ( SY4788 = empty_set )
| ~ ( subset @ SY4788 @ ( relation_field @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2145,plain,
! [SV72: $i,SV182: $i] :
( ( ( ~ ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2146,plain,
! [SV182: $i,SV72: $i] :
( ( ( ~ ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2147,plain,
! [SV183: $i,SV232: $i] :
( ( ( function @ SV232 )
= $false )
| ( ( ~ ( relation @ SV232 ) )
= $true )
| ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 )
| ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2148,plain,
! [SV184: $i,SV233: $i] :
( ( ( function @ SV233 )
= $false )
| ( ( ~ ( relation @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2149,plain,
! [SV185: $i] :
( ( ( ! [SY4799: $i,SY4800: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SY4799 @ SY4800 ) ) )
= $true )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2150,plain,
! [SV185: $i] :
( ( ( in @ ( sK50_B @ SV185 ) @ SV185 )
= $true )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2151,plain,
! [SV186: $i,SV285: $i] :
( ( ( SV285
= ( ordered_pair @ ( sK48_C @ SV285 @ SV186 ) @ ( sK49_SY4428 @ SV285 @ SV186 ) ) )
= $true )
| ( ( ~ ( in @ SV285 @ SV186 ) )
= $true )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2152,plain,
! [SV73: $i,SV286: $i] :
( ( ( ~ ( ~ ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) ) ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2153,plain,
! [SV73: $i,SV287: $i] :
( ( ( ( SV287
!= ( relation_dom @ SV73 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) )
| ~ ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2154,plain,
! [SV234: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 )
| ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2155,plain,
! [SV235: $i,SV188: $i] :
( ( ( ~ ( function @ SV188 )
| ~ ( relation @ SV188 ) )
= $true )
| ( ( ~ ( relation @ SV235 ) )
= $true )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2156,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2157,plain,
! [SV289: $i,SV74: $i] :
( ( ( ~ ( is_connected_in @ SV74 @ SV289 ) )
= $true )
| ( ( ! [SY4875: $i,SY4876: $i] :
( ( SY4875 = SY4876 )
| ~ ( in @ SY4875 @ SV289 )
| ~ ( in @ SY4876 @ SV289 )
| ( in @ ( ordered_pair @ SY4875 @ SY4876 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4876 @ SY4875 ) @ SV74 ) ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2158,plain,
! [SV189: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2159,plain,
! [SV190: $i] :
( ( ( connected @ SV190 )
= $false )
| ( ( ! [SY4804: $i,SY4805: $i] :
( ( SY4804 = SY4805 )
| ~ ( in @ SY4804 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4805 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SY4804 @ SY4805 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4805 @ SY4804 ) @ SV190 ) ) )
= $true )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2160,plain,
! [SV236: $i,SV75: $i,SV259: $i] :
( ( ( relation @ SV259 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SV259 )
| ( in @ SV75 @ ( relation_dom @ SV259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2161,plain,
! [SV237: $i,SV75: $i,SV260: $i] :
( ( ( relation @ SV260 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SV260 )
| ( in @ SV237 @ ( relation_rng @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2162,plain,
! [SV191: $i] :
( ( ( relation @ SV191 )
= $false )
| ( ( function @ SV191 )
= $false )
| ( ( ~ ( one_to_one @ SV191 )
| ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2163,plain,
! [SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( function @ SV192 )
= $false )
| ( ( ~ ( one_to_one @ SV192 )
| ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2164,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2165,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2166,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2167,plain,
! [SV291: $i,SV77: $i] :
( ( ( ~ ( is_transitive_in @ SV77 @ SV291 ) )
= $true )
| ( ( ! [SY4877: $i,SY4878: $i,SY4879: $i] :
( ~ ( in @ SY4877 @ SV291 )
| ~ ( in @ SY4878 @ SV291 )
| ~ ( in @ SY4879 @ SV291 )
| ~ ( in @ ( ordered_pair @ SY4877 @ SY4878 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4878 @ SY4879 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4877 @ SY4879 ) @ SV77 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2168,plain,
! [SV78: $i] :
( ( ( ! [SY4616: $i,SY4617: $i] :
( ~ ( ~ ( ! [SY4618: $i] :
( ~ ( in @ SY4618 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4618 @ SY4616 )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ SY4618 ) ) )
| ~ ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) @ SY4616 ) )
| ( ( sK61_D @ SY4617 @ SY4616 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4617 @ SY4616 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4617 @ SY4616 @ SV78 ) @ SY4617 ) ) )
| ( SY4617
= ( relation_image @ SV78 @ SY4616 ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2169,plain,
! [SV78: $i] :
( ( ( ! [SY4619: $i,SY4620: $i] :
( ( SY4620
!= ( relation_image @ SV78 @ SY4619 ) )
| ~ ( ~ ! [SY4621: $i] :
( ! [SY4622: $i] :
( ~ ( in @ SY4622 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4622 @ SY4619 )
| ( SY4621
!= ( apply @ SV78 @ SY4622 ) ) )
| ( in @ SY4621 @ SY4620 ) )
| ~ ! [SY4623: $i] :
( ~ ( in @ SY4623 @ SY4620 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) @ SY4619 ) )
| ( SY4623
!= ( apply @ SV78 @ ( sK60_E @ SY4623 @ SY4620 @ SY4619 @ SV78 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2170,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) ) )
| ( SV318
= ( fiber @ SV79 @ SV292 ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2171,plain,
! [SV293: $i,SV79: $i,SV319: $i] :
( ( ( ( SV319
!= ( fiber @ SV79 @ SV293 ) )
| ~ ( ~ ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) )
| ~ ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2172,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( relation @ SV294 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
| ( SV80 = SV294 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2173,plain,
! [SV80: $i,SV295: $i] :
( ( ( ~ ( relation @ SV295 ) )
= $true )
| ( ( ( SV80 != SV295 )
| ~ ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2174,plain,
! [SV195: $i] :
( ( ( function @ SV195 )
= $false )
| ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( ~ ( one_to_one @ SV195 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2175,plain,
! [SV196: $i] :
( ( ( function @ SV196 )
= $false )
| ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( ~ ( one_to_one @ SV196 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2176,plain,
! [SV197: $i] :
( ( ( relation @ SV197 )
= $false )
| ( ( function @ SV197 )
= $false )
| ( ( function @ ( function_inverse @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2177,plain,
! [SV198: $i] :
( ( ( relation @ SV198 )
= $false )
| ( ( function @ SV198 )
= $false )
| ( ( relation @ ( function_inverse @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2178,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_C @ SV296 @ SV81 ) @ SV296 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 ) ) )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2179,plain,
! [SV297: $i,SV81: $i] :
( ( ( ~ ( is_reflexive_in @ SV81 @ SV297 ) )
= $true )
| ( ( ! [SY4889: $i] :
( ~ ( in @ SY4889 @ SV297 )
| ( in @ ( ordered_pair @ SY4889 @ SY4889 ) @ SV81 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2180,plain,
! [SV82: $i,SV238: $i,SV261: $i] :
( ( ( ~ ( function @ SV261 ) )
= $true )
| ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2181,plain,
! [SV82: $i,SV320: $i] :
( ( ! [SY4926: $i] :
( ~ ( function @ SY4926 )
| ~ ( relation @ SY4926 )
| ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SY4926 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SY4926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2182,plain,
! [SV82: $i,SV321: $i] :
( ( ! [SY4927: $i] :
( ~ ( function @ SY4927 )
| ~ ( relation @ SY4927 )
| ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SY4927 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2183,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( relation @ SV322 )
| ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
| ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2184,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 )
| ( SV323
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2185,plain,
! [SV298: $i,SV84: $i] :
( ( ( ~ ( ~ ! [SY4890: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4890 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SY4890 @ ( sK39_C @ SV298 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2186,plain,
! [SV299: $i,SV84: $i] :
( ( ( ~ ( is_well_founded_in @ SV84 @ SV299 ) )
= $true )
| ( ( ! [SY4891: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) ) @ SY4891 )
| ~ ( in @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) @ SY4891 ) )
| ( SY4891 = empty_set )
| ~ ( subset @ SY4891 @ SV299 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2187,plain,
! [SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
| ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2188,plain,
! [SV204: $i] :
( ( ( antisymmetric @ SV204 )
= $false )
| ( ( ! [SY4806: $i,SY4807: $i] :
( ~ ( in @ ( ordered_pair @ SY4806 @ SY4807 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4807 @ SY4806 ) @ SV204 )
| ( SY4806 = SY4807 ) ) )
= $true )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2189,plain,
! [SV85: $i] :
( ( ( ~ ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2190,plain,
! [SV85: $i] :
( ( ( ~ ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2191,plain,
! [SV86: $i] :
( ( ( ! [SY4667: $i] :
( ~ ( ~ ( ! [SY4668: $i] :
( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ SY4668 ) )
| ~ ( in @ SY4668 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) )
| ~ ( ~ ( ( ( sK31_C @ SY4667 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SY4667 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SY4667 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SY4667 @ SV86 ) @ SY4667 ) ) )
| ( SY4667
= ( relation_rng @ SV86 ) ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2192,plain,
! [SV86: $i] :
( ( ( ! [SY4669: $i] :
( ( SY4669
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4670: $i] :
( ! [SY4671: $i] :
( ( SY4670
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4670 @ SY4669 ) )
| ~ ! [SY4672: $i] :
( ~ ( in @ SY4672 @ SY4669 )
| ~ ( ( SY4672
!= ( apply @ SV86 @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4672 @ SY4669 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2193,plain,
! [SV239: $i,SV87: $i,SV262: $i] :
( ( ( relation @ SV262 )
= $false )
| ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV262 @ SV239 ) ) )
| ( in @ SV87 @ ( relation_field @ SV262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2194,plain,
! [SV240: $i,SV87: $i,SV263: $i] :
( ( ( relation @ SV263 )
= $false )
| ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV263 @ SV240 ) ) )
| ( in @ SV87 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2195,plain,
! [SV205: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2196,plain,
! [SV206: $i] :
( ( ( transitive @ SV206 )
= $false )
| ( ( ! [SY4808: $i,SY4809: $i,SY4810: $i] :
( ~ ( in @ ( ordered_pair @ SY4808 @ SY4809 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4809 @ SY4810 ) @ SV206 )
| ( in @ ( ordered_pair @ SY4808 @ SY4810 ) @ SV206 ) ) )
= $true )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2197,plain,
! [SV88: $i] :
( ( ( ! [SY4677: $i,SY4678: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ~ ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) ) @ SY4677 )
| ( in @ ( sK57_D @ SY4678 @ SY4677 @ SV88 ) @ SY4678 ) ) ) )
| ( SY4678
= ( relation_inverse_image @ SV88 @ SY4677 ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2198,plain,
! [SV88: $i] :
( ( ( ! [SY4679: $i,SY4680: $i] :
( ( SY4680
!= ( relation_inverse_image @ SV88 @ SY4679 ) )
| ~ ( ~ ! [SY4681: $i] :
( ~ ( in @ SY4681 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4681 ) @ SY4679 )
| ( in @ SY4681 @ SY4680 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4680 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4683: $i] :
( ~ ( in @ SY4683 @ SY4680 )
| ( in @ ( apply @ SV88 @ SY4683 ) @ SY4679 ) ) ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2199,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)],[2040]) ).
thf(2200,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2040]) ).
thf(2201,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2202,plain,
( ( ~ ( epsilon_transitive @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2041]) ).
thf(2203,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2204,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2205,plain,
! [SV90: $i,SV300: $i] :
( ( ( ~ ( relation @ SV300 ) )
= $true )
| ( ( ~ ( subset @ SV90 @ SV300 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SV300 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2206,plain,
! [SV90: $i,SV301: $i] :
( ( ( ~ ( relation @ SV301 ) )
= $true )
| ( ( ~ ( subset @ SV90 @ SV301 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SV301 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2207,plain,
! [SV208: $i] :
( ( ( is_well_founded_in @ SV208 @ ( relation_field @ SV208 ) )
= $false )
| ( ( well_founded_relation @ SV208 )
= $true )
| ( ( relation @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2208,plain,
! [SV209: $i] :
( ( ( well_founded_relation @ SV209 )
= $false )
| ( ( is_well_founded_in @ SV209 @ ( relation_field @ SV209 ) )
= $true )
| ( ( relation @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2209,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2210,plain,
! [SV211: $i,SV242: $i] :
( ( ( ( SV242
!= ( identity_relation @ SV211 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) ) )
= $true )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2048]) ).
thf(2211,plain,
! [SV212: $i] :
( ( ( relation_empty_yielding @ SV212 )
= $false )
| ( ( relation @ SV212 )
= $false )
| ( ( ! [SY4824: $i] : ( relation @ ( relation_dom_restriction @ SV212 @ SY4824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2212,plain,
! [SV213: $i] :
( ( ( relation_empty_yielding @ SV213 )
= $false )
| ( ( relation @ SV213 )
= $false )
| ( ( ! [SY4825: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SY4825 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2213,plain,
! [SV91: $i,SV302: $i] :
( ( ( ~ ( ~ ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) ) ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2214,plain,
! [SV91: $i,SV303: $i] :
( ( ( ( SV303
!= ( relation_rng @ SV91 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) )
| ~ ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2215,plain,
! [SV243: $i,SV92: $i,SV264: $i] :
( ( ( relation @ SV264 )
= $false )
| ( ( ! [SY4856: $i] :
( ~ ( in @ SY4856 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SY4856 @ SV92 ) @ SV264 )
| ~ ( in @ SY4856 @ SV243 ) )
| ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2216,plain,
! [SV244: $i,SV92: $i,SV265: $i] :
( ( ( relation @ SV265 )
= $false )
| ( ( ~ ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2217,plain,
! [SV214: $i] :
( ( ( antisymmetric @ SV214 )
= $false )
| ( ( is_antisymmetric_in @ SV214 @ ( relation_field @ SV214 ) )
= $true )
| ( ( relation @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2218,plain,
! [SV215: $i] :
( ( ( is_antisymmetric_in @ SV215 @ ( relation_field @ SV215 ) )
= $false )
| ( ( antisymmetric @ SV215 )
= $true )
| ( ( relation @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2219,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2220,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2057]) ).
thf(2221,plain,
! [SV245: $i,SV94: $i,SV266: $i] :
( ( ( relation @ SV266 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SV266 )
| ( in @ SV94 @ ( relation_field @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2222,plain,
! [SV246: $i,SV94: $i,SV267: $i] :
( ( ( relation @ SV267 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SV267 )
| ( in @ SV246 @ ( relation_field @ SV267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2223,plain,
! [SV247: $i,SV95: $i,SV268: $i] :
( ( ( relation @ SV268 )
= $false )
| ( ( ~ ( in @ SV95 @ SV247 )
| ~ ( in @ SV95 @ ( relation_rng @ SV268 ) )
| ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2224,plain,
! [SV324: $i,SV95: $i] :
( ( ! [SY4934: $i] :
( ~ ( relation @ SY4934 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SY4934 ) ) )
| ( in @ SV95 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2225,plain,
! [SV325: $i,SV95: $i] :
( ( ! [SY4935: $i] :
( ~ ( relation @ SY4935 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SY4935 ) ) )
| ( in @ SV95 @ ( relation_rng @ SY4935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2226,plain,
( ( ~ ( function @ sK3_SY4404 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2227,plain,
( ( ~ ( relation @ sK3_SY4404 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2228,plain,
( ( ~ ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2229,plain,
( ( ~ ~ ( well_ordering @ sK2_SY4402 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2230,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( relation @ SV326 )
| ~ ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
| ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2231,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( ~ ( relation @ SV327 )
| ( SV327
!= ( relation_dom_restriction @ SV96 @ SV305 ) )
| ~ ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2232,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) ) )
| ( SV328
= ( relation_image @ SV97 @ SV306 ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2233,plain,
! [SV307: $i,SV97: $i,SV329: $i] :
( ( ( ( SV329
!= ( relation_image @ SV97 @ SV307 ) )
| ~ ( ~ ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) )
| ~ ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2234,plain,
! [SV250: $i,SV220: $i] :
( ( ( empty @ SV220 )
= $false )
| ( ( ~ ( relation @ SV250 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV220 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2235,plain,
! [SV251: $i,SV221: $i] :
( ( ( empty @ SV221 )
= $false )
| ( ( ~ ( relation @ SV251 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV221 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2236,plain,
! [SV222: $i,SV252: $i] :
( ( ( function @ SV252 )
= $false )
| ( ( ~ ( relation @ SV252 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 )
| ( SV252
= ( identity_relation @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2237,plain,
! [SV308: $i,SV330: $i] :
( ( ~ ( function @ SV330 )
| ~ ( relation @ SV330 )
| ( SV330
!= ( identity_relation @ SV308 ) )
| ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2238,plain,
! [SV309: $i,SV331: $i] :
( ( ~ ( function @ SV331 )
| ~ ( relation @ SV331 )
| ( SV331
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SV331 )
= SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2239,plain,
! [SV115: $i,SV21: $i,SV269: $i] :
( ( ( ~ ( function @ SV269 ) )
= $true )
| ( ( ~ ( relation @ SV269 ) )
= $true )
| ( ( ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) ) )
= $true )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2240,plain,
! [SV117: $i,SV23: $i,SV270: $i] :
( ( ( ~ ( function @ SV270 ) )
= $true )
| ( ( ~ ( relation @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) ) )
= $true )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2241,plain,
! [SV149: $i,SV34: $i,SV271: $i] :
( ( ( ~ ( function @ SV271 ) )
= $true )
| ( ( ~ ( relation @ SV271 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2242,plain,
! [SV37: $i,SV142: $i,SV124: $i] :
( ( ( in @ SV124 @ ( relation_dom @ ( relation_dom_restriction @ SV142 @ SV37 ) ) )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV142 @ SV37 ) @ SV124 )
= ( apply @ SV142 @ SV124 ) )
= $true )
| ( ( function @ SV142 )
= $false )
| ( ( relation @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2243,plain,
! [SV143: $i,SV38: $i,SV125: $i] :
( ( ( in @ SV125 @ SV38 )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV143 @ SV38 ) @ SV125 )
= ( apply @ SV143 @ SV125 ) )
= $true )
| ( ( function @ SV143 )
= $false )
| ( ( relation @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2244,plain,
! [SV153: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2245,plain,
! [SV154: $i] :
( ( ( ~ ( one_to_one @ SV154 ) )
= $true )
| ( ( ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2246,plain,
! [SV155: $i,SV223: $i] :
( ( ( relation @ SV223 )
= $false )
| ( ( function @ SV223 )
= $false )
| ( ( function @ ( relation_rng_restriction @ SV155 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2247,plain,
! [SV156: $i,SV224: $i] :
( ( ( relation @ SV224 )
= $false )
| ( ( function @ SV224 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV156 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2248,plain,
! [SV159: $i] :
( ( ( ~ ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) ) )
= $false )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2249,plain,
! [SV159: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
= $false )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2250,plain,
! [SV160: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_field @ SV160 ) )
| ( in @ ( ordered_pair @ SV332 @ SV332 ) @ SV160 ) )
= $true )
| ( ( reflexive @ SV160 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2251,plain,
! [SV60: $i] :
( ( ( ~ ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2252,plain,
! [SV60: $i] :
( ( ( ~ ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2094]) ).
thf(2253,plain,
! [SV135: $i,SV253: $i,SV61: $i,SV272: $i] :
( ( ( relation @ SV272 )
= $false )
| ( ( ~ ( in @ SV61 @ SV253 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2254,plain,
! [SV333: $i,SV135: $i,SV61: $i] :
( ( ! [SY4947: $i] :
( ~ ( relation @ SY4947 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SY4947 ) )
| ( in @ SV61 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2255,plain,
! [SV334: $i,SV135: $i,SV61: $i] :
( ( ! [SY4948: $i] :
( ~ ( relation @ SY4948 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SY4948 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SY4948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2256,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( ( ( sK33_C @ SV273 @ SV62 )
!= ( sK34_SY4421 @ SV273 @ SV62 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2257,plain,
! [SV274: $i,SV62: $i] :
( ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( ! [SY4857: $i,SY4858: $i] :
( ~ ( in @ SY4857 @ SV274 )
| ~ ( in @ SY4858 @ SV274 )
| ~ ( in @ ( ordered_pair @ SY4857 @ SY4858 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4858 @ SY4857 ) @ SV62 )
| ( SY4857 = SY4858 ) ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2258,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ~ ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) ) ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2259,plain,
! [SV276: $i,SV63: $i,SV311: $i] :
( ( ( ( SV311
!= ( relation_inverse_image @ SV63 @ SV276 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) )
| ~ ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2260,plain,
! [SV225: $i,SV254: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV254 )
| ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) )
= $true )
| ( ( relation @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2261,plain,
! [SV312: $i,SV64: $i,SV335: $i] :
( ( ~ ( relation @ SV335 )
| ~ ( in @ SV64 @ ( relation_restriction @ SV335 @ SV312 ) )
| ( in @ SV64 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2262,plain,
! [SV313: $i,SV64: $i,SV336: $i] :
( ( ~ ( relation @ SV336 )
| ~ ( in @ SV64 @ ( relation_restriction @ SV336 @ SV313 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2263,plain,
! [SV65: $i,SV277: $i] :
( ( ( relation @ SV277 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
| ( subset @ SV65 @ SV277 ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2264,plain,
! [SV65: $i,SV278: $i] :
( ( ( relation @ SV278 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV278 )
| ! [SY4865: $i,SY4866: $i] :
( ~ ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV278 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2265,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 )
| ~ ( is_transitive_in @ SV66 @ SV279 )
| ~ ( is_antisymmetric_in @ SV66 @ SV279 )
| ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2266,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2267,plain,
! [SV66: $i] :
( ( ( ! [SY4546: $i] :
( ~ ( well_orders @ SV66 @ SY4546 )
| ( is_well_founded_in @ SV66 @ SY4546 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2268,plain,
! [SV163: $i] :
( ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 )
| ~ ( antisymmetric @ SV163 ) )
= $true )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2269,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)],[2113]) ).
thf(2270,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2271,plain,
! [SV280: $i] :
( ( ( relation @ SV280 )
= $false )
| ( ( ~ ( well_ordering @ SV280 )
| ( well_founded_relation @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2272,plain,
! [SV281: $i] :
( ( ( ~ ( empty @ SV281 )
| ~ ( relation @ SV281 ) )
= $true )
| ( ( ~ ( function @ SV281 ) )
= $true )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2273,plain,
! [SV282: $i] :
( ( ( ~ ( empty @ SV282 )
| ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( function @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2274,plain,
! [SV164: $i] :
( ( ( relation @ SV164 )
= $false )
| ( ( empty @ SV164 )
= $false )
| ( ( ~ ( function @ SV164 ) )
= $true )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2275,plain,
! [SV169: $i,SV226: $i] :
( ( ( relation @ SV226 )
= $false )
| ( ( empty @ SV169 )
= $false )
| ( ( empty @ ( relation_composition @ SV226 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2276,plain,
! [SV170: $i,SV227: $i] :
( ( ( relation @ SV227 )
= $false )
| ( ( empty @ SV170 )
= $false )
| ( ( relation @ ( relation_composition @ SV227 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2277,plain,
! [SV337: $i,SV171: $i] :
( ( ( function @ ( relation_dom_restriction @ SV171 @ SV337 ) )
= $true )
| ( ( function @ SV171 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2278,plain,
! [SV338: $i,SV172: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV172 @ SV338 ) )
= $true )
| ( ( function @ SV172 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2279,plain,
! [SV67: $i,SV228: $i,SV255: $i] :
( ( ( function @ SV255 )
= $false )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2280,plain,
! [SV314: $i,SV67: $i,SV339: $i] :
( ( ~ ( function @ SV339 )
| ~ ( relation @ SV339 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
| ( SV314
= ( apply @ SV339 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2281,plain,
! [SV315: $i,SV67: $i,SV340: $i] :
( ( ~ ( function @ SV340 )
| ~ ( relation @ SV340 )
| ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
| ( in @ SV67 @ ( relation_dom @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2282,plain,
! [SV229: $i,SV68: $i,SV256: $i] :
( ( ( ! [SY4855: $i] :
( ~ ( in @ SY4855 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SY4855 ) @ SV256 )
| ~ ( in @ SY4855 @ SV229 ) ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2283,plain,
! [SV230: $i,SV257: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) ) )
= $true )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2284,plain,
! [SV69: $i,SV175: $i] :
( ( ( ! [SY4774: $i] :
( ~ ( function @ SY4774 )
| ~ ( relation @ SY4774 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY4774 @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) ) @ ( apply @ SY4774 @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SY4774 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SY4774 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SY4774 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SY4774 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SY4774 )
| ( relation_isomorphism @ SV69 @ SV175 @ SY4774 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2132]) ).
thf(2285,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2286,plain,
! [SV258: $i,SV231: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV231 )
| ~ ( in @ SV70 @ ( relation_dom @ SV258 ) ) )
= $true )
| ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2287,plain,
! [SV316: $i,SV70: $i,SV341: $i] :
( ( ~ ( relation @ SV341 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV341 @ SV316 ) ) )
| ( in @ SV70 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2288,plain,
! [SV317: $i,SV70: $i,SV342: $i] :
( ( ~ ( relation @ SV342 )
| ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV342 @ SV317 ) ) )
| ( in @ SV70 @ ( relation_dom @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2289,plain,
! [SV71: $i,SV283: $i] :
( ( ( relation @ SV283 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
| ( SV283
= ( relation_inverse @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2290,plain,
! [SV71: $i,SV284: $i] :
( ( ( relation @ SV284 )
= $false )
| ( ( ( SV284
!= ( relation_inverse @ SV71 ) )
| ~ ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2291,plain,
! [SV180: $i] :
( ( ( ~ ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2292,plain,
! [SV180: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2293,plain,
! [SV343: $i,SV181: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
| ~ ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 ) )
| ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2294,plain,
! [SV72: $i,SV182: $i] :
( ( ( ! [SY4789: $i] :
( ~ ( relation @ SY4789 )
| ~ ( ~ ( ! [SY4790: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ SY4790 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4790 @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SY4789 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SY4789 @ SV182 @ SV72 ) ) @ SY4789 ) ) )
| ( SY4789
= ( relation_composition @ SV72 @ SV182 ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2295,plain,
! [SV182: $i,SV72: $i] :
( ( ( ! [SY4791: $i] :
( ~ ( relation @ SY4791 )
| ( SY4791
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4792: $i,SY4793: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4792 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4793 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4792 @ SY4793 ) @ SY4791 ) )
| ~ ! [SY4795: $i,SY4796: $i] :
( ~ ( in @ ( ordered_pair @ SY4795 @ SY4796 ) @ SY4791 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4795 @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4796 @ SY4795 @ SY4791 @ SV182 @ SV72 ) @ SY4796 ) @ SV182 ) ) ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2296,plain,
! [SV183: $i,SV232: $i] :
( ( ( relation @ SV232 )
= $false )
| ( ( function @ SV232 )
= $false )
| ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 )
| ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2297,plain,
! [SV184: $i,SV233: $i] :
( ( ( relation @ SV233 )
= $false )
| ( ( function @ SV233 )
= $false )
| ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 )
| ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2298,plain,
! [SV344: $i,SV185: $i] :
( ( ( ! [SY4949: $i] :
( ( sK50_B @ SV185 )
!= ( ordered_pair @ SV344 @ SY4949 ) ) )
= $true )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2299,plain,
! [SV186: $i,SV285: $i] :
( ( ( in @ SV285 @ SV186 )
= $false )
| ( ( SV285
= ( ordered_pair @ ( sK48_C @ SV285 @ SV186 ) @ ( sK49_SY4428 @ SV285 @ SV186 ) ) )
= $true )
| ( ( relation @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2300,plain,
! [SV73: $i,SV286: $i] :
( ( ( ~ ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) ) )
= $false )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2301,plain,
! [SV73: $i,SV287: $i] :
( ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( ~ ( ~ ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) )
| ~ ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2302,plain,
! [SV234: $i,SV187: $i] :
( ( ( ~ ( function @ SV187 ) )
= $true )
| ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2303,plain,
! [SV235: $i,SV188: $i] :
( ( ( ~ ( function @ SV188 ) )
= $true )
| ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( ~ ( relation @ SV235 ) )
= $true )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2304,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2305,plain,
! [SV289: $i,SV74: $i] :
( ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( ! [SY4875: $i,SY4876: $i] :
( ( SY4875 = SY4876 )
| ~ ( in @ SY4875 @ SV289 )
| ~ ( in @ SY4876 @ SV289 )
| ( in @ ( ordered_pair @ SY4875 @ SY4876 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4876 @ SY4875 ) @ SV74 ) ) )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2306,plain,
! [SV189: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2307,plain,
! [SV189: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2308,plain,
! [SV190: $i,SV345: $i] :
( ( ( ! [SY4950: $i] :
( ( SV345 = SY4950 )
| ~ ( in @ SV345 @ ( relation_field @ SV190 ) )
| ~ ( in @ SY4950 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SV345 @ SY4950 ) @ SV190 )
| ( in @ ( ordered_pair @ SY4950 @ SV345 ) @ SV190 ) ) )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2309,plain,
! [SV259: $i,SV236: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SV259 ) )
= $true )
| ( ( in @ SV75 @ ( relation_dom @ SV259 ) )
= $true )
| ( ( relation @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2310,plain,
! [SV260: $i,SV237: $i,SV75: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SV260 ) )
= $true )
| ( ( in @ SV237 @ ( relation_rng @ SV260 ) )
= $true )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2311,plain,
! [SV191: $i] :
( ( ( ~ ( one_to_one @ SV191 ) )
= $true )
| ( ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) )
= $true )
| ( ( function @ SV191 )
= $false )
| ( ( relation @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2162]) ).
thf(2312,plain,
! [SV192: $i] :
( ( ( ~ ( one_to_one @ SV192 ) )
= $true )
| ( ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) )
= $true )
| ( ( function @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2313,plain,
! [SV136: $i,SV76: $i] :
( ( ( ! [SY4749: $i] :
( ~ ( function @ SY4749 )
| ~ ( relation @ SY4749 )
| ~ ( in @ SV76 @ ( relation_dom @ SY4749 ) )
| ~ ( in @ ( apply @ SY4749 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4749 @ SV136 ) ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2314,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2165]) ).
thf(2315,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2316,plain,
! [SV291: $i,SV77: $i] :
( ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( ! [SY4877: $i,SY4878: $i,SY4879: $i] :
( ~ ( in @ SY4877 @ SV291 )
| ~ ( in @ SY4878 @ SV291 )
| ~ ( in @ SY4879 @ SV291 )
| ~ ( in @ ( ordered_pair @ SY4877 @ SY4878 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4878 @ SY4879 ) @ SV77 )
| ( in @ ( ordered_pair @ SY4877 @ SY4879 ) @ SV77 ) ) )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2317,plain,
! [SV346: $i,SV78: $i] :
( ( ( ! [SY4951: $i] :
( ~ ( ~ ( ! [SY4952: $i] :
( ~ ( in @ SY4952 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4952 @ SV346 )
| ( ( sK61_D @ SY4951 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4952 ) ) )
| ~ ( in @ ( sK61_D @ SY4951 @ SV346 @ SV78 ) @ SY4951 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SY4951 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SY4951 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SY4951 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SY4951 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SY4951 @ SV346 @ SV78 ) @ SY4951 ) ) )
| ( SY4951
= ( relation_image @ SV78 @ SV346 ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2318,plain,
! [SV347: $i,SV78: $i] :
( ( ( ! [SY4953: $i] :
( ( SY4953
!= ( relation_image @ SV78 @ SV347 ) )
| ~ ( ~ ! [SY4954: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4954
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4954 @ SY4953 ) )
| ~ ! [SY4956: $i] :
( ~ ( in @ SY4956 @ SY4953 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4956 @ SY4953 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4956 @ SY4953 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4956
!= ( apply @ SV78 @ ( sK60_E @ SY4956 @ SY4953 @ SV347 @ SV78 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2319,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) ) ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2320,plain,
! [SV293: $i,SV79: $i,SV319: $i] :
( ( ( ( SV319
!= ( fiber @ SV79 @ SV293 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) )
| ~ ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2321,plain,
! [SV80: $i,SV294: $i] :
( ( ( relation @ SV294 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
| ( SV80 = SV294 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2322,plain,
! [SV80: $i,SV295: $i] :
( ( ( relation @ SV295 )
= $false )
| ( ( ( SV80 != SV295 )
| ~ ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2323,plain,
! [SV195: $i] :
( ( ( relation @ SV195 )
= $false )
| ( ( function @ SV195 )
= $false )
| ( ( ~ ( one_to_one @ SV195 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2324,plain,
! [SV196: $i] :
( ( ( relation @ SV196 )
= $false )
| ( ( function @ SV196 )
= $false )
| ( ( ~ ( one_to_one @ SV196 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2325,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV296 @ SV81 ) @ SV296 )
| ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 ) )
= $false )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2326,plain,
! [SV297: $i,SV81: $i] :
( ( ( is_reflexive_in @ SV81 @ SV297 )
= $false )
| ( ( ! [SY4889: $i] :
( ~ ( in @ SY4889 @ SV297 )
| ( in @ ( ordered_pair @ SY4889 @ SY4889 ) @ SV81 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2327,plain,
! [SV82: $i,SV238: $i,SV261: $i] :
( ( ( function @ SV261 )
= $false )
| ( ( ~ ( relation @ SV261 ) )
= $true )
| ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2328,plain,
! [SV82: $i,SV320: $i,SV348: $i] :
( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 )
| ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2329,plain,
! [SV82: $i,SV321: $i,SV349: $i] :
( ( ~ ( function @ SV349 )
| ~ ( relation @ SV349 )
| ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2330,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( relation @ SV322 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
| ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2331,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 ) )
= $true )
| ( ( ( SV323
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2332,plain,
! [SV298: $i,SV84: $i] :
( ( ( ~ ! [SY4890: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4890 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SY4890 @ ( sK39_C @ SV298 @ SV84 ) ) )
| ~ ~ ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2333,plain,
! [SV299: $i,SV84: $i] :
( ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( ! [SY4891: $i] :
( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) ) @ SY4891 )
| ~ ( in @ ( sK38_D @ SY4891 @ SV299 @ SV84 ) @ SY4891 ) )
| ( SY4891 = empty_set )
| ~ ( subset @ SY4891 @ SV299 ) ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2334,plain,
! [SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2187]) ).
thf(2335,plain,
! [SV203: $i] :
( ( ( ~ ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2187]) ).
thf(2336,plain,
! [SV204: $i,SV350: $i] :
( ( ( ! [SY4957: $i] :
( ~ ( in @ ( ordered_pair @ SV350 @ SY4957 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SY4957 @ SV350 ) @ SV204 )
| ( SV350 = SY4957 ) ) )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2337,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) )
| ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2338,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) )
| ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2339,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ~ ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
| ~ ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) ) )
| ( SV351
= ( relation_rng @ SV86 ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2340,plain,
! [SV86: $i,SV352: $i] :
( ( ( ( SV352
!= ( relation_rng @ SV86 ) )
| ~ ( ~ ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) )
| ~ ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2341,plain,
! [SV239: $i,SV262: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV262 @ SV239 ) ) ) )
= $true )
| ( ( in @ SV87 @ ( relation_field @ SV262 ) )
= $true )
| ( ( relation @ SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2342,plain,
! [SV240: $i,SV263: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV263 @ SV240 ) ) ) )
= $true )
| ( ( in @ SV87 @ SV240 )
= $true )
| ( ( relation @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2343,plain,
! [SV205: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2344,plain,
! [SV205: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2345,plain,
! [SV206: $i,SV353: $i] :
( ( ( ! [SY4962: $i,SY4963: $i] :
( ~ ( in @ ( ordered_pair @ SV353 @ SY4962 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SY4962 @ SY4963 ) @ SV206 )
| ( in @ ( ordered_pair @ SV353 @ SY4963 ) @ SV206 ) ) )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2346,plain,
! [SV88: $i,SV354: $i] :
( ( ( ! [SY4964: $i] :
( ~ ( ~ ( ~ ( in @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) @ SY4964 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) @ SY4964 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SY4964 @ SV354 @ SV88 ) @ SY4964 ) ) ) )
| ( SY4964
= ( relation_inverse_image @ SV88 @ SV354 ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2347,plain,
! [SV355: $i,SV88: $i] :
( ( ( ! [SY4965: $i] :
( ( SY4965
!= ( relation_inverse_image @ SV88 @ SV355 ) )
| ~ ( ~ ! [SY4966: $i] :
( ~ ( in @ SY4966 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4966 ) @ SV355 )
| ( in @ SY4966 @ SY4965 ) )
| ~ ~ ( ~ ! [SY4682: $i] :
( ~ ( in @ SY4682 @ SY4965 )
| ( in @ SY4682 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4968: $i] :
( ~ ( in @ SY4968 @ SY4965 )
| ( in @ ( apply @ SV88 @ SY4968 ) @ SV355 ) ) ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2348,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)],[2199]) ).
thf(2349,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2350,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2351,plain,
( ( epsilon_transitive @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2352,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2353,plain,
! [SV207: $i,SV89: $i] :
( ( ( ! [SY4815: $i] :
( ~ ( function @ SY4815 )
| ~ ( relation @ SY4815 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4815 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2354,plain,
! [SV90: $i,SV300: $i] :
( ( ( relation @ SV300 )
= $false )
| ( ( ~ ( subset @ SV90 @ SV300 )
| ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SV300 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2355,plain,
! [SV90: $i,SV301: $i] :
( ( ( relation @ SV301 )
= $false )
| ( ( ~ ( subset @ SV90 @ SV301 )
| ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SV301 ) ) )
= $true )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2356,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2357,plain,
! [SV211: $i,SV242: $i] :
( ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( ~ ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) ) )
= $true )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2358,plain,
! [SV356: $i,SV212: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV212 @ SV356 ) )
= $true )
| ( ( relation @ SV212 )
= $false )
| ( ( relation_empty_yielding @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2359,plain,
! [SV357: $i,SV213: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV213 @ SV357 ) )
= $true )
| ( ( relation @ SV213 )
= $false )
| ( ( relation_empty_yielding @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2360,plain,
! [SV91: $i,SV302: $i] :
( ( ( ~ ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2361,plain,
! [SV91: $i,SV303: $i] :
( ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( ~ ( ~ ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) )
| ~ ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2362,plain,
! [SV243: $i,SV92: $i,SV264: $i] :
( ( ( ! [SY4856: $i] :
( ~ ( in @ SY4856 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SY4856 @ SV92 ) @ SV264 )
| ~ ( in @ SY4856 @ SV243 ) ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2363,plain,
! [SV244: $i,SV265: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2364,plain,
! [SV93: $i,SV138: $i] :
( ( ( ! [SY4760: $i] :
( ~ ( function @ SY4760 )
| ~ ( relation @ SY4760 )
| ~ ( ~ ( in @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) )
!= ( apply @ SY4760 @ ( sK67_D @ SY4760 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SY4760 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SY4760 @ SV93 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2365,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2366,plain,
! [SV266: $i,SV245: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SV266 ) )
= $true )
| ( ( in @ SV94 @ ( relation_field @ SV266 ) )
= $true )
| ( ( relation @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2367,plain,
! [SV267: $i,SV246: $i,SV94: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SV267 ) )
= $true )
| ( ( in @ SV246 @ ( relation_field @ SV267 ) )
= $true )
| ( ( relation @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2368,plain,
! [SV268: $i,SV247: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV247 )
| ~ ( in @ SV95 @ ( relation_rng @ SV268 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) )
= $true )
| ( ( relation @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2369,plain,
! [SV324: $i,SV95: $i,SV358: $i] :
( ( ~ ( relation @ SV358 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SV358 ) ) )
| ( in @ SV95 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2370,plain,
! [SV325: $i,SV95: $i,SV359: $i] :
( ( ~ ( relation @ SV359 )
| ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SV359 ) ) )
| ( in @ SV95 @ ( relation_rng @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2371,plain,
( ( function @ sK3_SY4404 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2372,plain,
( ( relation @ sK3_SY4404 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2373,plain,
( ( ~ ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2374,plain,
( ( ~ ( well_ordering @ sK2_SY4402 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2229]) ).
thf(2375,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( relation @ SV326 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
| ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2376,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( ~ ( relation @ SV327 ) )
= $true )
| ( ( ( SV327
!= ( relation_dom_restriction @ SV96 @ SV305 ) )
| ~ ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2377,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) ) ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2378,plain,
! [SV307: $i,SV97: $i,SV329: $i] :
( ( ( ( SV329
!= ( relation_image @ SV97 @ SV307 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) )
| ~ ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2379,plain,
! [SV220: $i,SV250: $i] :
( ( ( relation @ SV250 )
= $false )
| ( ( empty @ SV220 )
= $false )
| ( ( empty @ ( relation_composition @ SV220 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2380,plain,
! [SV221: $i,SV251: $i] :
( ( ( relation @ SV251 )
= $false )
| ( ( empty @ SV221 )
= $false )
| ( ( relation @ ( relation_composition @ SV221 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2381,plain,
! [SV222: $i,SV252: $i] :
( ( ( relation @ SV252 )
= $false )
| ( ( function @ SV252 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 )
| ( SV252
= ( identity_relation @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2382,plain,
! [SV308: $i,SV330: $i] :
( ( ( ~ ( function @ SV330 )
| ~ ( relation @ SV330 ) )
= $true )
| ( ( ( SV330
!= ( identity_relation @ SV308 ) )
| ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2383,plain,
! [SV309: $i,SV331: $i] :
( ( ( ~ ( function @ SV331 )
| ~ ( relation @ SV331 ) )
= $true )
| ( ( ( SV331
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SV331 )
= SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2384,plain,
! [SV115: $i,SV21: $i,SV269: $i] :
( ( ( function @ SV269 )
= $false )
| ( ( ~ ( relation @ SV269 ) )
= $true )
| ( ( ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) ) )
= $true )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2385,plain,
! [SV117: $i,SV23: $i,SV270: $i] :
( ( ( function @ SV270 )
= $false )
| ( ( ~ ( relation @ SV270 ) )
= $true )
| ( ( ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) ) )
= $true )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2386,plain,
! [SV149: $i,SV34: $i,SV271: $i] :
( ( ( function @ SV271 )
= $false )
| ( ( ~ ( relation @ SV271 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2387,plain,
! [SV153: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
| ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2388,plain,
! [SV154: $i] :
( ( ( one_to_one @ SV154 )
= $false )
| ( ( ! [SY4765: $i,SY4766: $i] :
( ~ ( in @ SY4765 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4766 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SY4765 )
!= ( apply @ SV154 @ SY4766 ) )
| ( SY4765 = SY4766 ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2389,plain,
! [SV159: $i] :
( ( ( in @ ( sK82_B @ SV159 ) @ ( relation_field @ SV159 ) )
= $true )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2390,plain,
! [SV159: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 ) )
= $true )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2391,plain,
! [SV160: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( relation_field @ SV160 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV332 @ SV332 ) @ SV160 )
= $true )
| ( ( reflexive @ SV160 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2392,plain,
! [SV60: $i] :
( ( ( ! [SY4501: $i] :
( ~ ( function @ SY4501 )
| ~ ( relation @ SY4501 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SY4501 @ SV60 )
= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SY4501 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SY4501 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SY4501 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SY4501 @ SV60 )
!= ( apply @ SY4501 @ ( sK70_C @ SY4501 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SY4501 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SY4501 )
!= ( relation_rng @ SV60 ) )
| ( SY4501
= ( function_inverse @ SV60 ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2393,plain,
! [SV60: $i] :
( ( ( ~ ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2394,plain,
! [SV272: $i,SV135: $i,SV253: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV253 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2395,plain,
! [SV333: $i,SV135: $i,SV61: $i,SV360: $i] :
( ( ~ ( relation @ SV360 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SV360 ) )
| ( in @ SV61 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2396,plain,
! [SV334: $i,SV135: $i,SV61: $i,SV361: $i] :
( ( ~ ( relation @ SV361 )
| ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SV361 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2397,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2398,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ( ( sK33_C @ SV273 @ SV62 )
!= ( sK34_SY4421 @ SV273 @ SV62 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2399,plain,
! [SV62: $i,SV274: $i,SV362: $i] :
( ( ( ! [SY4969: $i] :
( ~ ( in @ SV362 @ SV274 )
| ~ ( in @ SY4969 @ SV274 )
| ~ ( in @ ( ordered_pair @ SV362 @ SY4969 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SY4969 @ SV362 ) @ SV62 )
| ( SV362 = SY4969 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2400,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) ) )
= $false )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2401,plain,
! [SV276: $i,SV63: $i,SV311: $i] :
( ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( ~ ( ~ ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) )
| ~ ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2402,plain,
! [SV225: $i,SV254: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV254 ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) )
= $true )
| ( ( relation @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2403,plain,
! [SV312: $i,SV64: $i,SV335: $i] :
( ( ( ~ ( relation @ SV335 ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV335 @ SV312 ) )
| ( in @ SV64 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2404,plain,
! [SV313: $i,SV64: $i,SV336: $i] :
( ( ( ~ ( relation @ SV336 ) )
= $true )
| ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV336 @ SV313 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2405,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) ) )
= $true )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2406,plain,
! [SV278: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV278 ) )
= $true )
| ( ( ! [SY4865: $i,SY4866: $i] :
( ~ ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV278 ) ) )
= $true )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2407,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 )
| ~ ( is_transitive_in @ SV66 @ SV279 )
| ~ ( is_antisymmetric_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2408,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
| ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2409,plain,
! [SV363: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV363 )
| ( is_well_founded_in @ SV66 @ SV363 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2410,plain,
! [SV163: $i] :
( ( ( ~ ( reflexive @ SV163 )
| ~ ( transitive @ SV163 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV163 ) )
= $true )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2411,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)],[2269]) ).
thf(2412,plain,
! [SV364: $i] :
( ( ~ ( relation @ SV364 )
| ~ ( well_ordering @ SV364 )
| ( connected @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2413,plain,
! [SV280: $i] :
( ( ( ~ ( well_ordering @ SV280 ) )
= $true )
| ( ( well_founded_relation @ SV280 )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2414,plain,
! [SV281: $i] :
( ( ( ~ ( empty @ SV281 ) )
= $true )
| ( ( ~ ( relation @ SV281 ) )
= $true )
| ( ( ~ ( function @ SV281 ) )
= $true )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2415,plain,
! [SV282: $i] :
( ( ( ~ ( empty @ SV282 ) )
= $true )
| ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( function @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2416,plain,
! [SV164: $i] :
( ( ( function @ SV164 )
= $false )
| ( ( empty @ SV164 )
= $false )
| ( ( relation @ SV164 )
= $false )
| ( ( one_to_one @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2417,plain,
! [SV67: $i,SV228: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( function @ SV255 )
= $false )
| ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) )
| ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2418,plain,
! [SV314: $i,SV67: $i,SV339: $i] :
( ( ( ~ ( function @ SV339 )
| ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
| ( SV314
= ( apply @ SV339 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2419,plain,
! [SV315: $i,SV67: $i,SV340: $i] :
( ( ( ~ ( function @ SV340 )
| ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
| ( in @ SV67 @ ( relation_dom @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2420,plain,
! [SV229: $i,SV68: $i,SV256: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 )
| ~ ( in @ SV365 @ SV229 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2421,plain,
! [SV230: $i,SV257: $i,SV68: $i] :
( ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) ) )
= $true )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2422,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( function @ SV366 )
| ~ ( relation @ SV366 )
| ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 )
| ( relation_isomorphism @ SV69 @ SV175 @ SV366 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2423,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2424,plain,
! [SV258: $i,SV231: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ SV258 ) ) )
= $true )
| ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2425,plain,
! [SV316: $i,SV70: $i,SV341: $i] :
( ( ( ~ ( relation @ SV341 ) )
= $true )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV341 @ SV316 ) ) )
| ( in @ SV70 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2426,plain,
! [SV317: $i,SV70: $i,SV342: $i] :
( ( ( ~ ( relation @ SV342 ) )
= $true )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV342 @ SV317 ) ) )
| ( in @ SV70 @ ( relation_dom @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2427,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) ) )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2428,plain,
! [SV71: $i,SV284: $i] :
( ( ( ( SV284
!= ( relation_inverse @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) ) )
= $true )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2429,plain,
! [SV180: $i] :
( ( ( ! [SY4787: $i] :
( ~ ( disjoint @ ( fiber @ SV180 @ SY4787 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SY4787 @ ( sK43_B @ SV180 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2430,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2431,plain,
! [SV343: $i,SV181: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
| ~ ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 ) ) )
= $true )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2432,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( relation @ SV367 )
| ~ ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
| ( SV367
= ( relation_composition @ SV72 @ SV182 ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2433,plain,
! [SV182: $i,SV72: $i,SV368: $i] :
( ( ( ~ ( relation @ SV368 )
| ( SV368
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2434,plain,
! [SV232: $i,SV183: $i] :
( ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) )
| ~ ( one_to_one @ SV232 ) )
= $true )
| ( ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) )
= $true )
| ( ( function @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2435,plain,
! [SV233: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) )
| ~ ( one_to_one @ SV233 ) )
= $true )
| ( ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) )
= $true )
| ( ( function @ SV233 )
= $false )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2436,plain,
! [SV369: $i,SV344: $i,SV185: $i] :
( ( ( ( ( sK50_B @ SV185 )
!= ( ordered_pair @ SV344 @ SV369 ) ) )
= $true )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2437,plain,
! [SV73: $i,SV286: $i] :
( ( ( ~ ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) ) )
= $false )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2300]) ).
thf(2438,plain,
! [SV73: $i,SV286: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) ) )
= $false )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2300]) ).
thf(2439,plain,
! [SV287: $i,SV73: $i] :
( ( ( ~ ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) )
| ~ ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) )
= $false )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2440,plain,
! [SV234: $i,SV187: $i] :
( ( ( function @ SV187 )
= $false )
| ( ( ~ ( relation @ SV187 ) )
= $true )
| ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2441,plain,
! [SV235: $i,SV188: $i] :
( ( ( function @ SV188 )
= $false )
| ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( ~ ( relation @ SV235 ) )
= $true )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2442,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2443,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2444,plain,
! [SV74: $i,SV289: $i,SV370: $i] :
( ( ( ! [SY4976: $i] :
( ( SV370 = SY4976 )
| ~ ( in @ SV370 @ SV289 )
| ~ ( in @ SY4976 @ SV289 )
| ( in @ ( ordered_pair @ SV370 @ SY4976 ) @ SV74 )
| ( in @ ( ordered_pair @ SY4976 @ SV370 ) @ SV74 ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2445,plain,
! [SV189: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2446,plain,
! [SV189: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2447,plain,
! [SV190: $i,SV371: $i,SV345: $i] :
( ( ( ( SV345 = SV371 )
| ~ ( in @ SV345 @ ( relation_field @ SV190 ) )
| ~ ( in @ SV371 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
| ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 ) )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2448,plain,
! [SV259: $i,SV236: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV236 ) @ SV259 )
= $false )
| ( ( in @ SV75 @ ( relation_dom @ SV259 ) )
= $true )
| ( ( relation @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2449,plain,
! [SV260: $i,SV237: $i,SV75: $i] :
( ( ( in @ ( ordered_pair @ SV75 @ SV237 ) @ SV260 )
= $false )
| ( ( in @ SV237 @ ( relation_rng @ SV260 ) )
= $true )
| ( ( relation @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2450,plain,
! [SV191: $i] :
( ( ( one_to_one @ SV191 )
= $false )
| ( ( ( relation_rng @ SV191 )
= ( relation_dom @ ( function_inverse @ SV191 ) ) )
= $true )
| ( ( function @ SV191 )
= $false )
| ( ( relation @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2451,plain,
! [SV192: $i] :
( ( ( one_to_one @ SV192 )
= $false )
| ( ( ( relation_dom @ SV192 )
= ( relation_rng @ ( function_inverse @ SV192 ) ) )
= $true )
| ( ( function @ SV192 )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2452,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( ~ ( function @ SV372 )
| ~ ( relation @ SV372 )
| ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2453,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) )
| ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2454,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2455,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2456,plain,
! [SV77: $i,SV291: $i,SV373: $i] :
( ( ( ! [SY4977: $i,SY4978: $i] :
( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SY4977 @ SV291 )
| ~ ( in @ SY4978 @ SV291 )
| ~ ( in @ ( ordered_pair @ SV373 @ SY4977 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SY4977 @ SY4978 ) @ SV77 )
| ( in @ ( ordered_pair @ SV373 @ SY4978 ) @ SV77 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2457,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ~ ( ~ ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) )
| ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) ) )
| ( SV374
= ( relation_image @ SV78 @ SV346 ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2458,plain,
! [SV347: $i,SV78: $i,SV375: $i] :
( ( ( ( SV375
!= ( relation_image @ SV78 @ SV347 ) )
| ~ ( ~ ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) )
| ~ ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2459,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2460,plain,
! [SV293: $i,SV79: $i,SV319: $i] :
( ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( ~ ( ~ ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) )
| ~ ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2461,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) ) )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2321]) ).
thf(2462,plain,
! [SV295: $i,SV80: $i] :
( ( ( ( SV80 != SV295 ) )
= $true )
| ( ( ~ ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2463,plain,
! [SV195: $i] :
( ( ( one_to_one @ SV195 )
= $false )
| ( ( function @ SV195 )
= $false )
| ( ( relation @ SV195 )
= $false )
| ( ( function @ ( relation_inverse @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2464,plain,
! [SV196: $i] :
( ( ( one_to_one @ SV196 )
= $false )
| ( ( function @ SV196 )
= $false )
| ( ( relation @ SV196 )
= $false )
| ( ( relation @ ( relation_inverse @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2465,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ( in @ ( sK47_C @ SV296 @ SV81 ) @ SV296 ) )
= $false )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2466,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 ) )
= $false )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2467,plain,
! [SV81: $i,SV297: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV297 )
| ( in @ ( ordered_pair @ SV376 @ SV376 ) @ SV81 ) )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV297 )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2468,plain,
! [SV82: $i,SV238: $i,SV261: $i] :
( ( ( relation @ SV261 )
= $false )
| ( ( function @ SV261 )
= $false )
| ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 )
| ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2469,plain,
! [SV82: $i,SV320: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 )
| ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SV348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2470,plain,
! [SV82: $i,SV321: $i,SV349: $i] :
( ( ( ~ ( function @ SV349 )
| ~ ( relation @ SV349 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2471,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( relation @ SV322 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
| ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2472,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( relation @ SV323 )
= $false )
| ( ( ( SV323
!= ( relation_rng_restriction @ SV83 @ SV137 ) )
| ~ ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2473,plain,
! [SV298: $i,SV84: $i] :
( ( ( ~ ! [SY4890: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4890 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SY4890 @ ( sK39_C @ SV298 @ SV84 ) ) ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2474,plain,
! [SV84: $i,SV298: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2475,plain,
! [SV299: $i,SV377: $i,SV84: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
| ~ ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 ) )
| ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2476,plain,
! [SV203: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) ) )
= $true )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2477,plain,
! [SV203: $i] :
( ( ( ( ( sK77_B @ SV203 )
!= ( sK78_SY4443 @ SV203 ) ) )
= $true )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2335]) ).
thf(2478,plain,
! [SV204: $i,SV378: $i,SV350: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV350 @ SV378 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SV378 @ SV350 ) @ SV204 )
| ( SV350 = SV378 ) )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2479,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2480,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2481,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2482,plain,
! [SV85: $i] :
( ( ( ~ ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2483,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ~ ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
| ~ ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) ) ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2484,plain,
! [SV86: $i,SV352: $i] :
( ( ( ( SV352
!= ( relation_rng @ SV86 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) )
| ~ ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2485,plain,
! [SV239: $i,SV262: $i,SV87: $i] :
( ( ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV262 @ SV239 ) ) )
= $false )
| ( ( in @ SV87 @ ( relation_field @ SV262 ) )
= $true )
| ( ( relation @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2486,plain,
! [SV240: $i,SV263: $i,SV87: $i] :
( ( ( in @ SV87 @ ( relation_field @ ( relation_restriction @ SV263 @ SV240 ) ) )
= $false )
| ( ( in @ SV87 @ SV240 )
= $true )
| ( ( relation @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2487,plain,
! [SV205: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) ) )
= $true )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2488,plain,
! [SV205: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
= $true )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2489,plain,
! [SV206: $i,SV379: $i,SV353: $i] :
( ( ( ! [SY4983: $i] :
( ~ ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SV379 @ SY4983 ) @ SV206 )
| ( in @ ( ordered_pair @ SV353 @ SY4983 ) @ SV206 ) ) )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2490,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) ) )
| ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2491,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ( SV381
!= ( relation_inverse_image @ SV88 @ SV355 ) )
| ~ ( ~ ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) )
| ~ ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2492,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)],[2348]) ).
thf(2493,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2494,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
| ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2495,plain,
! [SV207: $i,SV89: $i,SV382: $i] :
( ( ( ~ ( function @ SV382 )
| ~ ( relation @ SV382 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2496,plain,
! [SV300: $i,SV90: $i] :
( ( ( ~ ( subset @ SV90 @ SV300 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SV300 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2497,plain,
! [SV301: $i,SV90: $i] :
( ( ( ~ ( subset @ SV90 @ SV301 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SV301 ) )
= $true )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2498,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2499,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2500,plain,
! [SV242: $i,SV211: $i] :
( ( ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) )
| ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2501,plain,
! [SV91: $i,SV302: $i] :
( ( ( ~ ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2502,plain,
! [SV91: $i,SV302: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) ) )
= $false )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2503,plain,
! [SV303: $i,SV91: $i] :
( ( ( ~ ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) )
| ~ ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) )
= $false )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2504,plain,
! [SV243: $i,SV92: $i,SV264: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 )
| ~ ( in @ SV383 @ SV243 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2505,plain,
! [SV244: $i,SV265: $i,SV92: $i] :
( ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) ) )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2506,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( function @ SV384 )
| ~ ( relation @ SV384 )
| ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2507,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) )
| ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2508,plain,
! [SV266: $i,SV245: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ SV245 ) @ SV266 )
= $false )
| ( ( in @ SV94 @ ( relation_field @ SV266 ) )
= $true )
| ( ( relation @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2509,plain,
! [SV267: $i,SV246: $i,SV94: $i] :
( ( ( in @ ( ordered_pair @ SV94 @ SV246 ) @ SV267 )
= $false )
| ( ( in @ SV246 @ ( relation_field @ SV267 ) )
= $true )
| ( ( relation @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2510,plain,
! [SV268: $i,SV247: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV247 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV268 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) )
= $true )
| ( ( relation @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2511,plain,
! [SV324: $i,SV95: $i,SV358: $i] :
( ( ( ~ ( relation @ SV358 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SV358 ) ) )
| ( in @ SV95 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2512,plain,
! [SV325: $i,SV95: $i,SV359: $i] :
( ( ( ~ ( relation @ SV359 ) )
= $true )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SV359 ) ) )
| ( in @ SV95 @ ( relation_rng @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2513,plain,
( ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
| ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2514,plain,
( ( well_ordering @ sK2_SY4402 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2515,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( relation @ SV326 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
| ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2516,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( relation @ SV327 )
= $false )
| ( ( ( SV327
!= ( relation_dom_restriction @ SV96 @ SV305 ) )
| ~ ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2517,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2518,plain,
! [SV307: $i,SV97: $i,SV329: $i] :
( ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( ~ ( ~ ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) )
| ~ ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2519,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
| ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2520,plain,
! [SV308: $i,SV330: $i] :
( ( ( ~ ( function @ SV330 ) )
= $true )
| ( ( ~ ( relation @ SV330 ) )
= $true )
| ( ( ( SV330
!= ( identity_relation @ SV308 ) )
| ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2521,plain,
! [SV309: $i,SV331: $i] :
( ( ( ~ ( function @ SV331 ) )
= $true )
| ( ( ~ ( relation @ SV331 ) )
= $true )
| ( ( ( SV331
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SV331 )
= SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2522,plain,
! [SV115: $i,SV21: $i,SV269: $i] :
( ( ( relation @ SV269 )
= $false )
| ( ( function @ SV269 )
= $false )
| ( ( ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
| ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) ) )
= $true )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2523,plain,
! [SV117: $i,SV23: $i,SV270: $i] :
( ( ( relation @ SV270 )
= $false )
| ( ( function @ SV270 )
= $false )
| ( ( ~ ( in @ SV23 @ ( relation_dom @ SV117 ) )
| ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) ) )
= $true )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2524,plain,
! [SV149: $i,SV34: $i,SV271: $i] :
( ( ( relation @ SV271 )
= $false )
| ( ( function @ SV271 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
| ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2525,plain,
! [SV153: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2526,plain,
! [SV153: $i] :
( ( ( ~ ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2527,plain,
! [SV154: $i,SV385: $i] :
( ( ( ! [SY4987: $i] :
( ~ ( in @ SV385 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY4987 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SY4987 ) )
| ( SV385 = SY4987 ) ) )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2528,plain,
! [SV159: $i] :
( ( ( in @ ( ordered_pair @ ( sK82_B @ SV159 ) @ ( sK82_B @ SV159 ) ) @ SV159 )
= $false )
| ( ( reflexive @ SV159 )
= $true )
| ( ( relation @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2529,plain,
! [SV160: $i,SV332: $i] :
( ( ( in @ SV332 @ ( relation_field @ SV160 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV332 @ SV332 ) @ SV160 )
= $true )
| ( ( reflexive @ SV160 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2530,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( function @ SV386 )
| ~ ( relation @ SV386 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) )
| ( SV386
= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2531,plain,
! [SV60: $i] :
( ( ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
| ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2532,plain,
! [SV272: $i,SV135: $i,SV253: $i,SV61: $i] :
( ( ( ~ ( in @ SV61 @ SV253 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2533,plain,
! [SV333: $i,SV135: $i,SV61: $i,SV360: $i] :
( ( ( ~ ( relation @ SV360 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SV360 ) )
| ( in @ SV61 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2534,plain,
! [SV334: $i,SV135: $i,SV61: $i,SV361: $i] :
( ( ( ~ ( relation @ SV361 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SV361 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2535,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2536,plain,
! [SV62: $i,SV273: $i] :
( ( ( ( ( sK33_C @ SV273 @ SV62 )
!= ( sK34_SY4421 @ SV273 @ SV62 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2537,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV274 )
| ~ ( in @ SV387 @ SV274 )
| ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 )
| ( SV362 = SV387 ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2538,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) ) )
= $false )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2539,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) ) )
= $false )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2540,plain,
! [SV311: $i,SV276: $i,SV63: $i] :
( ( ( ~ ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) )
| ~ ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2541,plain,
! [SV225: $i,SV254: $i,SV64: $i] :
( ( ( in @ SV64 @ SV254 )
= $false )
| ( ( ~ ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) ) )
= $true )
| ( ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) )
= $true )
| ( ( relation @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2542,plain,
! [SV312: $i,SV64: $i,SV335: $i] :
( ( ( relation @ SV335 )
= $false )
| ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV335 @ SV312 ) )
| ( in @ SV64 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2543,plain,
! [SV313: $i,SV64: $i,SV336: $i] :
( ( ( relation @ SV336 )
= $false )
| ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV336 @ SV313 ) )
| ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2544,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
| ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
= $false )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2545,plain,
! [SV278: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV278 )
= $false )
| ( ( ! [SY4865: $i,SY4866: $i] :
( ~ ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV65 )
| ( in @ ( ordered_pair @ SY4865 @ SY4866 ) @ SV278 ) ) )
= $true )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2546,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 )
| ~ ( is_transitive_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2547,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2548,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2549,plain,
! [SV363: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV363 ) )
= $true )
| ( ( is_well_founded_in @ SV66 @ SV363 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2550,plain,
! [SV163: $i] :
( ( ( ~ ( reflexive @ SV163 ) )
= $true )
| ( ( ~ ( transitive @ SV163 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV163 ) )
= $true )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2551,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)],[2411]) ).
thf(2552,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2411]) ).
thf(2553,plain,
! [SV364: $i] :
( ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ~ ( well_ordering @ SV364 )
| ( connected @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2554,plain,
! [SV280: $i] :
( ( ( well_ordering @ SV280 )
= $false )
| ( ( well_founded_relation @ SV280 )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2555,plain,
! [SV281: $i] :
( ( ( empty @ SV281 )
= $false )
| ( ( ~ ( relation @ SV281 ) )
= $true )
| ( ( ~ ( function @ SV281 ) )
= $true )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2556,plain,
! [SV282: $i] :
( ( ( empty @ SV282 )
= $false )
| ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( function @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2557,plain,
! [SV67: $i,SV255: $i,SV228: $i] :
( ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) )
| ~ ( in @ SV67 @ ( relation_dom @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2558,plain,
! [SV314: $i,SV67: $i,SV339: $i] :
( ( ( ~ ( function @ SV339 ) )
= $true )
| ( ( ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
| ( SV314
= ( apply @ SV339 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2559,plain,
! [SV315: $i,SV67: $i,SV340: $i] :
( ( ( ~ ( function @ SV340 ) )
= $true )
| ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
| ( in @ SV67 @ ( relation_dom @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2560,plain,
! [SV229: $i,SV68: $i,SV256: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( relation_rng @ SV256 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV229 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2561,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
| ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2562,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( function @ SV366 )
| ~ ( relation @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 )
| ( relation_isomorphism @ SV69 @ SV175 @ SV366 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2563,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2564,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2565,plain,
! [SV258: $i,SV231: $i,SV70: $i] :
( ( ( in @ SV70 @ SV231 )
= $false )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ SV258 ) ) )
= $true )
| ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2566,plain,
! [SV316: $i,SV70: $i,SV341: $i] :
( ( ( relation @ SV341 )
= $false )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV341 @ SV316 ) ) )
| ( in @ SV70 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2567,plain,
! [SV317: $i,SV70: $i,SV342: $i] :
( ( ( relation @ SV342 )
= $false )
| ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV342 @ SV317 ) ) )
| ( in @ SV70 @ ( relation_dom @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2568,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
= $false )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2569,plain,
! [SV71: $i,SV284: $i] :
( ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( ~ ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) ) )
= $true )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2570,plain,
! [SV388: $i,SV180: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV180 @ SV388 ) @ ( sK43_B @ SV180 ) )
| ~ ( in @ SV388 @ ( sK43_B @ SV180 ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2571,plain,
! [SV180: $i] :
( ( ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) )
| ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2572,plain,
! [SV343: $i,SV181: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
| ~ ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 ) )
= $false )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2573,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( relation @ SV367 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
| ( SV367
= ( relation_composition @ SV72 @ SV182 ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2574,plain,
! [SV182: $i,SV72: $i,SV368: $i] :
( ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ( SV368
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2575,plain,
! [SV232: $i,SV183: $i] :
( ( ( ~ ( in @ SV183 @ ( relation_rng @ SV232 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV232 ) )
= $true )
| ( ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) )
= $true )
| ( ( function @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2576,plain,
! [SV233: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( relation_rng @ SV233 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV233 ) )
= $true )
| ( ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) )
= $true )
| ( ( function @ SV233 )
= $false )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2577,plain,
! [SV369: $i,SV344: $i,SV185: $i] :
( ( ( ( sK50_B @ SV185 )
= ( ordered_pair @ SV344 @ SV369 ) )
= $false )
| ( ( relation @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2578,plain,
! [SV73: $i,SV286: $i] :
( ( ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 )
| ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2579,plain,
! [SV73: $i,SV286: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
| ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2438]) ).
thf(2580,plain,
! [SV287: $i,SV73: $i] :
( ( ( ~ ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) ) )
= $false )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2581,plain,
! [SV73: $i,SV287: $i] :
( ( ( ~ ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) )
= $false )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2582,plain,
! [SV234: $i,SV187: $i] :
( ( ( relation @ SV187 )
= $false )
| ( ( function @ SV187 )
= $false )
| ( ( ~ ( relation @ SV234 ) )
= $true )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2583,plain,
! [SV235: $i,SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( function @ SV188 )
= $false )
| ( ( ~ ( relation @ SV235 ) )
= $true )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2584,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2442]) ).
thf(2585,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2586,plain,
! [SV74: $i,SV289: $i,SV389: $i,SV370: $i] :
( ( ( ( SV370 = SV389 )
| ~ ( in @ SV370 @ SV289 )
| ~ ( in @ SV389 @ SV289 )
| ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
| ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2587,plain,
! [SV189: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2588,plain,
! [SV189: $i] :
( ( ( in @ ( ordered_pair @ ( sK76_SY4442 @ SV189 ) @ ( sK75_B @ SV189 ) ) @ SV189 )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2589,plain,
! [SV190: $i,SV371: $i,SV345: $i] :
( ( ( ( SV345 = SV371 )
| ~ ( in @ SV345 @ ( relation_field @ SV190 ) )
| ~ ( in @ SV371 @ ( relation_field @ SV190 ) )
| ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2590,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( ~ ( function @ SV372 )
| ~ ( relation @ SV372 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2591,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2592,plain,
! [SV136: $i,SV76: $i] :
( ( ( ~ ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2593,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2594,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2595,plain,
! [SV77: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ! [SY4988: $i] :
( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 )
| ~ ( in @ SY4988 @ SV291 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SV390 @ SY4988 ) @ SV77 )
| ( in @ ( ordered_pair @ SV373 @ SY4988 ) @ SV77 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2596,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ~ ( ~ ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) )
| ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) ) ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2597,plain,
! [SV347: $i,SV78: $i,SV375: $i] :
( ( ( ( SV375
!= ( relation_image @ SV78 @ SV347 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) )
| ~ ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2598,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2459]) ).
thf(2599,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2459]) ).
thf(2600,plain,
! [SV319: $i,SV79: $i,SV293: $i] :
( ( ( ~ ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) )
| ~ ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2601,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
= $false )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2602,plain,
! [SV295: $i,SV80: $i] :
( ( ( SV80 = SV295 )
= $false )
| ( ( ~ ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2603,plain,
! [SV81: $i,SV296: $i] :
( ( ( in @ ( sK47_C @ SV296 @ SV81 ) @ SV296 )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2604,plain,
! [SV81: $i,SV296: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 ) )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2605,plain,
! [SV81: $i,SV297: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV297 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV376 @ SV376 ) @ SV81 )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV297 )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2606,plain,
! [SV82: $i,SV261: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) )
| ~ ( in @ SV238 @ SV82 ) )
= $true )
| ( ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2607,plain,
! [SV82: $i,SV320: $i,SV348: $i] :
( ( ( ~ ( function @ SV348 ) )
= $true )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SV348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2608,plain,
! [SV82: $i,SV321: $i,SV349: $i] :
( ( ( ~ ( function @ SV349 ) )
= $true )
| ( ( ~ ( relation @ SV349 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2609,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2610,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ( SV323
!= ( relation_rng_restriction @ SV83 @ SV137 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2611,plain,
! [SV298: $i,SV84: $i] :
( ( ( ! [SY4890: $i] :
( ~ ( disjoint @ ( fiber @ SV84 @ SY4890 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SY4890 @ ( sK39_C @ SV298 @ SV84 ) ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2612,plain,
! [SV84: $i,SV298: $i] :
( ( ( ~ ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2613,plain,
! [SV299: $i,SV377: $i,SV84: $i] :
( ( ( ~ ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
| ~ ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 ) ) )
= $true )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2614,plain,
! [SV203: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
| ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2615,plain,
! [SV203: $i] :
( ( ( ( sK77_B @ SV203 )
= ( sK78_SY4443 @ SV203 ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2616,plain,
! [SV204: $i,SV378: $i,SV350: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV350 @ SV378 ) @ SV204 )
| ~ ( in @ ( ordered_pair @ SV378 @ SV350 ) @ SV204 ) )
= $true )
| ( ( SV350 = SV378 )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2617,plain,
! [SV85: $i] :
( ( ( ! [SY4659: $i] :
( ~ ( in @ SY4659 @ ( relation_dom @ SV85 ) )
| ! [SY4660: $i] :
( ( SY4660
!= ( apply @ SV85 @ SY4659 ) )
| ( in @ ( ordered_pair @ SY4659 @ SY4660 ) @ SV85 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2479]) ).
thf(2618,plain,
! [SV85: $i] :
( ( ( ! [SY4661: $i] :
( ~ ( in @ SY4661 @ ( relation_dom @ SV85 ) )
| ! [SY4662: $i] :
( ~ ( in @ ( ordered_pair @ SY4661 @ SY4662 ) @ SV85 )
| ( SY4662
= ( apply @ SV85 @ SY4661 ) ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2619,plain,
! [SV85: $i] :
( ( ( ! [SY4663: $i] :
( ( in @ SY4663 @ ( relation_dom @ SV85 ) )
| ! [SY4664: $i] :
( ( SY4664
!= ( apply @ SV85 @ SY4663 ) )
| ( SY4664 = empty_set ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2620,plain,
! [SV85: $i] :
( ( ( ! [SY4665: $i] :
( ( in @ SY4665 @ ( relation_dom @ SV85 ) )
| ! [SY4666: $i] :
( ( SY4666 != empty_set )
| ( SY4666
= ( apply @ SV85 @ SY4665 ) ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2482]) ).
thf(2621,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
| ~ ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) ) )
= $false )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2622,plain,
! [SV86: $i,SV352: $i] :
( ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( ~ ( ~ ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) )
| ~ ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2623,plain,
! [SV205: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
| ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2624,plain,
! [SV205: $i] :
( ( ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2625,plain,
! [SV391: $i,SV206: $i,SV379: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV206 )
| ( in @ ( ordered_pair @ SV353 @ SV391 ) @ SV206 ) )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2626,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) ) ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2627,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ( SV381
!= ( relation_inverse_image @ SV88 @ SV355 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) )
| ~ ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2628,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2629,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2492]) ).
thf(2630,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2493]) ).
thf(2631,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2493]) ).
thf(2632,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2633,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2494]) ).
thf(2634,plain,
! [SV207: $i,SV89: $i,SV382: $i] :
( ( ( ~ ( function @ SV382 )
| ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2635,plain,
! [SV300: $i,SV90: $i] :
( ( ( subset @ SV90 @ SV300 )
= $false )
| ( ( subset @ ( relation_dom @ SV90 ) @ ( relation_dom @ SV300 ) )
= $true )
| ( ( relation @ SV300 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2636,plain,
! [SV301: $i,SV90: $i] :
( ( ( subset @ SV90 @ SV301 )
= $false )
| ( ( subset @ ( relation_rng @ SV90 ) @ ( relation_rng @ SV301 ) )
= $true )
| ( ( relation @ SV301 )
= $false )
| ( ( relation @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2637,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2498]) ).
thf(2638,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2639,plain,
! [SV242: $i,SV211: $i] :
( ( ( ~ ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2640,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2641,plain,
! [SV91: $i,SV302: $i] :
( ( ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2501]) ).
thf(2642,plain,
! [SV91: $i,SV302: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
| ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2643,plain,
! [SV303: $i,SV91: $i] :
( ( ( ~ ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) ) )
= $false )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2644,plain,
! [SV91: $i,SV303: $i] :
( ( ( ~ ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) )
= $false )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2645,plain,
! [SV243: $i,SV92: $i,SV264: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( relation_dom @ SV264 ) )
| ~ ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 ) )
= $true )
| ( ( ~ ( in @ SV383 @ SV243 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2646,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
| ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2647,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( function @ SV384 )
| ~ ( relation @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2648,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2649,plain,
! [SV93: $i,SV138: $i] :
( ( ( ~ ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2507]) ).
thf(2650,plain,
! [SV268: $i,SV247: $i,SV95: $i] :
( ( ( in @ SV95 @ SV247 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ SV268 ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) )
= $true )
| ( ( relation @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2651,plain,
! [SV324: $i,SV95: $i,SV358: $i] :
( ( ( relation @ SV358 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SV358 ) ) )
| ( in @ SV95 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2652,plain,
! [SV325: $i,SV95: $i,SV359: $i] :
( ( ( relation @ SV359 )
= $false )
| ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SV359 ) ) )
| ( in @ SV95 @ ( relation_rng @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2653,plain,
( ( ~ ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2654,plain,
( ( ~ ( well_ordering @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2655,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2656,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( ( SV327
!= ( relation_dom_restriction @ SV96 @ SV305 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2657,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2517]) ).
thf(2658,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) ) )
= $false )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2517]) ).
thf(2659,plain,
! [SV329: $i,SV307: $i,SV97: $i] :
( ( ( ~ ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) )
| ~ ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2660,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2661,plain,
! [SV308: $i,SV330: $i] :
( ( ( function @ SV330 )
= $false )
| ( ( ~ ( relation @ SV330 ) )
= $true )
| ( ( ( SV330
!= ( identity_relation @ SV308 ) )
| ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2662,plain,
! [SV309: $i,SV331: $i] :
( ( ( function @ SV331 )
= $false )
| ( ( ~ ( relation @ SV331 ) )
= $true )
| ( ( ( SV331
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SV331 )
= SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2663,plain,
! [SV115: $i,SV269: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) )
= $true )
| ( ( function @ SV269 )
= $false )
| ( ( relation @ SV269 )
= $false )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2664,plain,
! [SV270: $i,SV117: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( relation_dom @ SV117 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) )
= $true )
| ( ( function @ SV270 )
= $false )
| ( ( relation @ SV270 )
= $false )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2665,plain,
! [SV271: $i,SV149: $i,SV34: $i] :
( ( ( ~ ( relation_isomorphism @ SV34 @ SV149 @ SV271 ) )
= $true )
| ( ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) )
= $true )
| ( ( function @ SV271 )
= $false )
| ( ( relation @ SV271 )
= $false )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2666,plain,
! [SV153: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2667,plain,
! [SV153: $i] :
( ( ( ( ( sK19_B @ SV153 )
!= ( sK20_SY4413 @ SV153 ) ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2526]) ).
thf(2668,plain,
! [SV392: $i,SV154: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV392 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) )
| ( SV385 = SV392 ) )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2669,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( function @ SV386 )
| ~ ( relation @ SV386 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) )
| ( SV386
= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2670,plain,
! [SV60: $i] :
( ( ( ~ ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2671,plain,
! [SV60: $i] :
( ( ( ~ ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2531]) ).
thf(2672,plain,
! [SV272: $i,SV135: $i,SV253: $i,SV61: $i] :
( ( ( in @ SV61 @ SV253 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2673,plain,
! [SV333: $i,SV135: $i,SV61: $i,SV360: $i] :
( ( ( relation @ SV360 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SV360 ) )
| ( in @ SV61 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2674,plain,
! [SV334: $i,SV135: $i,SV61: $i,SV361: $i] :
( ( ( relation @ SV361 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SV361 ) )
| ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2675,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
| ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2676,plain,
! [SV62: $i,SV273: $i] :
( ( ( ( sK33_C @ SV273 @ SV62 )
= ( sK34_SY4421 @ SV273 @ SV62 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2677,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV274 )
| ~ ( in @ SV387 @ SV274 )
| ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 )
| ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2678,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) )
| ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2679,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
| ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2680,plain,
! [SV311: $i,SV276: $i,SV63: $i] :
( ( ( ~ ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) ) )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2540]) ).
thf(2681,plain,
! [SV63: $i,SV276: $i,SV311: $i] :
( ( ( ~ ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2540]) ).
thf(2682,plain,
! [SV254: $i,SV225: $i,SV64: $i] :
( ( ( in @ SV64 @ ( cartesian_product2 @ SV225 @ SV225 ) )
= $false )
| ( ( in @ SV64 @ SV254 )
= $false )
| ( ( in @ SV64 @ ( relation_restriction @ SV254 @ SV225 ) )
= $true )
| ( ( relation @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2683,plain,
! [SV312: $i,SV335: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV335 @ SV312 ) ) )
= $true )
| ( ( in @ SV64 @ SV335 )
= $true )
| ( ( relation @ SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2684,plain,
! [SV313: $i,SV336: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ ( relation_restriction @ SV336 @ SV313 ) ) )
= $true )
| ( ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) )
= $true )
| ( ( relation @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2685,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 ) )
= $false )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2686,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
= $false )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2687,plain,
! [SV278: $i,SV65: $i,SV393: $i] :
( ( ( ! [SY4989: $i] :
( ~ ( in @ ( ordered_pair @ SV393 @ SY4989 ) @ SV65 )
| ( in @ ( ordered_pair @ SV393 @ SY4989 ) @ SV278 ) ) )
= $true )
| ( ( subset @ SV65 @ SV278 )
= $false )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2688,plain,
! [SV279: $i,SV66: $i] :
( ( ( ~ ( is_reflexive_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_transitive_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2689,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2690,plain,
! [SV66: $i] :
( ( ( ! [SY4545: $i] :
( ~ ( well_orders @ SV66 @ SY4545 )
| ( is_connected_in @ SV66 @ SY4545 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2691,plain,
! [SV363: $i,SV66: $i] :
( ( ( well_orders @ SV66 @ SV363 )
= $false )
| ( ( is_well_founded_in @ SV66 @ SV363 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2692,plain,
! [SV163: $i] :
( ( ( reflexive @ SV163 )
= $false )
| ( ( ~ ( transitive @ SV163 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV163 ) )
= $true )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2693,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)],[2551]) ).
thf(2694,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2695,plain,
! [SV364: $i] :
( ( ( relation @ SV364 )
= $false )
| ( ( ~ ( well_ordering @ SV364 )
| ( connected @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2696,plain,
! [SV281: $i] :
( ( ( relation @ SV281 )
= $false )
| ( ( empty @ SV281 )
= $false )
| ( ( ~ ( function @ SV281 ) )
= $true )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2697,plain,
! [SV282: $i] :
( ( ( relation @ SV282 )
= $false )
| ( ( empty @ SV282 )
= $false )
| ( ( ~ ( function @ SV282 ) )
= $true )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2698,plain,
! [SV67: $i,SV255: $i,SV228: $i] :
( ( ( ( SV228
!= ( apply @ SV255 @ SV67 ) ) )
= $true )
| ( ( ~ ( in @ SV67 @ ( relation_dom @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2699,plain,
! [SV314: $i,SV67: $i,SV339: $i] :
( ( ( function @ SV339 )
= $false )
| ( ( ~ ( relation @ SV339 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
| ( SV314
= ( apply @ SV339 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2700,plain,
! [SV315: $i,SV67: $i,SV340: $i] :
( ( ( function @ SV340 )
= $false )
| ( ( ~ ( relation @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
| ( in @ SV67 @ ( relation_dom @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2701,plain,
! [SV229: $i,SV68: $i,SV256: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( relation_rng @ SV256 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV229 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2702,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2703,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2704,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( function @ SV366 ) )
= $true )
| ( ( ~ ( relation @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 )
| ( relation_isomorphism @ SV69 @ SV175 @ SV366 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2705,plain,
! [SV175: $i,SV69: $i] :
( ( ( ! [SY4775: $i] :
( ~ ( function @ SY4775 )
| ~ ( relation @ SY4775 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4775 )
| ~ ( ~ ! [SY4776: $i,SY4777: $i] :
( ~ ( in @ SY4776 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4777 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4776 ) @ ( apply @ SY4775 @ SY4777 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4776 @ SY4777 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY4782: $i,SY4783: $i] :
( ~ ( in @ ( ordered_pair @ SY4782 @ SY4783 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SY4775 @ SY4782 ) @ ( apply @ SY4775 @ SY4783 ) ) @ SV175 ) ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2706,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2707,plain,
! [SV231: $i,SV258: $i,SV70: $i] :
( ( ( in @ SV70 @ ( relation_dom @ SV258 ) )
= $false )
| ( ( in @ SV70 @ SV231 )
= $false )
| ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV258 @ SV231 ) ) )
= $true )
| ( ( relation @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2708,plain,
! [SV316: $i,SV341: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV341 @ SV316 ) ) ) )
= $true )
| ( ( in @ SV70 @ SV316 )
= $true )
| ( ( relation @ SV341 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2709,plain,
! [SV317: $i,SV342: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV342 @ SV317 ) ) ) )
= $true )
| ( ( in @ SV70 @ ( relation_dom @ SV342 ) )
= $true )
| ( ( relation @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2710,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
= $false )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2711,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) ) )
= $false )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2712,plain,
! [SV71: $i,SV284: $i] :
( ( ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) )
| ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) )
= $false )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2713,plain,
! [SV388: $i,SV180: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV180 @ SV388 ) @ ( sK43_B @ SV180 ) ) )
= $true )
| ( ( ~ ( in @ SV388 @ ( sK43_B @ SV180 ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2714,plain,
! [SV180: $i] :
( ( ( ~ ( ( ( sK43_B @ SV180 )
!= empty_set ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2715,plain,
! [SV180: $i] :
( ( ( ~ ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2571]) ).
thf(2716,plain,
! [SV343: $i,SV181: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 ) )
= $false )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2717,plain,
! [SV181: $i,SV343: $i] :
( ( ( ~ ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 ) )
= $false )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2718,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( relation @ SV367 )
= $false )
| ( ( ~ ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
| ( SV367
= ( relation_composition @ SV72 @ SV182 ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2719,plain,
! [SV182: $i,SV72: $i,SV368: $i] :
( ( ( relation @ SV368 )
= $false )
| ( ( ( SV368
!= ( relation_composition @ SV72 @ SV182 ) )
| ~ ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) ) )
= $true )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2720,plain,
! [SV232: $i,SV183: $i] :
( ( ( in @ SV183 @ ( relation_rng @ SV232 ) )
= $false )
| ( ( ~ ( one_to_one @ SV232 ) )
= $true )
| ( ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) )
= $true )
| ( ( function @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2721,plain,
! [SV233: $i,SV184: $i] :
( ( ( in @ SV184 @ ( relation_rng @ SV233 ) )
= $false )
| ( ( ~ ( one_to_one @ SV233 ) )
= $true )
| ( ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) )
= $true )
| ( ( function @ SV233 )
= $false )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2722,plain,
! [SV73: $i,SV286: $i] :
( ( ( ! [SY4871: $i] :
~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SY4871 ) @ SV73 ) )
= $true )
| ( ( ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2723,plain,
! [SV73: $i,SV286: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ ( sK37_SY4423 @ SV286 @ SV73 ) ) @ SV73 )
= $true )
| ( ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2724,plain,
! [SV287: $i,SV73: $i] :
( ( ( ! [SY4872: $i] :
( ! [SY4597: $i] :
~ ( in @ ( ordered_pair @ SY4872 @ SY4597 ) @ SV73 )
| ( in @ SY4872 @ SV287 ) ) )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2725,plain,
! [SV73: $i,SV287: $i] :
( ( ( ! [SY4874: $i] :
( ~ ( in @ SY4874 @ SV287 )
| ( in @ ( ordered_pair @ SY4874 @ ( sK35_D @ SY4874 @ SV287 @ SV73 ) ) @ SV73 ) ) )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2726,plain,
! [SV187: $i,SV234: $i] :
( ( ( relation @ SV234 )
= $false )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV187 )
= $false )
| ( ( ~ ( function @ SV234 ) )
= $true )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2727,plain,
! [SV188: $i,SV235: $i] :
( ( ( relation @ SV235 )
= $false )
| ( ( function @ SV188 )
= $false )
| ( ( relation @ SV188 )
= $false )
| ( ( ~ ( function @ SV235 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2728,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2729,plain,
! [SV74: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ ( sK26_SY4416 @ SV288 @ SV74 ) @ ( sK25_C @ SV288 @ SV74 ) ) @ SV74 )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2730,plain,
! [SV74: $i,SV289: $i,SV389: $i,SV370: $i] :
( ( ( ( SV370 = SV389 )
| ~ ( in @ SV370 @ SV289 )
| ~ ( in @ SV389 @ SV289 )
| ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(2731,plain,
! [SV189: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2587]) ).
thf(2732,plain,
! [SV189: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2587]) ).
thf(2733,plain,
! [SV190: $i,SV371: $i,SV345: $i] :
( ( ( ( SV345 = SV371 )
| ~ ( in @ SV345 @ ( relation_field @ SV190 ) )
| ~ ( in @ SV371 @ ( relation_field @ SV190 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2734,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( ~ ( function @ SV372 ) )
= $true )
| ( ( ~ ( relation @ SV372 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2735,plain,
! [SV136: $i,SV76: $i] :
( ( ( ! [SY4750: $i] :
( ~ ( function @ SY4750 )
| ~ ( relation @ SY4750 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4750 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SY4750 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2736,plain,
! [SV136: $i,SV76: $i] :
( ( ( ! [SY4751: $i] :
( ~ ( function @ SY4751 )
| ~ ( relation @ SY4751 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SY4751 @ SV136 ) ) )
| ( in @ ( apply @ SY4751 @ SV76 ) @ ( relation_dom @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2592]) ).
thf(2737,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2738,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2739,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 )
| ~ ( in @ SV394 @ SV291 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 )
| ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2740,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ~ ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) )
| ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2741,plain,
! [SV347: $i,SV78: $i,SV375: $i] :
( ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( ~ ( ~ ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) )
| ~ ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2742,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2743,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2744,plain,
! [SV319: $i,SV79: $i,SV293: $i] :
( ( ( ~ ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2600]) ).
thf(2745,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ~ ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2600]) ).
thf(2746,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
= $false )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2747,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) ) )
= $false )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2601]) ).
thf(2748,plain,
! [SV295: $i,SV80: $i] :
( ( ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) )
| ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) )
= $false )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2749,plain,
! [SV81: $i,SV296: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_C @ SV296 @ SV81 ) @ ( sK47_C @ SV296 @ SV81 ) ) @ SV81 )
= $false )
| ( ( is_reflexive_in @ SV81 @ SV296 )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2750,plain,
! [SV81: $i,SV297: $i,SV376: $i] :
( ( ( in @ SV376 @ SV297 )
= $false )
| ( ( in @ ( ordered_pair @ SV376 @ SV376 ) @ SV81 )
= $true )
| ( ( is_reflexive_in @ SV81 @ SV297 )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2751,plain,
! [SV82: $i,SV261: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ ( relation_dom @ SV261 ) ) )
= $true )
| ( ( ~ ( in @ SV238 @ SV82 ) )
= $true )
| ( ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2752,plain,
! [SV82: $i,SV320: $i,SV348: $i] :
( ( ( function @ SV348 )
= $false )
| ( ( ~ ( relation @ SV348 ) )
= $true )
| ( ( ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SV348 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2753,plain,
! [SV82: $i,SV321: $i,SV349: $i] :
( ( ( function @ SV349 )
= $false )
| ( ( ~ ( relation @ SV349 ) )
= $true )
| ( ( ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2754,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2755,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( ~ ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) ) )
= $true )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2756,plain,
! [SV298: $i,SV395: $i,SV84: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV84 @ SV395 ) @ ( sK39_C @ SV298 @ SV84 ) )
| ~ ( in @ SV395 @ ( sK39_C @ SV298 @ SV84 ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2757,plain,
! [SV84: $i,SV298: $i] :
( ( ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
| ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2758,plain,
! [SV299: $i,SV377: $i,SV84: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
| ~ ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 ) )
= $false )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2759,plain,
! [SV203: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2614]) ).
thf(2760,plain,
! [SV203: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 ) )
= $false )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2614]) ).
thf(2761,plain,
! [SV204: $i,SV378: $i,SV350: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV350 @ SV378 ) @ SV204 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV378 @ SV350 ) @ SV204 ) )
= $true )
| ( ( SV350 = SV378 )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2762,plain,
! [SV85: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( relation_dom @ SV85 ) )
| ! [SY4990: $i] :
( ( SY4990
!= ( apply @ SV85 @ SV396 ) )
| ( in @ ( ordered_pair @ SV396 @ SY4990 ) @ SV85 ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2763,plain,
! [SV85: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ ( relation_dom @ SV85 ) )
| ! [SY4991: $i] :
( ~ ( in @ ( ordered_pair @ SV397 @ SY4991 ) @ SV85 )
| ( SY4991
= ( apply @ SV85 @ SV397 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(2764,plain,
! [SV85: $i,SV398: $i] :
( ( ( ( in @ SV398 @ ( relation_dom @ SV85 ) )
| ! [SY4992: $i] :
( ( SY4992
!= ( apply @ SV85 @ SV398 ) )
| ( SY4992 = empty_set ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2765,plain,
! [SV85: $i,SV399: $i] :
( ( ( ( in @ SV399 @ ( relation_dom @ SV85 ) )
| ! [SY4993: $i] :
( ( SY4993 != empty_set )
| ( SY4993
= ( apply @ SV85 @ SV399 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(2766,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) ) )
= $false )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2767,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) ) )
= $false )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2621]) ).
thf(2768,plain,
! [SV352: $i,SV86: $i] :
( ( ( ~ ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) )
| ~ ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2769,plain,
! [SV205: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2770,plain,
! [SV205: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 ) )
= $false )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2771,plain,
! [SV391: $i,SV206: $i,SV379: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 )
| ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV206 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV353 @ SV391 ) @ SV206 )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2772,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ~ ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2773,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( ~ ( ~ ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) )
| ~ ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2774,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2775,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2776,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2777,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2778,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2779,plain,
! [SV207: $i,SV89: $i] :
( ( ( ! [SY4814: $i] :
( ~ ( function @ SY4814 )
| ~ ( relation @ SY4814 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4814 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2780,plain,
! [SV207: $i,SV89: $i,SV382: $i] :
( ( ( ~ ( function @ SV382 ) )
= $true )
| ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(2781,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2782,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
| ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2783,plain,
! [SV242: $i,SV211: $i] :
( ( ( ! [SY4842: $i,SY4843: $i] :
( ( SY4842 != SY4843 )
| ~ ( in @ SY4842 @ SV211 )
| ( in @ ( ordered_pair @ SY4842 @ SY4843 ) @ SV242 ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2784,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2785,plain,
! [SV91: $i,SV302: $i] :
( ( ( ! [SY4892: $i] :
~ ( in @ ( ordered_pair @ SY4892 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2786,plain,
! [SV91: $i,SV302: $i] :
( ( ( in @ ( ordered_pair @ ( sK29_SY4418 @ SV302 @ SV91 ) @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
= $true )
| ( ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2787,plain,
! [SV303: $i,SV91: $i] :
( ( ( ! [SY4893: $i] :
( ! [SY4696: $i] :
~ ( in @ ( ordered_pair @ SY4696 @ SY4893 ) @ SV91 )
| ( in @ SY4893 @ SV303 ) ) )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2788,plain,
! [SV91: $i,SV303: $i] :
( ( ( ! [SY4895: $i] :
( ~ ( in @ SY4895 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SY4895 @ SV303 @ SV91 ) @ SY4895 ) @ SV91 ) ) )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2644]) ).
thf(2789,plain,
! [SV243: $i,SV92: $i,SV264: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( relation_dom @ SV264 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 ) )
= $true )
| ( ( ~ ( in @ SV383 @ SV243 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2790,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2791,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2646]) ).
thf(2792,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( function @ SV384 ) )
= $true )
| ( ( ~ ( relation @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2793,plain,
! [SV93: $i,SV138: $i] :
( ( ( ! [SY4761: $i] :
( ~ ( function @ SY4761 )
| ~ ( relation @ SY4761 )
| ( SV138
!= ( relation_dom_restriction @ SY4761 @ SV93 ) )
| ! [SY4762: $i] :
( ~ ( in @ SY4762 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY4762 )
= ( apply @ SY4761 @ SY4762 ) ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2648]) ).
thf(2794,plain,
! [SV93: $i,SV138: $i] :
( ( ( ! [SY4763: $i] :
( ~ ( function @ SY4763 )
| ~ ( relation @ SY4763 )
| ( SV138
!= ( relation_dom_restriction @ SY4763 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SY4763 ) @ SV93 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2795,plain,
! [SV247: $i,SV268: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_rng @ SV268 ) )
= $false )
| ( ( in @ SV95 @ SV247 )
= $false )
| ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV247 @ SV268 ) ) )
= $true )
| ( ( relation @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2796,plain,
! [SV358: $i,SV324: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SV358 ) ) ) )
= $true )
| ( ( in @ SV95 @ SV324 )
= $true )
| ( ( relation @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2797,plain,
! [SV359: $i,SV325: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SV359 ) ) ) )
= $true )
| ( ( in @ SV95 @ ( relation_rng @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2798,plain,
( ( relation_isomorphism @ sK1_A @ sK2_SY4402 @ sK3_SY4404 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2653]) ).
thf(2799,plain,
( ( well_ordering @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2800,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2801,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( ~ ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) ) )
= $true )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2802,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) )
| ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2657]) ).
thf(2803,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
| ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2658]) ).
thf(2804,plain,
! [SV329: $i,SV307: $i,SV97: $i] :
( ( ( ~ ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) ) )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2659]) ).
thf(2805,plain,
! [SV97: $i,SV307: $i,SV329: $i] :
( ( ( ~ ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2659]) ).
thf(2806,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
| ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2807,plain,
! [SV308: $i,SV330: $i] :
( ( ( relation @ SV330 )
= $false )
| ( ( function @ SV330 )
= $false )
| ( ( ( SV330
!= ( identity_relation @ SV308 ) )
| ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2808,plain,
! [SV309: $i,SV331: $i] :
( ( ( relation @ SV331 )
= $false )
| ( ( function @ SV331 )
= $false )
| ( ( ( SV331
!= ( identity_relation @ SV309 ) )
| ( ( relation_dom @ SV331 )
= SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2809,plain,
! [SV115: $i,SV269: $i,SV21: $i] :
( ( ( in @ SV21 @ ( relation_dom @ ( relation_composition @ SV269 @ SV115 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV269 @ SV115 ) @ SV21 )
= ( apply @ SV115 @ ( apply @ SV269 @ SV21 ) ) )
= $true )
| ( ( function @ SV269 )
= $false )
| ( ( relation @ SV269 )
= $false )
| ( ( function @ SV115 )
= $false )
| ( ( relation @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2810,plain,
! [SV270: $i,SV117: $i,SV23: $i] :
( ( ( in @ SV23 @ ( relation_dom @ SV117 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV117 @ SV270 ) @ SV23 )
= ( apply @ SV270 @ ( apply @ SV117 @ SV23 ) ) )
= $true )
| ( ( function @ SV270 )
= $false )
| ( ( relation @ SV270 )
= $false )
| ( ( function @ SV117 )
= $false )
| ( ( relation @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2811,plain,
! [SV271: $i,SV149: $i,SV34: $i] :
( ( ( relation_isomorphism @ SV34 @ SV149 @ SV271 )
= $false )
| ( ( relation_isomorphism @ SV149 @ SV34 @ ( function_inverse @ SV271 ) )
= $true )
| ( ( function @ SV271 )
= $false )
| ( ( relation @ SV271 )
= $false )
| ( ( relation @ SV149 )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2812,plain,
! [SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
| ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2813,plain,
! [SV153: $i] :
( ( ( ( sK19_B @ SV153 )
= ( sK20_SY4413 @ SV153 ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2814,plain,
! [SV392: $i,SV154: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV392 @ ( relation_dom @ SV154 ) )
| ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) ) )
= $true )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2815,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( function @ SV386 ) )
= $true )
| ( ( ~ ( relation @ SV386 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) )
| ( SV386
= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2816,plain,
! [SV60: $i] :
( ( ( ! [SY4502: $i] :
( ~ ( function @ SY4502 )
| ~ ( relation @ SY4502 )
| ( SY4502
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY4503: $i,SY4504: $i] :
( ( SY4504
!= ( apply @ SY4502 @ SY4503 ) )
| ~ ( in @ SY4503 @ ( relation_rng @ SV60 ) )
| ( SY4503
= ( apply @ SV60 @ SY4504 ) ) )
| ~ ! [SY4505: $i,SY4506: $i] :
( ( SY4506
!= ( apply @ SY4502 @ SY4505 ) )
| ~ ( in @ SY4505 @ ( relation_rng @ SV60 ) )
| ( in @ SY4506 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY4507: $i,SY4508: $i] :
( ( SY4507
!= ( apply @ SV60 @ SY4508 ) )
| ~ ( in @ SY4508 @ ( relation_dom @ SV60 ) )
| ( SY4508
= ( apply @ SY4502 @ SY4507 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2670]) ).
thf(2817,plain,
! [SV60: $i] :
( ( ( ! [SY4511: $i] :
( ~ ( function @ SY4511 )
| ~ ( relation @ SY4511 )
| ( SY4511
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SY4511 )
= ( relation_rng @ SV60 ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2818,plain,
! [SV253: $i,SV272: $i,SV135: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV272 )
= $false )
| ( ( in @ SV61 @ SV253 )
= $false )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV253 ) @ SV272 ) )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2819,plain,
! [SV360: $i,SV333: $i,SV135: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SV360 ) ) )
= $true )
| ( ( in @ SV61 @ SV333 )
= $true )
| ( ( relation @ SV360 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2820,plain,
! [SV361: $i,SV334: $i,SV135: $i,SV61: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SV361 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV361 )
= $true )
| ( ( relation @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2821,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2822,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2675]) ).
thf(2823,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV274 )
| ~ ( in @ SV387 @ SV274 )
| ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2824,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ! [SY4913: $i] :
( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SY4913 ) @ SV63 )
| ~ ( in @ SY4913 @ SV275 ) ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2825,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) ) )
= $true )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2826,plain,
! [SV311: $i,SV276: $i,SV63: $i] :
( ( ( ! [SY4914: $i] :
( ! [SY4863: $i] :
( ~ ( in @ ( ordered_pair @ SY4914 @ SY4863 ) @ SV63 )
| ~ ( in @ SY4863 @ SV276 ) )
| ( in @ SY4914 @ SV311 ) ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2827,plain,
! [SV63: $i,SV276: $i,SV311: $i] :
( ( ( ! [SY4916: $i] :
( ~ ( in @ SY4916 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4916 @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SY4916 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2681]) ).
thf(2828,plain,
! [SV312: $i,SV335: $i,SV64: $i] :
( ( ( in @ SV64 @ ( relation_restriction @ SV335 @ SV312 ) )
= $false )
| ( ( in @ SV64 @ SV335 )
= $true )
| ( ( relation @ SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2829,plain,
! [SV313: $i,SV336: $i,SV64: $i] :
( ( ( in @ SV64 @ ( relation_restriction @ SV336 @ SV313 ) )
= $false )
| ( ( in @ SV64 @ ( cartesian_product2 @ SV313 @ SV313 ) )
= $true )
| ( ( relation @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2830,plain,
! [SV65: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV65 )
= $true )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2831,plain,
! [SV65: $i,SV277: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 ) )
= $true )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2832,plain,
! [SV278: $i,SV65: $i,SV400: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV65 )
| ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV278 ) )
= $true )
| ( ( subset @ SV65 @ SV278 )
= $false )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(2833,plain,
! [SV279: $i,SV66: $i] :
( ( ( is_reflexive_in @ SV66 @ SV279 )
= $false )
| ( ( ~ ( is_transitive_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_antisymmetric_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2834,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
| ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2835,plain,
! [SV401: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV401 )
| ( is_connected_in @ SV66 @ SV401 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(2836,plain,
! [SV163: $i] :
( ( ( transitive @ SV163 )
= $false )
| ( ( reflexive @ SV163 )
= $false )
| ( ( ~ ( antisymmetric @ SV163 ) )
= $true )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2837,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)],[2693]) ).
thf(2838,plain,
! [SV402: $i] :
( ( ~ ( relation @ SV402 )
| ~ ( well_ordering @ SV402 )
| ( antisymmetric @ SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(2839,plain,
! [SV364: $i] :
( ( ( ~ ( well_ordering @ SV364 ) )
= $true )
| ( ( connected @ SV364 )
= $true )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2840,plain,
! [SV281: $i] :
( ( ( function @ SV281 )
= $false )
| ( ( empty @ SV281 )
= $false )
| ( ( relation @ SV281 )
= $false )
| ( ( function @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2841,plain,
! [SV282: $i] :
( ( ( function @ SV282 )
= $false )
| ( ( empty @ SV282 )
= $false )
| ( ( relation @ SV282 )
= $false )
| ( ( relation @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2842,plain,
! [SV67: $i,SV255: $i,SV228: $i] :
( ( ( SV228
= ( apply @ SV255 @ SV67 ) )
= $false )
| ( ( ~ ( in @ SV67 @ ( relation_dom @ SV255 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2843,plain,
! [SV314: $i,SV67: $i,SV339: $i] :
( ( ( relation @ SV339 )
= $false )
| ( ( function @ SV339 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
| ( SV314
= ( apply @ SV339 @ SV67 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2844,plain,
! [SV315: $i,SV67: $i,SV340: $i] :
( ( ( relation @ SV340 )
= $false )
| ( ( function @ SV340 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
| ( in @ SV67 @ ( relation_dom @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2845,plain,
! [SV229: $i,SV68: $i,SV256: $i,SV365: $i] :
( ( ( in @ SV365 @ ( relation_rng @ SV256 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV365 @ SV229 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2846,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2702]) ).
thf(2847,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ SV230 )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2848,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( function @ SV366 )
= $false )
| ( ( ~ ( relation @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 )
| ( relation_isomorphism @ SV69 @ SV175 @ SV366 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2849,plain,
! [SV175: $i,SV69: $i,SV403: $i] :
( ( ( ~ ( function @ SV403 )
| ~ ( relation @ SV403 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
| ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(2850,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
| ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2851,plain,
! [SV316: $i,SV341: $i,SV70: $i] :
( ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV341 @ SV316 ) ) )
= $false )
| ( ( in @ SV70 @ SV316 )
= $true )
| ( ( relation @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2852,plain,
! [SV317: $i,SV342: $i,SV70: $i] :
( ( ( in @ SV70 @ ( relation_dom @ ( relation_dom_restriction @ SV342 @ SV317 ) ) )
= $false )
| ( ( in @ SV70 @ ( relation_dom @ SV342 ) )
= $true )
| ( ( relation @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2853,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2710]) ).
thf(2854,plain,
! [SV71: $i,SV283: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
| ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2855,plain,
! [SV71: $i,SV284: $i] :
( ( ( ~ ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) ) )
= $false )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2856,plain,
! [SV284: $i,SV71: $i] :
( ( ( ~ ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) )
= $false )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2857,plain,
! [SV388: $i,SV180: $i] :
( ( ( disjoint @ ( fiber @ SV180 @ SV388 ) @ ( sK43_B @ SV180 ) )
= $false )
| ( ( ~ ( in @ SV388 @ ( sK43_B @ SV180 ) ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2858,plain,
! [SV180: $i] :
( ( ( ( ( sK43_B @ SV180 )
!= empty_set ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2859,plain,
! [SV180: $i] :
( ( ( subset @ ( sK43_B @ SV180 ) @ ( relation_field @ SV180 ) )
= $true )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2860,plain,
! [SV343: $i,SV181: $i] :
( ( ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
= $true )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2716]) ).
thf(2861,plain,
! [SV181: $i,SV343: $i] :
( ( ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 )
= $true )
| ( ( ( SV343 = empty_set )
| ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2717]) ).
thf(2862,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(2863,plain,
! [SV182: $i,SV72: $i,SV368: $i] :
( ( ( ( SV368
!= ( relation_composition @ SV72 @ SV182 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) ) )
= $true )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2864,plain,
! [SV183: $i,SV232: $i] :
( ( ( one_to_one @ SV232 )
= $false )
| ( ( in @ SV183 @ ( relation_rng @ SV232 ) )
= $false )
| ( ( SV183
= ( apply @ SV232 @ ( apply @ ( function_inverse @ SV232 ) @ SV183 ) ) )
= $true )
| ( ( function @ SV232 )
= $false )
| ( ( relation @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2865,plain,
! [SV184: $i,SV233: $i] :
( ( ( one_to_one @ SV233 )
= $false )
| ( ( in @ SV184 @ ( relation_rng @ SV233 ) )
= $false )
| ( ( SV184
= ( apply @ ( relation_composition @ ( function_inverse @ SV233 ) @ SV233 ) @ SV184 ) )
= $true )
| ( ( function @ SV233 )
= $false )
| ( ( relation @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2866,plain,
! [SV404: $i,SV73: $i,SV286: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SV404 ) @ SV73 ) )
= $true )
| ( ( ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2867,plain,
! [SV287: $i,SV73: $i,SV405: $i] :
( ( ( ! [SY5002: $i] :
~ ( in @ ( ordered_pair @ SV405 @ SY5002 ) @ SV73 )
| ( in @ SV405 @ SV287 ) )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(2868,plain,
! [SV73: $i,SV287: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV287 )
| ( in @ ( ordered_pair @ SV406 @ ( sK35_D @ SV406 @ SV287 @ SV73 ) ) @ SV73 ) )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2869,plain,
! [SV187: $i,SV234: $i] :
( ( ( function @ SV234 )
= $false )
| ( ( relation @ SV187 )
= $false )
| ( ( function @ SV187 )
= $false )
| ( ( relation @ SV234 )
= $false )
| ( ( function @ ( relation_composition @ SV187 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2870,plain,
! [SV188: $i,SV235: $i] :
( ( ( function @ SV235 )
= $false )
| ( ( relation @ SV188 )
= $false )
| ( ( function @ SV188 )
= $false )
| ( ( relation @ SV235 )
= $false )
| ( ( relation @ ( relation_composition @ SV188 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2871,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2872,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2873,plain,
! [SV74: $i,SV289: $i,SV389: $i,SV370: $i] :
( ( ( ( SV370 = SV389 )
| ~ ( in @ SV370 @ SV289 )
| ~ ( in @ SV389 @ SV289 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2874,plain,
! [SV189: $i] :
( ( ( ~ ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2875,plain,
! [SV189: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2732]) ).
thf(2876,plain,
! [SV190: $i,SV371: $i,SV345: $i] :
( ( ( SV345 = SV371 )
= $true )
| ( ( ~ ( in @ SV345 @ ( relation_field @ SV190 ) )
| ~ ( in @ SV371 @ ( relation_field @ SV190 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(2877,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( function @ SV372 )
= $false )
| ( ( ~ ( relation @ SV372 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2878,plain,
! [SV136: $i,SV76: $i,SV407: $i] :
( ( ( ~ ( function @ SV407 )
| ~ ( relation @ SV407 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(2879,plain,
! [SV136: $i,SV76: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 )
| ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
| ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(2880,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(2881,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2737]) ).
thf(2882,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 )
| ~ ( in @ SV394 @ SV291 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 )
| ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2883,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ~ ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) )
| ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2884,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) ) )
= $false )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2740]) ).
thf(2885,plain,
! [SV375: $i,SV347: $i,SV78: $i] :
( ( ( ~ ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) )
| ~ ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2886,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
| ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2887,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2888,plain,
! [SV319: $i,SV79: $i,SV293: $i] :
( ( ( ! [SY4923: $i] :
( ( SY4923 = SV293 )
| ~ ( in @ ( ordered_pair @ SY4923 @ SV293 ) @ SV79 )
| ( in @ SY4923 @ SV319 ) ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2889,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ~ ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(2890,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2746]) ).
thf(2891,plain,
! [SV80: $i,SV294: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
| ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2747]) ).
thf(2892,plain,
! [SV295: $i,SV80: $i] :
( ( ( ~ ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) ) )
= $false )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2893,plain,
! [SV80: $i,SV295: $i] :
( ( ( ~ ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) )
= $false )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2748]) ).
thf(2894,plain,
! [SV82: $i,SV261: $i,SV238: $i] :
( ( ( in @ SV238 @ ( relation_dom @ SV261 ) )
= $false )
| ( ( ~ ( in @ SV238 @ SV82 ) )
= $true )
| ( ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2895,plain,
! [SV82: $i,SV320: $i,SV348: $i] :
( ( ( relation @ SV348 )
= $false )
| ( ( function @ SV348 )
= $false )
| ( ( ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
| ( in @ SV320 @ ( relation_dom @ SV348 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2896,plain,
! [SV82: $i,SV321: $i,SV349: $i] :
( ( ( relation @ SV349 )
= $false )
| ( ( function @ SV349 )
= $false )
| ( ( ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
| ( in @ SV321 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2897,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2898,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2754]) ).
thf(2899,plain,
! [SV323: $i,SV137: $i,SV83: $i] :
( ( ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) )
| ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2900,plain,
! [SV298: $i,SV395: $i,SV84: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV84 @ SV395 ) @ ( sK39_C @ SV298 @ SV84 ) ) )
= $true )
| ( ( ~ ( in @ SV395 @ ( sK39_C @ SV298 @ SV84 ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2901,plain,
! [SV84: $i,SV298: $i] :
( ( ( ~ ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2902,plain,
! [SV84: $i,SV298: $i] :
( ( ( ~ ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2903,plain,
! [SV299: $i,SV377: $i,SV84: $i] :
( ( ( ~ ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 ) )
= $false )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2758]) ).
thf(2904,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 ) )
= $false )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2758]) ).
thf(2905,plain,
! [SV203: $i] :
( ( ( in @ ( ordered_pair @ ( sK77_B @ SV203 ) @ ( sK78_SY4443 @ SV203 ) ) @ SV203 )
= $true )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2906,plain,
! [SV203: $i] :
( ( ( in @ ( ordered_pair @ ( sK78_SY4443 @ SV203 ) @ ( sK77_B @ SV203 ) ) @ SV203 )
= $true )
| ( ( antisymmetric @ SV203 )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2907,plain,
! [SV204: $i,SV378: $i,SV350: $i] :
( ( ( in @ ( ordered_pair @ SV350 @ SV378 ) @ SV204 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV378 @ SV350 ) @ SV204 ) )
= $true )
| ( ( SV350 = SV378 )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2908,plain,
! [SV85: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ ( relation_dom @ SV85 ) ) )
= $true )
| ( ( ! [SY4990: $i] :
( ( SY4990
!= ( apply @ SV85 @ SV396 ) )
| ( in @ ( ordered_pair @ SV396 @ SY4990 ) @ SV85 ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2909,plain,
! [SV85: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ ( relation_dom @ SV85 ) ) )
= $true )
| ( ( ! [SY4991: $i] :
( ~ ( in @ ( ordered_pair @ SV397 @ SY4991 ) @ SV85 )
| ( SY4991
= ( apply @ SV85 @ SV397 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2910,plain,
! [SV85: $i,SV398: $i] :
( ( ( in @ SV398 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( ! [SY4992: $i] :
( ( SY4992
!= ( apply @ SV85 @ SV398 ) )
| ( SY4992 = empty_set ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2911,plain,
! [SV85: $i,SV399: $i] :
( ( ( in @ SV399 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( ! [SY4993: $i] :
( ( SY4993 != empty_set )
| ( SY4993
= ( apply @ SV85 @ SV399 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2912,plain,
! [SV86: $i,SV351: $i] :
( ( ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) )
| ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2913,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
| ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2914,plain,
! [SV352: $i,SV86: $i] :
( ( ( ~ ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) ) )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2915,plain,
! [SV86: $i,SV352: $i] :
( ( ( ~ ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2768]) ).
thf(2916,plain,
! [SV205: $i] :
( ( ( in @ ( ordered_pair @ ( sK79_B @ SV205 ) @ ( sK80_SY4444 @ SV205 ) ) @ SV205 )
= $true )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2769]) ).
thf(2917,plain,
! [SV205: $i] :
( ( ( in @ ( ordered_pair @ ( sK80_SY4444 @ SV205 ) @ ( sK81_SY4446 @ SV205 ) ) @ SV205 )
= $true )
| ( ( transitive @ SV205 )
= $true )
| ( ( relation @ SV205 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2918,plain,
! [SV391: $i,SV206: $i,SV379: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV206 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV353 @ SV391 ) @ SV206 )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(2919,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2920,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2921,plain,
! [SV381: $i,SV355: $i,SV88: $i] :
( ( ( ~ ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) )
| ~ ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2922,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2923,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2924,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
| ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2925,plain,
! [SV207: $i,SV89: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(2926,plain,
! [SV207: $i,SV89: $i,SV382: $i] :
( ( ( function @ SV382 )
= $false )
| ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2927,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( ( sK65_C @ SV241 @ SV210 )
!= ( sK66_SY4439 @ SV241 @ SV210 ) ) )
= $true )
| ( ( ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(2928,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2929,plain,
! [SV210: $i,SV241: $i] :
( ( ( ~ ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) ) )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2930,plain,
! [SV242: $i,SV211: $i,SV410: $i] :
( ( ( ! [SY5003: $i] :
( ( SV410 != SY5003 )
| ~ ( in @ SV410 @ SV211 )
| ( in @ ( ordered_pair @ SV410 @ SY5003 ) @ SV242 ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(2931,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) )
| ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2932,plain,
! [SV91: $i,SV302: $i,SV411: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV411 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 ) )
= $true )
| ( ( ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(2933,plain,
! [SV303: $i,SV91: $i,SV412: $i] :
( ( ( ! [SY5004: $i] :
~ ( in @ ( ordered_pair @ SY5004 @ SV412 ) @ SV91 )
| ( in @ SV412 @ SV303 ) )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(2934,plain,
! [SV91: $i,SV303: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV303 )
| ( in @ ( ordered_pair @ ( sK27_D @ SV413 @ SV303 @ SV91 ) @ SV413 ) @ SV91 ) )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(2935,plain,
! [SV243: $i,SV92: $i,SV264: $i,SV383: $i] :
( ( ( in @ SV383 @ ( relation_dom @ SV264 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 ) )
= $true )
| ( ( ~ ( in @ SV383 @ SV243 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2936,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2937,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV244 )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2791]) ).
thf(2938,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( function @ SV384 )
= $false )
| ( ( ~ ( relation @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2939,plain,
! [SV93: $i,SV138: $i,SV414: $i] :
( ( ( ~ ( function @ SV414 )
| ~ ( relation @ SV414 )
| ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) )
| ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(2940,plain,
! [SV93: $i,SV138: $i,SV415: $i] :
( ( ( ~ ( function @ SV415 )
| ~ ( relation @ SV415 )
| ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(2941,plain,
! [SV358: $i,SV324: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV324 @ SV358 ) ) )
= $false )
| ( ( in @ SV95 @ SV324 )
= $true )
| ( ( relation @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2942,plain,
! [SV359: $i,SV325: $i,SV95: $i] :
( ( ( in @ SV95 @ ( relation_rng @ ( relation_rng_restriction @ SV325 @ SV359 ) ) )
= $false )
| ( ( in @ SV95 @ ( relation_rng @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2943,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2944,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2945,plain,
! [SV327: $i,SV96: $i,SV305: $i] :
( ( ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) )
| ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2946,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ! [SY4942: $i] :
( ~ ( in @ ( ordered_pair @ SY4942 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SY4942 @ SV306 ) ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2947,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) ) )
= $true )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2948,plain,
! [SV329: $i,SV307: $i,SV97: $i] :
( ( ( ! [SY4943: $i] :
( ! [SY4908: $i] :
( ~ ( in @ ( ordered_pair @ SY4908 @ SY4943 ) @ SV97 )
| ~ ( in @ SY4908 @ SV307 ) )
| ( in @ SY4943 @ SV329 ) ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2949,plain,
! [SV97: $i,SV307: $i,SV329: $i] :
( ( ( ! [SY4945: $i] :
( ~ ( in @ SY4945 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SY4945 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SY4945 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2950,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 ) )
= $false )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2951,plain,
! [SV222: $i,SV252: $i] :
( ( ( ~ ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2952,plain,
! [SV308: $i,SV330: $i] :
( ( ( ( SV330
!= ( identity_relation @ SV308 ) ) )
= $true )
| ( ( ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true )
| ( ( function @ SV330 )
= $false )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(2953,plain,
! [SV309: $i,SV331: $i] :
( ( ( ( SV331
!= ( identity_relation @ SV309 ) ) )
= $true )
| ( ( ( relation_dom @ SV331 )
= SV309 )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(2954,plain,
! [SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2955,plain,
! [SV153: $i] :
( ( ( ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
!= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2956,plain,
! [SV392: $i,SV154: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV392 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) ) )
= $true )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(2957,plain,
! [SV60: $i,SV386: $i] :
( ( ( function @ SV386 )
= $false )
| ( ( ~ ( relation @ SV386 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) )
| ( SV386
= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2958,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ( function @ SV416 )
| ~ ( relation @ SV416 )
| ( SV416
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(2959,plain,
! [SV60: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 )
| ( SV417
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(2960,plain,
! [SV360: $i,SV333: $i,SV135: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV333 ) @ SV360 ) )
= $false )
| ( ( in @ SV61 @ SV333 )
= $true )
| ( ( relation @ SV360 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2961,plain,
! [SV361: $i,SV334: $i,SV135: $i,SV61: $i] :
( ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ ( relation_composition @ ( identity_relation @ SV334 ) @ SV361 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV61 @ SV135 ) @ SV361 )
= $true )
| ( ( relation @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(2962,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2821]) ).
thf(2963,plain,
! [SV62: $i,SV273: $i] :
( ( ( in @ ( ordered_pair @ ( sK34_SY4421 @ SV273 @ SV62 ) @ ( sK33_C @ SV273 @ SV62 ) ) @ SV62 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2964,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV274 )
| ~ ( in @ SV387 @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(2965,plain,
! [SV418: $i,SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV418 ) @ SV63 )
| ~ ( in @ SV418 @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(2966,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
= $false )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2967,plain,
! [SV311: $i,SV276: $i,SV63: $i,SV419: $i] :
( ( ( ! [SY5014: $i] :
( ~ ( in @ ( ordered_pair @ SV419 @ SY5014 ) @ SV63 )
| ~ ( in @ SY5014 @ SV276 ) )
| ( in @ SV419 @ SV311 ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(2968,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV311 )
| ~ ( ~ ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(2969,plain,
! [SV65: $i,SV277: $i] :
( ( ( in @ ( ordered_pair @ ( sK40_C @ SV277 @ SV65 ) @ ( sK41_SY4425 @ SV277 @ SV65 ) ) @ SV277 )
= $false )
| ( ( subset @ SV65 @ SV277 )
= $true )
| ( ( relation @ SV277 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2970,plain,
! [SV278: $i,SV65: $i,SV400: $i,SV393: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV65 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV278 )
= $true )
| ( ( subset @ SV65 @ SV278 )
= $false )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2971,plain,
! [SV279: $i,SV66: $i] :
( ( ( is_transitive_in @ SV66 @ SV279 )
= $false )
| ( ( is_reflexive_in @ SV66 @ SV279 )
= $false )
| ( ( ~ ( is_antisymmetric_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(2972,plain,
! [SV66: $i] :
( ( ( ~ ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2973,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2834]) ).
thf(2974,plain,
! [SV401: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV401 ) )
= $true )
| ( ( is_connected_in @ SV66 @ SV401 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(2975,plain,
! [SV163: $i] :
( ( ( antisymmetric @ SV163 )
= $false )
| ( ( reflexive @ SV163 )
= $false )
| ( ( transitive @ SV163 )
= $false )
| ( ( ~ ( connected @ SV163 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2976,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2977,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2837]) ).
thf(2978,plain,
! [SV402: $i] :
( ( ( ~ ( relation @ SV402 ) )
= $true )
| ( ( ~ ( well_ordering @ SV402 )
| ( antisymmetric @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2979,plain,
! [SV364: $i] :
( ( ( well_ordering @ SV364 )
= $false )
| ( ( connected @ SV364 )
= $true )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2980,plain,
! [SV228: $i,SV255: $i,SV67: $i] :
( ( ( in @ SV67 @ ( relation_dom @ SV255 ) )
= $false )
| ( ( SV228
= ( apply @ SV255 @ SV67 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV228 ) @ SV255 )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2981,plain,
! [SV339: $i,SV314: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 ) )
= $true )
| ( ( SV314
= ( apply @ SV339 @ SV67 ) )
= $true )
| ( ( function @ SV339 )
= $false )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2982,plain,
! [SV340: $i,SV315: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 ) )
= $true )
| ( ( in @ SV67 @ ( relation_dom @ SV340 ) )
= $true )
| ( ( function @ SV340 )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2983,plain,
! [SV229: $i,SV256: $i,SV365: $i,SV68: $i] :
( ( ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 )
= $false )
| ( ( in @ SV365 @ ( relation_rng @ SV256 ) )
= $false )
| ( ( ~ ( in @ SV365 @ SV229 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2984,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
| ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2985,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( relation @ SV366 )
= $false )
| ( ( function @ SV366 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 )
| ( relation_isomorphism @ SV69 @ SV175 @ SV366 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2986,plain,
! [SV175: $i,SV69: $i,SV403: $i] :
( ( ( ~ ( function @ SV403 )
| ~ ( relation @ SV403 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
| ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2987,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2988,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2989,plain,
! [SV71: $i,SV283: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(2990,plain,
! [SV71: $i,SV283: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2991,plain,
! [SV71: $i,SV284: $i] :
( ( ( ! [SY4867: $i,SY4868: $i] :
( ~ ( in @ ( ordered_pair @ SY4867 @ SY4868 ) @ SV284 )
| ( in @ ( ordered_pair @ SY4868 @ SY4867 ) @ SV71 ) ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2855]) ).
thf(2992,plain,
! [SV284: $i,SV71: $i] :
( ( ( ! [SY4869: $i,SY4870: $i] :
( ~ ( in @ ( ordered_pair @ SY4870 @ SY4869 ) @ SV71 )
| ( in @ ( ordered_pair @ SY4869 @ SY4870 ) @ SV284 ) ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2993,plain,
! [SV180: $i,SV388: $i] :
( ( ( in @ SV388 @ ( sK43_B @ SV180 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV180 @ SV388 ) @ ( sK43_B @ SV180 ) )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2994,plain,
! [SV180: $i] :
( ( ( ( sK43_B @ SV180 )
= empty_set )
= $false )
| ( ( well_founded_relation @ SV180 )
= $true )
| ( ( relation @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2995,plain,
! [SV181: $i,SV343: $i] :
( ( ( SV343 = empty_set )
= $true )
| ( ( ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2996,plain,
! [SV181: $i,SV343: $i] :
( ( ( SV343 = empty_set )
= $true )
| ( ( ~ ( subset @ SV343 @ ( relation_field @ SV181 ) ) )
= $true )
| ( ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2997,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
= $false )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2998,plain,
! [SV182: $i,SV72: $i,SV368: $i] :
( ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) ) )
= $true )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2999,plain,
! [SV404: $i,SV73: $i,SV286: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SV404 ) @ SV73 )
= $false )
| ( ( ~ ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 ) )
= $true )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(3000,plain,
! [SV287: $i,SV73: $i,SV405: $i] :
( ( ( ! [SY5002: $i] :
~ ( in @ ( ordered_pair @ SV405 @ SY5002 ) @ SV73 ) )
= $true )
| ( ( in @ SV405 @ SV287 )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3001,plain,
! [SV73: $i,SV287: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV287 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV406 @ ( sK35_D @ SV406 @ SV287 @ SV73 ) ) @ SV73 )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3002,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(3003,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(3004,plain,
! [SV74: $i,SV289: $i,SV389: $i,SV370: $i] :
( ( ( SV370 = SV389 )
= $true )
| ( ( ~ ( in @ SV370 @ SV289 )
| ~ ( in @ SV389 @ SV289 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3005,plain,
! [SV189: $i] :
( ( ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
| ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3006,plain,
! [SV189: $i] :
( ( ( in @ ( ordered_pair @ ( sK75_B @ SV189 ) @ ( sK76_SY4442 @ SV189 ) ) @ SV189 )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(3007,plain,
! [SV371: $i,SV190: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( relation_field @ SV190 ) ) )
= $true )
| ( ( ~ ( in @ SV371 @ ( relation_field @ SV190 ) ) )
= $true )
| ( ( SV345 = SV371 )
= $true )
| ( ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3008,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( relation @ SV372 )
= $false )
| ( ( function @ SV372 )
= $false )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
| ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3009,plain,
! [SV136: $i,SV76: $i,SV407: $i] :
( ( ( ~ ( function @ SV407 )
| ~ ( relation @ SV407 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3010,plain,
! [SV136: $i,SV76: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
| ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(3011,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(3012,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_SY4405 @ SV290 @ SV77 ) @ ( sK14_SY4407 @ SV290 @ SV77 ) ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(3013,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 )
| ~ ( in @ SV394 @ SV291 )
| ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3014,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) )
| ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2883]) ).
thf(3015,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
| ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2884]) ).
thf(3016,plain,
! [SV375: $i,SV347: $i,SV78: $i] :
( ( ( ~ ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) ) )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3017,plain,
! [SV78: $i,SV347: $i,SV375: $i] :
( ( ( ~ ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3018,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3019,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(3020,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) ) )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(3021,plain,
! [SV319: $i,SV79: $i,SV293: $i,SV421: $i] :
( ( ( ( SV421 = SV293 )
| ~ ( in @ ( ordered_pair @ SV421 @ SV293 ) @ SV79 )
| ( in @ SV421 @ SV319 ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3022,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) )
| ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3023,plain,
! [SV80: $i,SV294: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3024,plain,
! [SV80: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3025,plain,
! [SV295: $i,SV80: $i] :
( ( ( ! [SY4885: $i,SY4886: $i] :
( ~ ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV80 )
| ( in @ ( ordered_pair @ SY4885 @ SY4886 ) @ SV295 ) ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(3026,plain,
! [SV80: $i,SV295: $i] :
( ( ( ! [SY4887: $i,SY4888: $i] :
( ~ ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV295 )
| ( in @ ( ordered_pair @ SY4887 @ SY4888 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(3027,plain,
! [SV261: $i,SV82: $i,SV238: $i] :
( ( ( in @ SV238 @ SV82 )
= $false )
| ( ( in @ SV238 @ ( relation_dom @ SV261 ) )
= $false )
| ( ( in @ SV238 @ ( relation_dom @ ( relation_dom_restriction @ SV261 @ SV82 ) ) )
= $true )
| ( ( function @ SV261 )
= $false )
| ( ( relation @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(3028,plain,
! [SV82: $i,SV348: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) ) )
= $true )
| ( ( in @ SV320 @ ( relation_dom @ SV348 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3029,plain,
! [SV82: $i,SV349: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) ) )
= $true )
| ( ( in @ SV321 @ SV82 )
= $true )
| ( ( function @ SV349 )
= $false )
| ( ( relation @ SV349 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3030,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(3031,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3032,plain,
! [SV323: $i,SV137: $i,SV83: $i] :
( ( ( ~ ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3033,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3034,plain,
! [SV298: $i,SV395: $i,SV84: $i] :
( ( ( disjoint @ ( fiber @ SV84 @ SV395 ) @ ( sK39_C @ SV298 @ SV84 ) )
= $false )
| ( ( ~ ( in @ SV395 @ ( sK39_C @ SV298 @ SV84 ) ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(3035,plain,
! [SV84: $i,SV298: $i] :
( ( ( ( ( sK39_C @ SV298 @ SV84 )
!= empty_set ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(3036,plain,
! [SV84: $i,SV298: $i] :
( ( ( subset @ ( sK39_C @ SV298 @ SV84 ) @ SV298 )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(3037,plain,
! [SV299: $i,SV377: $i,SV84: $i] :
( ( ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
= $true )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3038,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 )
= $true )
| ( ( ( SV377 = empty_set )
| ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2904]) ).
thf(3039,plain,
! [SV204: $i,SV350: $i,SV378: $i] :
( ( ( in @ ( ordered_pair @ SV378 @ SV350 ) @ SV204 )
= $false )
| ( ( in @ ( ordered_pair @ SV350 @ SV378 ) @ SV204 )
= $false )
| ( ( SV350 = SV378 )
= $true )
| ( ( antisymmetric @ SV204 )
= $false )
| ( ( relation @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3040,plain,
! [SV85: $i,SV396: $i] :
( ( ( in @ SV396 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( ! [SY4990: $i] :
( ( SY4990
!= ( apply @ SV85 @ SV396 ) )
| ( in @ ( ordered_pair @ SV396 @ SY4990 ) @ SV85 ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3041,plain,
! [SV85: $i,SV397: $i] :
( ( ( in @ SV397 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( ! [SY4991: $i] :
( ~ ( in @ ( ordered_pair @ SV397 @ SY4991 ) @ SV85 )
| ( SY4991
= ( apply @ SV85 @ SV397 ) ) ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(3042,plain,
! [SV398: $i,SV85: $i,SV422: $i] :
( ( ( ( SV422
!= ( apply @ SV85 @ SV398 ) )
| ( SV422 = empty_set ) )
= $true )
| ( ( in @ SV398 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3043,plain,
! [SV399: $i,SV85: $i,SV423: $i] :
( ( ( ( SV423 != empty_set )
| ( SV423
= ( apply @ SV85 @ SV399 ) ) )
= $true )
| ( ( in @ SV399 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3044,plain,
! [SV86: $i,SV351: $i] :
( ( ( ! [SY4958: $i] :
( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SY4958 ) )
| ~ ( in @ SY4958 @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3045,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3046,plain,
! [SV352: $i,SV86: $i] :
( ( ( ! [SY4959: $i] :
( ! [SY4671: $i] :
( ( SY4959
!= ( apply @ SV86 @ SY4671 ) )
| ~ ( in @ SY4671 @ ( relation_dom @ SV86 ) ) )
| ( in @ SY4959 @ SV352 ) ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2914]) ).
thf(3047,plain,
! [SV86: $i,SV352: $i] :
( ( ( ! [SY4961: $i] :
( ~ ( in @ SY4961 @ SV352 )
| ~ ( ( SY4961
!= ( apply @ SV86 @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SY4961 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(3048,plain,
! [SV391: $i,SV206: $i,SV379: $i,SV353: $i] :
( ( ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV206 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV353 @ SV391 ) @ SV206 )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3049,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(3050,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(3051,plain,
! [SV381: $i,SV355: $i,SV88: $i] :
( ( ( ~ ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3052,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ~ ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3053,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(3054,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(3055,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3056,plain,
( ( ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2923]) ).
thf(3057,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2924]) ).
thf(3058,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2924]) ).
thf(3059,plain,
! [SV207: $i,SV89: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3060,plain,
! [SV207: $i,SV89: $i,SV382: $i] :
( ( ( relation @ SV382 )
= $false )
| ( ( function @ SV382 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
| ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3061,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
= $false )
| ( ( ~ ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3062,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(3063,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
| ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2929]) ).
thf(3064,plain,
! [SV242: $i,SV211: $i,SV424: $i,SV410: $i] :
( ( ( ( SV410 != SV424 )
| ~ ( in @ SV410 @ SV211 )
| ( in @ ( ordered_pair @ SV410 @ SV424 ) @ SV242 ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3065,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(3066,plain,
! [SV211: $i,SV242: $i] :
( ( ( ~ ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) )
= $false )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2931]) ).
thf(3067,plain,
! [SV91: $i,SV302: $i,SV411: $i] :
( ( ( in @ ( ordered_pair @ SV411 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
= $false )
| ( ( ~ ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 ) )
= $true )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3068,plain,
! [SV303: $i,SV91: $i,SV412: $i] :
( ( ( ! [SY5004: $i] :
~ ( in @ ( ordered_pair @ SY5004 @ SV412 ) @ SV91 ) )
= $true )
| ( ( in @ SV412 @ SV303 )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(3069,plain,
! [SV91: $i,SV303: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV303 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK27_D @ SV413 @ SV303 @ SV91 ) @ SV413 ) @ SV91 )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3070,plain,
! [SV243: $i,SV264: $i,SV92: $i,SV383: $i] :
( ( ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 )
= $false )
| ( ( in @ SV383 @ ( relation_dom @ SV264 ) )
= $false )
| ( ( ~ ( in @ SV383 @ SV243 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3071,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
| ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3072,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( relation @ SV384 )
= $false )
| ( ( function @ SV384 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
| ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3073,plain,
! [SV93: $i,SV138: $i,SV414: $i] :
( ( ( ~ ( function @ SV414 )
| ~ ( relation @ SV414 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) )
| ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3074,plain,
! [SV93: $i,SV138: $i,SV415: $i] :
( ( ( ~ ( function @ SV415 )
| ~ ( relation @ SV415 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3075,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(3076,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(3077,plain,
! [SV327: $i,SV96: $i,SV305: $i] :
( ( ( ~ ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3078,plain,
! [SV96: $i,SV305: $i,SV327: $i] :
( ( ( ~ ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3079,plain,
! [SV97: $i,SV306: $i,SV328: $i,SV425: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV425 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ SV425 @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3080,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
| ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
= $false )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3081,plain,
! [SV329: $i,SV307: $i,SV97: $i,SV426: $i] :
( ( ( ! [SY5015: $i] :
( ~ ( in @ ( ordered_pair @ SY5015 @ SV426 ) @ SV97 )
| ~ ( in @ SY5015 @ SV307 ) )
| ( in @ SV426 @ SV329 ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3082,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV329 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3083,plain,
! [SV222: $i,SV252: $i] :
( ( ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
= $true )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2950]) ).
thf(3084,plain,
! [SV222: $i,SV252: $i] :
( ( ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
!= ( sK72_C @ SV252 @ SV222 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2951]) ).
thf(3085,plain,
! [SV308: $i,SV330: $i] :
( ( ( SV330
= ( identity_relation @ SV308 ) )
= $false )
| ( ( ! [SY4946: $i] :
( ~ ( in @ SY4946 @ SV308 )
| ( ( apply @ SV330 @ SY4946 )
= SY4946 ) ) )
= $true )
| ( ( function @ SV330 )
= $false )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(3086,plain,
! [SV309: $i,SV331: $i] :
( ( ( SV331
= ( identity_relation @ SV309 ) )
= $false )
| ( ( ( relation_dom @ SV331 )
= SV309 )
= $true )
| ( ( function @ SV331 )
= $false )
| ( ( relation @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3087,plain,
! [SV153: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2954]) ).
thf(3088,plain,
! [SV153: $i] :
( ( ( ( apply @ SV153 @ ( sK19_B @ SV153 ) )
= ( apply @ SV153 @ ( sK20_SY4413 @ SV153 ) ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2955]) ).
thf(3089,plain,
! [SV392: $i,SV154: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ~ ( in @ SV392 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) ) )
= $true )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3090,plain,
! [SV60: $i,SV386: $i] :
( ( ( relation @ SV386 )
= $false )
| ( ( function @ SV386 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) )
| ( SV386
= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3091,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ( function @ SV416 )
| ~ ( relation @ SV416 ) )
= $true )
| ( ( ( SV416
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3092,plain,
! [SV60: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 ) )
= $true )
| ( ( ( SV417
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3093,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
| ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3094,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV274 ) )
= $true )
| ( ( ~ ( in @ SV387 @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2964]) ).
thf(3095,plain,
! [SV418: $i,SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV418 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV418 @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3096,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3097,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( ~ ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 ) )
= $false )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3098,plain,
! [SV311: $i,SV276: $i,SV63: $i,SV419: $i] :
( ( ( ! [SY5014: $i] :
( ~ ( in @ ( ordered_pair @ SV419 @ SY5014 ) @ SV63 )
| ~ ( in @ SY5014 @ SV276 ) ) )
= $true )
| ( ( in @ SV419 @ SV311 )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3099,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3100,plain,
! [SV278: $i,SV65: $i,SV400: $i,SV393: $i] :
( ( ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV65 )
= $false )
| ( ( in @ ( ordered_pair @ SV393 @ SV400 ) @ SV278 )
= $true )
| ( ( subset @ SV65 @ SV278 )
= $false )
| ( ( relation @ SV278 )
= $false )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3101,plain,
! [SV279: $i,SV66: $i] :
( ( ( is_antisymmetric_in @ SV66 @ SV279 )
= $false )
| ( ( is_reflexive_in @ SV66 @ SV279 )
= $false )
| ( ( is_transitive_in @ SV66 @ SV279 )
= $false )
| ( ( ~ ( is_connected_in @ SV66 @ SV279 ) )
= $true )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3102,plain,
! [SV66: $i] :
( ( ( ~ ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2972]) ).
thf(3103,plain,
! [SV66: $i] :
( ( ( ! [SY4544: $i] :
( ~ ( well_orders @ SV66 @ SY4544 )
| ( is_antisymmetric_in @ SV66 @ SY4544 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2973]) ).
thf(3104,plain,
! [SV401: $i,SV66: $i] :
( ( ( well_orders @ SV66 @ SV401 )
= $false )
| ( ( is_connected_in @ SV66 @ SV401 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3105,plain,
! [SV163: $i] :
( ( ( connected @ SV163 )
= $false )
| ( ( transitive @ SV163 )
= $false )
| ( ( reflexive @ SV163 )
= $false )
| ( ( antisymmetric @ SV163 )
= $false )
| ( ( ~ ( well_founded_relation @ SV163 ) )
= $true )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3106,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3107,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( well_ordering @ SX0 )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2977]) ).
thf(3108,plain,
! [SV402: $i] :
( ( ( relation @ SV402 )
= $false )
| ( ( ~ ( well_ordering @ SV402 )
| ( antisymmetric @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3109,plain,
! [SV339: $i,SV314: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV314 ) @ SV339 )
= $false )
| ( ( SV314
= ( apply @ SV339 @ SV67 ) )
= $true )
| ( ( function @ SV339 )
= $false )
| ( ( relation @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3110,plain,
! [SV340: $i,SV315: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV315 ) @ SV340 )
= $false )
| ( ( in @ SV67 @ ( relation_dom @ SV340 ) )
= $true )
| ( ( function @ SV340 )
= $false )
| ( ( relation @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3111,plain,
! [SV68: $i,SV256: $i,SV229: $i,SV365: $i] :
( ( ( in @ SV365 @ SV229 )
= $false )
| ( ( in @ SV365 @ ( relation_rng @ SV256 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV68 @ SV365 ) @ SV256 )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV256 @ SV229 ) )
= $true )
| ( ( relation @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3112,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3113,plain,
! [SV230: $i,SV257: $i,SV68: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 ) )
= $false )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2984]) ).
thf(3114,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
| ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3115,plain,
! [SV175: $i,SV69: $i,SV403: $i] :
( ( ( ~ ( function @ SV403 ) )
= $true )
| ( ( ~ ( relation @ SV403 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
| ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3116,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2987]) ).
thf(3117,plain,
! [SV175: $i,SV69: $i] :
( ( ( ! [SY4786: $i] :
( ~ ( function @ SY4786 )
| ~ ( relation @ SY4786 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4786 )
| ( one_to_one @ SY4786 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3118,plain,
! [SV71: $i,SV283: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 ) )
= $true )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3119,plain,
! [SV71: $i,SV284: $i,SV428: $i] :
( ( ( ! [SY5016: $i] :
( ~ ( in @ ( ordered_pair @ SV428 @ SY5016 ) @ SV284 )
| ( in @ ( ordered_pair @ SY5016 @ SV428 ) @ SV71 ) ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3120,plain,
! [SV284: $i,SV71: $i,SV429: $i] :
( ( ( ! [SY5017: $i] :
( ~ ( in @ ( ordered_pair @ SY5017 @ SV429 ) @ SV71 )
| ( in @ ( ordered_pair @ SV429 @ SY5017 ) @ SV284 ) ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3121,plain,
! [SV181: $i,SV343: $i] :
( ( ( subset @ SV343 @ ( relation_field @ SV181 ) )
= $false )
| ( ( SV343 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV181 @ ( sK42_C @ SV343 @ SV181 ) ) @ SV343 )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3122,plain,
! [SV181: $i,SV343: $i] :
( ( ( subset @ SV343 @ ( relation_field @ SV181 ) )
= $false )
| ( ( SV343 = empty_set )
= $true )
| ( ( in @ ( sK42_C @ SV343 @ SV181 ) @ SV343 )
= $true )
| ( ( well_founded_relation @ SV181 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3123,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
= $false )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2997]) ).
thf(3124,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) ) )
= $false )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2997]) ).
thf(3125,plain,
! [SV368: $i,SV182: $i,SV72: $i] :
( ( ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) )
| ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3126,plain,
! [SV404: $i,SV73: $i,SV286: $i] :
( ( ( in @ ( sK36_C @ SV286 @ SV73 ) @ SV286 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK36_C @ SV286 @ SV73 ) @ SV404 ) @ SV73 )
= $false )
| ( ( SV286
= ( relation_dom @ SV73 ) )
= $true )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3127,plain,
! [SV287: $i,SV73: $i,SV430: $i,SV405: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV405 @ SV430 ) @ SV73 ) )
= $true )
| ( ( in @ SV405 @ SV287 )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3128,plain,
! [SV73: $i,SV287: $i,SV406: $i] :
( ( ( in @ SV406 @ SV287 )
= $false )
| ( ( in @ ( ordered_pair @ SV406 @ ( sK35_D @ SV406 @ SV287 @ SV73 ) ) @ SV73 )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3129,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
| ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3130,plain,
! [SV74: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ ( sK25_C @ SV288 @ SV74 ) @ ( sK26_SY4416 @ SV288 @ SV74 ) ) @ SV74 )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3131,plain,
! [SV74: $i,SV389: $i,SV289: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV289 ) )
= $true )
| ( ( ~ ( in @ SV389 @ SV289 ) )
= $true )
| ( ( SV370 = SV389 )
= $true )
| ( ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3132,plain,
! [SV189: $i] :
( ( ( ~ ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3005]) ).
thf(3133,plain,
! [SV189: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3005]) ).
thf(3134,plain,
! [SV371: $i,SV190: $i,SV345: $i] :
( ( ( in @ SV345 @ ( relation_field @ SV190 ) )
= $false )
| ( ( ~ ( in @ SV371 @ ( relation_field @ SV190 ) ) )
= $true )
| ( ( SV345 = SV371 )
= $true )
| ( ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3135,plain,
! [SV136: $i,SV372: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) )
| ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) )
= $true )
| ( ( function @ SV372 )
= $false )
| ( ( relation @ SV372 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3136,plain,
! [SV136: $i,SV76: $i,SV407: $i] :
( ( ( ~ ( function @ SV407 ) )
= $true )
| ( ( ~ ( relation @ SV407 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3137,plain,
! [SV136: $i,SV76: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 ) )
= $true )
| ( ( ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
| ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3138,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3139,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 )
| ~ ( in @ SV394 @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3140,plain,
! [SV374: $i,SV346: $i,SV78: $i] :
( ( ( ! [SY4979: $i] :
( ~ ( in @ SY4979 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4979 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SY4979 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3141,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3142,plain,
! [SV375: $i,SV347: $i,SV78: $i] :
( ( ( ! [SY4980: $i] :
( ! [SY4955: $i] :
( ~ ( in @ SY4955 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY4955 @ SV347 )
| ( SY4980
!= ( apply @ SV78 @ SY4955 ) ) )
| ( in @ SY4980 @ SV375 ) ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3143,plain,
! [SV78: $i,SV347: $i,SV375: $i] :
( ( ( ! [SY4982: $i] :
( ~ ( in @ SY4982 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SY4982
!= ( apply @ SV78 @ ( sK60_E @ SY4982 @ SV375 @ SV347 @ SV78 ) ) ) ) ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3017]) ).
thf(3144,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
= $false )
| ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3145,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3146,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
| ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 ) )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3020]) ).
thf(3147,plain,
! [SV319: $i,SV79: $i,SV293: $i,SV421: $i] :
( ( ( ( SV421 = SV293 )
| ~ ( in @ ( ordered_pair @ SV421 @ SV293 ) @ SV79 ) )
= $true )
| ( ( in @ SV421 @ SV319 )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3148,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ~ ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3149,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ~ ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3150,plain,
! [SV80: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 ) )
= $true )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3151,plain,
! [SV295: $i,SV80: $i,SV431: $i] :
( ( ( ! [SY5018: $i] :
( ~ ( in @ ( ordered_pair @ SV431 @ SY5018 ) @ SV80 )
| ( in @ ( ordered_pair @ SV431 @ SY5018 ) @ SV295 ) ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3152,plain,
! [SV80: $i,SV295: $i,SV432: $i] :
( ( ( ! [SY5019: $i] :
( ~ ( in @ ( ordered_pair @ SV432 @ SY5019 ) @ SV295 )
| ( in @ ( ordered_pair @ SV432 @ SY5019 ) @ SV80 ) ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3153,plain,
! [SV82: $i,SV348: $i,SV320: $i] :
( ( ( in @ SV320 @ ( relation_dom @ ( relation_dom_restriction @ SV348 @ SV82 ) ) )
= $false )
| ( ( in @ SV320 @ ( relation_dom @ SV348 ) )
= $true )
| ( ( function @ SV348 )
= $false )
| ( ( relation @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3154,plain,
! [SV82: $i,SV349: $i,SV321: $i] :
( ( ( in @ SV321 @ ( relation_dom @ ( relation_dom_restriction @ SV349 @ SV82 ) ) )
= $false )
| ( ( in @ SV321 @ SV82 )
= $true )
| ( ( function @ SV349 )
= $false )
| ( ( relation @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3155,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3156,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3157,plain,
! [SV323: $i,SV137: $i,SV83: $i] :
( ( ( ! [SY4928: $i,SY4929: $i] :
( ~ ( in @ SY4929 @ SV83 )
| ~ ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV137 )
| ( in @ ( ordered_pair @ SY4928 @ SY4929 ) @ SV323 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3032]) ).
thf(3158,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3159,plain,
! [SV84: $i,SV298: $i,SV395: $i] :
( ( ( in @ SV395 @ ( sK39_C @ SV298 @ SV84 ) )
= $false )
| ( ( disjoint @ ( fiber @ SV84 @ SV395 ) @ ( sK39_C @ SV298 @ SV84 ) )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3160,plain,
! [SV84: $i,SV298: $i] :
( ( ( ( sK39_C @ SV298 @ SV84 )
= empty_set )
= $false )
| ( ( is_well_founded_in @ SV84 @ SV298 )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3161,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( SV377 = empty_set )
= $true )
| ( ( ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3162,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( SV377 = empty_set )
= $true )
| ( ( ~ ( subset @ SV377 @ SV299 ) )
= $true )
| ( ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3038]) ).
thf(3163,plain,
! [SV396: $i,SV85: $i,SV433: $i] :
( ( ( ( SV433
!= ( apply @ SV85 @ SV396 ) )
| ( in @ ( ordered_pair @ SV396 @ SV433 ) @ SV85 ) )
= $true )
| ( ( in @ SV396 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3164,plain,
! [SV85: $i,SV434: $i,SV397: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV397 @ SV434 ) @ SV85 )
| ( SV434
= ( apply @ SV85 @ SV397 ) ) )
= $true )
| ( ( in @ SV397 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3165,plain,
! [SV398: $i,SV85: $i,SV422: $i] :
( ( ( ( SV422
!= ( apply @ SV85 @ SV398 ) ) )
= $true )
| ( ( SV422 = empty_set )
= $true )
| ( ( in @ SV398 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3166,plain,
! [SV399: $i,SV85: $i,SV423: $i] :
( ( ( ( SV423 != empty_set ) )
= $true )
| ( ( SV423
= ( apply @ SV85 @ SV399 ) )
= $true )
| ( ( in @ SV399 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3167,plain,
! [SV435: $i,SV86: $i,SV351: $i] :
( ( ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SV435 ) )
| ~ ( in @ SV435 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3168,plain,
! [SV86: $i,SV351: $i] :
( ( ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
| ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
= $false )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3169,plain,
! [SV352: $i,SV86: $i,SV436: $i] :
( ( ( ! [SY5020: $i] :
( ( SV436
!= ( apply @ SV86 @ SY5020 ) )
| ~ ( in @ SY5020 @ ( relation_dom @ SV86 ) ) )
| ( in @ SV436 @ SV352 ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3170,plain,
! [SV86: $i,SV352: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV352 )
| ~ ( ( SV437
!= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3171,plain,
! [SV353: $i,SV206: $i,SV391: $i,SV379: $i] :
( ( ( in @ ( ordered_pair @ SV379 @ SV391 ) @ SV206 )
= $false )
| ( ( in @ ( ordered_pair @ SV353 @ SV379 ) @ SV206 )
= $false )
| ( ( in @ ( ordered_pair @ SV353 @ SV391 ) @ SV206 )
= $true )
| ( ( transitive @ SV206 )
= $false )
| ( ( relation @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3172,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3173,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
| ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3174,plain,
! [SV381: $i,SV355: $i,SV88: $i] :
( ( ( ! [SY4984: $i] :
( ~ ( in @ SY4984 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SY4984 ) @ SV355 )
| ( in @ SY4984 @ SV381 ) ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3175,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ~ ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3052]) ).
thf(3176,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3053]) ).
thf(3177,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3054]) ).
thf(3178,plain,
( ( ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3055]) ).
thf(3179,plain,
( ( one_to_one @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3056]) ).
thf(3180,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3057]) ).
thf(3181,plain,
! [SV207: $i,SV89: $i] :
( ( ( ! [SY4813: $i] :
( ~ ( function @ SY4813 )
| ~ ( relation @ SY4813 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4813 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3058]) ).
thf(3182,plain,
! [SV207: $i,SV89: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 ) )
= $true )
| ( ( ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3183,plain,
! [SV382: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV382 ) )
= $true )
| ( ( ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( function @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3184,plain,
! [SV210: $i,SV241: $i] :
( ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
= $false )
| ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 ) )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3185,plain,
! [SV210: $i,SV241: $i] :
( ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3186,plain,
! [SV210: $i,SV241: $i] :
( ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 )
= $true )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3187,plain,
! [SV242: $i,SV211: $i,SV424: $i,SV410: $i] :
( ( ( ( SV410 != SV424 )
| ~ ( in @ SV410 @ SV211 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV410 @ SV424 ) @ SV242 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3188,plain,
! [SV211: $i,SV242: $i] :
( ( ( ! [SY4844: $i,SY4845: $i] :
( ~ ( in @ ( ordered_pair @ SY4844 @ SY4845 ) @ SV242 )
| ( SY4844 = SY4845 ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3065]) ).
thf(3189,plain,
! [SV211: $i,SV242: $i] :
( ( ( ! [SY4846: $i] :
( ! [SY4847: $i] :
~ ( in @ ( ordered_pair @ SY4846 @ SY4847 ) @ SV242 )
| ( in @ SY4846 @ SV211 ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3066]) ).
thf(3190,plain,
! [SV411: $i,SV91: $i,SV302: $i] :
( ( ( in @ ( sK28_C @ SV302 @ SV91 ) @ SV302 )
= $false )
| ( ( in @ ( ordered_pair @ SV411 @ ( sK28_C @ SV302 @ SV91 ) ) @ SV91 )
= $false )
| ( ( SV302
= ( relation_rng @ SV91 ) )
= $true )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3191,plain,
! [SV303: $i,SV91: $i,SV412: $i,SV438: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV438 @ SV412 ) @ SV91 ) )
= $true )
| ( ( in @ SV412 @ SV303 )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3192,plain,
! [SV91: $i,SV303: $i,SV413: $i] :
( ( ( in @ SV413 @ SV303 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK27_D @ SV413 @ SV303 @ SV91 ) @ SV413 ) @ SV91 )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3193,plain,
! [SV92: $i,SV264: $i,SV243: $i,SV383: $i] :
( ( ( in @ SV383 @ SV243 )
= $false )
| ( ( in @ SV383 @ ( relation_dom @ SV264 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV383 @ SV92 ) @ SV264 )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV264 @ SV243 ) )
= $true )
| ( ( relation @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3194,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3195,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 ) )
= $false )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3071]) ).
thf(3196,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
| ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3197,plain,
! [SV93: $i,SV138: $i,SV414: $i] :
( ( ( ~ ( function @ SV414 ) )
= $true )
| ( ( ~ ( relation @ SV414 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) )
| ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3198,plain,
! [SV93: $i,SV138: $i,SV415: $i] :
( ( ( ~ ( function @ SV415 ) )
= $true )
| ( ( ~ ( relation @ SV415 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3199,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3200,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3201,plain,
! [SV327: $i,SV96: $i,SV305: $i] :
( ( ( ! [SY4936: $i,SY4937: $i] :
( ~ ( in @ SY4936 @ SV305 )
| ~ ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV96 )
| ( in @ ( ordered_pair @ SY4936 @ SY4937 ) @ SV327 ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3077]) ).
thf(3202,plain,
! [SV96: $i,SV305: $i,SV327: $i] :
( ( ( ~ ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3078]) ).
thf(3203,plain,
! [SV97: $i,SV306: $i,SV328: $i,SV425: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV425 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 ) )
= $true )
| ( ( ~ ( in @ SV425 @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3204,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 ) )
= $false )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3205,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( ~ ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 ) )
= $false )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3206,plain,
! [SV329: $i,SV307: $i,SV97: $i,SV426: $i] :
( ( ( ! [SY5015: $i] :
( ~ ( in @ ( ordered_pair @ SY5015 @ SV426 ) @ SV97 )
| ~ ( in @ SY5015 @ SV307 ) ) )
= $true )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3207,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV329 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3208,plain,
! [SV222: $i,SV252: $i] :
( ( ( ( relation_dom @ SV252 )
= SV222 )
= $false )
| ( ( in @ ( sK72_C @ SV252 @ SV222 ) @ SV222 )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3209,plain,
! [SV222: $i,SV252: $i] :
( ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
= ( sK72_C @ SV252 @ SV222 ) )
= $false )
| ( ( ( ( relation_dom @ SV252 )
!= SV222 ) )
= $true )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3210,plain,
! [SV330: $i,SV308: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV308 )
| ( ( apply @ SV330 @ SV439 )
= SV439 ) )
= $true )
| ( ( SV330
= ( identity_relation @ SV308 ) )
= $false )
| ( ( function @ SV330 )
= $false )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3211,plain,
! [SV153: $i] :
( ( ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
| ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3087]) ).
thf(3212,plain,
! [SV392: $i,SV154: $i,SV385: $i] :
( ( ( in @ SV385 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ~ ( in @ SV392 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) ) )
= $true )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3213,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3214,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ( function @ SV416 ) )
= $true )
| ( ( ~ ( relation @ SV416 ) )
= $true )
| ( ( ( SV416
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3215,plain,
! [SV60: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 ) )
= $true )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ( SV417
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3216,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3217,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3218,plain,
! [SV62: $i,SV387: $i,SV274: $i,SV362: $i] :
( ( ( in @ SV362 @ SV274 )
= $false )
| ( ( ~ ( in @ SV387 @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3219,plain,
! [SV418: $i,SV63: $i,SV275: $i,SV310: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV418 ) @ SV63 )
= $false )
| ( ( ~ ( in @ SV418 @ SV275 ) )
= $true )
| ( ( ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3220,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) ) @ SV63 )
= $true )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3221,plain,
! [SV63: $i,SV275: $i,SV310: $i] :
( ( ( in @ ( sK53_SY4432 @ SV310 @ SV275 @ SV63 ) @ SV275 )
= $true )
| ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3097]) ).
thf(3222,plain,
! [SV311: $i,SV276: $i,SV63: $i,SV440: $i,SV419: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV419 @ SV440 ) @ SV63 )
| ~ ( in @ SV440 @ SV276 ) )
= $true )
| ( ( in @ SV419 @ SV311 )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3223,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( in @ SV420 @ SV311 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 ) ) )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3224,plain,
! [SV279: $i,SV66: $i] :
( ( ( is_connected_in @ SV66 @ SV279 )
= $false )
| ( ( is_transitive_in @ SV66 @ SV279 )
= $false )
| ( ( is_reflexive_in @ SV66 @ SV279 )
= $false )
| ( ( is_antisymmetric_in @ SV66 @ SV279 )
= $false )
| ( ( ~ ( is_well_founded_in @ SV66 @ SV279 ) )
= $true )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3225,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) )
| ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3226,plain,
! [SV441: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV441 )
| ( is_antisymmetric_in @ SV66 @ SV441 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3227,plain,
! [SV163: $i] :
( ( ( well_founded_relation @ SV163 )
= $false )
| ( ( antisymmetric @ SV163 )
= $false )
| ( ( reflexive @ SV163 )
= $false )
| ( ( transitive @ SV163 )
= $false )
| ( ( connected @ SV163 )
= $false )
| ( ( well_ordering @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3228,plain,
! [SV442: $i] :
( ( ~ ( relation @ SV442 )
| ~ ( well_ordering @ SV442 )
| ( reflexive @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3229,plain,
! [SV443: $i] :
( ( ~ ( relation @ SV443 )
| ~ ( well_ordering @ SV443 )
| ( transitive @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3230,plain,
! [SV402: $i] :
( ( ( ~ ( well_ordering @ SV402 ) )
= $true )
| ( ( antisymmetric @ SV402 )
= $true )
| ( ( relation @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3231,plain,
! [SV68: $i,SV230: $i,SV257: $i] :
( ( ( in @ ( sK73_D @ SV257 @ SV230 @ SV68 ) @ ( relation_rng @ SV257 ) )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3232,plain,
! [SV230: $i,SV257: $i,SV68: $i] :
( ( ( in @ ( ordered_pair @ SV68 @ ( sK73_D @ SV257 @ SV230 @ SV68 ) ) @ SV257 )
= $true )
| ( ( in @ SV68 @ ( relation_inverse_image @ SV257 @ SV230 ) )
= $false )
| ( ( relation @ SV257 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3233,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3234,plain,
! [SV175: $i,SV69: $i,SV403: $i] :
( ( ( function @ SV403 )
= $false )
| ( ( ~ ( relation @ SV403 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
| ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3235,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) )
| ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3116]) ).
thf(3236,plain,
! [SV175: $i,SV69: $i,SV444: $i] :
( ( ( ~ ( function @ SV444 )
| ~ ( relation @ SV444 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
| ( one_to_one @ SV444 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3237,plain,
! [SV71: $i,SV283: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_SY4415 @ SV283 @ SV71 ) @ ( sK23_C @ SV283 @ SV71 ) ) @ SV71 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK23_C @ SV283 @ SV71 ) @ ( sK24_SY4415 @ SV283 @ SV71 ) ) @ SV283 )
= $false )
| ( ( SV283
= ( relation_inverse @ SV71 ) )
= $true )
| ( ( relation @ SV283 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3238,plain,
! [SV71: $i,SV284: $i,SV445: $i,SV428: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV284 )
| ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV71 ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3239,plain,
! [SV284: $i,SV71: $i,SV429: $i,SV446: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV429 ) @ SV71 )
| ( in @ ( ordered_pair @ SV429 @ SV446 ) @ SV284 ) )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3240,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3123]) ).
thf(3241,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
| ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3242,plain,
! [SV368: $i,SV182: $i,SV72: $i] :
( ( ( ~ ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) ) )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3243,plain,
! [SV72: $i,SV182: $i,SV368: $i] :
( ( ( ~ ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3125]) ).
thf(3244,plain,
! [SV287: $i,SV73: $i,SV430: $i,SV405: $i] :
( ( ( in @ ( ordered_pair @ SV405 @ SV430 ) @ SV73 )
= $false )
| ( ( in @ SV405 @ SV287 )
= $true )
| ( ( SV287
= ( relation_dom @ SV73 ) )
= $false )
| ( ( relation @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3245,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3246,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3129]) ).
thf(3247,plain,
! [SV74: $i,SV389: $i,SV289: $i,SV370: $i] :
( ( ( in @ SV370 @ SV289 )
= $false )
| ( ( ~ ( in @ SV389 @ SV289 ) )
= $true )
| ( ( SV370 = SV389 )
= $true )
| ( ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3248,plain,
! [SV189: $i] :
( ( ( ( ( sK75_B @ SV189 )
!= ( sK76_SY4442 @ SV189 ) ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3132]) ).
thf(3249,plain,
! [SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3250,plain,
! [SV345: $i,SV190: $i,SV371: $i] :
( ( ( in @ SV371 @ ( relation_field @ SV190 ) )
= $false )
| ( ( in @ SV345 @ ( relation_field @ SV190 ) )
= $false )
| ( ( SV345 = SV371 )
= $true )
| ( ( in @ ( ordered_pair @ SV345 @ SV371 ) @ SV190 )
= $true )
| ( ( in @ ( ordered_pair @ SV371 @ SV345 ) @ SV190 )
= $true )
| ( ( connected @ SV190 )
= $false )
| ( ( relation @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3251,plain,
! [SV136: $i,SV372: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_dom @ SV372 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) )
= $true )
| ( ( function @ SV372 )
= $false )
| ( ( relation @ SV372 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3252,plain,
! [SV136: $i,SV76: $i,SV407: $i] :
( ( ( function @ SV407 )
= $false )
| ( ( ~ ( relation @ SV407 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3253,plain,
! [SV136: $i,SV76: $i,SV408: $i] :
( ( ( function @ SV408 )
= $false )
| ( ( ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
| ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3254,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3255,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3256,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 )
| ~ ( in @ SV390 @ SV291 ) )
= $true )
| ( ( ~ ( in @ SV394 @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3257,plain,
! [SV374: $i,SV346: $i,SV78: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SV447 @ SV346 )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3258,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
| ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3259,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i] :
( ( ( ! [SY5021: $i] :
( ~ ( in @ SY5021 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY5021 @ SV347 )
| ( SV448
!= ( apply @ SV78 @ SY5021 ) ) )
| ( in @ SV448 @ SV375 ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3260,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ SV375 )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SV449
!= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) ) ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3261,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 )
= $false )
| ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
= $false )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3262,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
!= SV292 ) )
= $true )
| ( ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3263,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( in @ ( ordered_pair @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV292 ) @ SV79 )
= $true )
| ( ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3264,plain,
! [SV319: $i,SV79: $i,SV293: $i,SV421: $i] :
( ( ( SV421 = SV293 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV421 @ SV293 ) @ SV79 ) )
= $true )
| ( ( in @ SV421 @ SV319 )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3265,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ! [SY4924: $i] :
( ~ ( in @ SY4924 @ SV319 )
| ( SY4924 != SV293 ) ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3266,plain,
! [SV79: $i,SV293: $i,SV319: $i] :
( ( ( ! [SY4925: $i] :
( ~ ( in @ SY4925 @ SV319 )
| ( in @ ( ordered_pair @ SY4925 @ SV293 ) @ SV79 ) ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3149]) ).
thf(3267,plain,
! [SV80: $i,SV294: $i] :
( ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV294 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK44_C @ SV294 @ SV80 ) @ ( sK45_SY4427 @ SV294 @ SV80 ) ) @ SV80 )
= $false )
| ( ( SV80 = SV294 )
= $true )
| ( ( relation @ SV294 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3268,plain,
! [SV295: $i,SV80: $i,SV450: $i,SV431: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV80 )
| ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV295 ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3269,plain,
! [SV80: $i,SV295: $i,SV451: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV295 )
| ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV80 ) )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3270,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3271,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3272,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) ) )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3156]) ).
thf(3273,plain,
! [SV323: $i,SV137: $i,SV452: $i,SV83: $i] :
( ( ( ! [SY5022: $i] :
( ~ ( in @ SY5022 @ SV83 )
| ~ ( in @ ( ordered_pair @ SV452 @ SY5022 ) @ SV137 )
| ( in @ ( ordered_pair @ SV452 @ SY5022 ) @ SV323 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3274,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) )
| ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3275,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( subset @ SV377 @ SV299 )
= $false )
| ( ( SV377 = empty_set )
= $true )
| ( ( disjoint @ ( fiber @ SV84 @ ( sK38_D @ SV377 @ SV299 @ SV84 ) ) @ SV377 )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3276,plain,
! [SV84: $i,SV299: $i,SV377: $i] :
( ( ( subset @ SV377 @ SV299 )
= $false )
| ( ( SV377 = empty_set )
= $true )
| ( ( in @ ( sK38_D @ SV377 @ SV299 @ SV84 ) @ SV377 )
= $true )
| ( ( is_well_founded_in @ SV84 @ SV299 )
= $false )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3277,plain,
! [SV396: $i,SV85: $i,SV433: $i] :
( ( ( ( SV433
!= ( apply @ SV85 @ SV396 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV396 @ SV433 ) @ SV85 )
= $true )
| ( ( in @ SV396 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3278,plain,
! [SV85: $i,SV434: $i,SV397: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV397 @ SV434 ) @ SV85 ) )
= $true )
| ( ( SV434
= ( apply @ SV85 @ SV397 ) )
= $true )
| ( ( in @ SV397 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3279,plain,
! [SV398: $i,SV85: $i,SV422: $i] :
( ( ( SV422
= ( apply @ SV85 @ SV398 ) )
= $false )
| ( ( SV422 = empty_set )
= $true )
| ( ( in @ SV398 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3280,plain,
! [SV399: $i,SV85: $i,SV423: $i] :
( ( ( SV423 = empty_set )
= $false )
| ( ( SV423
= ( apply @ SV85 @ SV399 ) )
= $true )
| ( ( in @ SV399 @ ( relation_dom @ SV85 ) )
= $true )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3281,plain,
! [SV435: $i,SV86: $i,SV351: $i] :
( ( ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ SV435 ) ) )
= $true )
| ( ( ~ ( in @ SV435 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3282,plain,
! [SV86: $i,SV351: $i] :
( ( ( ( ( sK31_C @ SV351 @ SV86 )
!= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) ) )
= $false )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3168]) ).
thf(3283,plain,
! [SV86: $i,SV351: $i] :
( ( ( ~ ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
= $false )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3168]) ).
thf(3284,plain,
! [SV352: $i,SV86: $i,SV436: $i] :
( ( ( ! [SY5020: $i] :
( ( SV436
!= ( apply @ SV86 @ SY5020 ) )
| ~ ( in @ SY5020 @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( in @ SV436 @ SV352 )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3285,plain,
! [SV86: $i,SV352: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ SV352 ) )
= $true )
| ( ( ~ ( ( SV437
!= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3286,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3287,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ~ ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3288,plain,
! [SV354: $i,SV380: $i,SV88: $i] :
( ( ( ~ ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3289,plain,
! [SV381: $i,SV355: $i,SV88: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SV453 ) @ SV355 )
| ( in @ SV453 @ SV381 ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3290,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) )
| ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3291,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3292,plain,
( ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3293,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
| ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3294,plain,
! [SV207: $i,SV89: $i,SV454: $i] :
( ( ( ~ ( function @ SV454 )
| ~ ( relation @ SV454 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3295,plain,
! [SV207: $i,SV89: $i,SV409: $i] :
( ( ( function @ SV409 )
= $false )
| ( ( ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3296,plain,
! [SV382: $i,SV207: $i,SV89: $i] :
( ( ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
= $false )
| ( ( ~ ( well_founded_relation @ SV89 )
| ( well_founded_relation @ SV207 ) )
= $true )
| ( ( function @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3297,plain,
! [SV210: $i,SV241: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_C @ SV241 @ SV210 ) @ ( sK66_SY4439 @ SV241 @ SV210 ) ) @ SV241 )
= $false )
| ( ( ( sK65_C @ SV241 @ SV210 )
= ( sK66_SY4439 @ SV241 @ SV210 ) )
= $false )
| ( ( in @ ( sK65_C @ SV241 @ SV210 ) @ SV210 )
= $false )
| ( ( SV241
= ( identity_relation @ SV210 ) )
= $true )
| ( ( relation @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3298,plain,
! [SV242: $i,SV211: $i,SV424: $i,SV410: $i] :
( ( ( ( SV410 != SV424 ) )
= $true )
| ( ( ~ ( in @ SV410 @ SV211 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV410 @ SV424 ) @ SV242 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3299,plain,
! [SV211: $i,SV242: $i,SV455: $i] :
( ( ( ! [SY5023: $i] :
( ~ ( in @ ( ordered_pair @ SV455 @ SY5023 ) @ SV242 )
| ( SV455 = SY5023 ) ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3300,plain,
! [SV211: $i,SV242: $i,SV456: $i] :
( ( ( ! [SY5024: $i] :
~ ( in @ ( ordered_pair @ SV456 @ SY5024 ) @ SV242 )
| ( in @ SV456 @ SV211 ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3301,plain,
! [SV303: $i,SV91: $i,SV412: $i,SV438: $i] :
( ( ( in @ ( ordered_pair @ SV438 @ SV412 ) @ SV91 )
= $false )
| ( ( in @ SV412 @ SV303 )
= $true )
| ( ( SV303
= ( relation_rng @ SV91 ) )
= $false )
| ( ( relation @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3302,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( in @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ ( relation_dom @ SV265 ) )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3303,plain,
! [SV92: $i,SV244: $i,SV265: $i] :
( ( ( in @ ( ordered_pair @ ( sK74_D @ SV265 @ SV244 @ SV92 ) @ SV92 ) @ SV265 )
= $true )
| ( ( in @ SV92 @ ( relation_image @ SV265 @ SV244 ) )
= $false )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3195]) ).
thf(3304,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3305,plain,
! [SV93: $i,SV138: $i,SV414: $i] :
( ( ( function @ SV414 )
= $false )
| ( ( ~ ( relation @ SV414 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) )
| ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3306,plain,
! [SV93: $i,SV138: $i,SV415: $i] :
( ( ( function @ SV415 )
= $false )
| ( ( ~ ( relation @ SV415 ) )
= $true )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3307,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3308,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3309,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) ) )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3310,plain,
! [SV327: $i,SV96: $i,SV305: $i,SV457: $i] :
( ( ( ! [SY5025: $i] :
( ~ ( in @ SV457 @ SV305 )
| ~ ( in @ ( ordered_pair @ SV457 @ SY5025 ) @ SV96 )
| ( in @ ( ordered_pair @ SV457 @ SY5025 ) @ SV327 ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3311,plain,
! [SV96: $i,SV305: $i,SV327: $i] :
( ( ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) )
| ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3312,plain,
! [SV97: $i,SV306: $i,SV328: $i,SV425: $i] :
( ( ( in @ ( ordered_pair @ SV425 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
= $false )
| ( ( ~ ( in @ SV425 @ SV306 ) )
= $true )
| ( ( ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3313,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
= $true )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3204]) ).
thf(3314,plain,
! [SV97: $i,SV306: $i,SV328: $i] :
( ( ( in @ ( sK56_SY4434 @ SV328 @ SV306 @ SV97 ) @ SV306 )
= $true )
| ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3315,plain,
! [SV329: $i,SV307: $i,SV97: $i,SV426: $i,SV458: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV458 @ SV426 ) @ SV97 )
| ~ ( in @ SV458 @ SV307 ) )
= $true )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3316,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( in @ SV427 @ SV329 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 ) ) )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3317,plain,
! [SV222: $i,SV252: $i] :
( ( ( ( relation_dom @ SV252 )
= SV222 )
= $false )
| ( ( ( apply @ SV252 @ ( sK72_C @ SV252 @ SV222 ) )
= ( sK72_C @ SV252 @ SV222 ) )
= $false )
| ( ( SV252
= ( identity_relation @ SV222 ) )
= $true )
| ( ( function @ SV252 )
= $false )
| ( ( relation @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3318,plain,
! [SV330: $i,SV308: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV308 ) )
= $true )
| ( ( ( apply @ SV330 @ SV439 )
= SV439 )
= $true )
| ( ( SV330
= ( identity_relation @ SV308 ) )
= $false )
| ( ( function @ SV330 )
= $false )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3319,plain,
! [SV153: $i] :
( ( ( ~ ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3320,plain,
! [SV153: $i] :
( ( ( ~ ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) ) )
= $false )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3321,plain,
! [SV385: $i,SV154: $i,SV392: $i] :
( ( ( in @ SV392 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( in @ SV385 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ( ( apply @ SV154 @ SV385 )
!= ( apply @ SV154 @ SV392 ) ) )
= $true )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3322,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3323,plain,
! [SV60: $i,SV416: $i] :
( ( ( function @ SV416 )
= $false )
| ( ( ~ ( relation @ SV416 ) )
= $true )
| ( ( ( SV416
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3324,plain,
! [SV60: $i,SV417: $i] :
( ( ( function @ SV417 )
= $false )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ( SV417
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3325,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3216]) ).
thf(3326,plain,
! [SV62: $i,SV273: $i] :
( ( ( in @ ( ordered_pair @ ( sK33_C @ SV273 @ SV62 ) @ ( sK34_SY4421 @ SV273 @ SV62 ) ) @ SV62 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3327,plain,
! [SV62: $i,SV362: $i,SV274: $i,SV387: $i] :
( ( ( in @ SV387 @ SV274 )
= $false )
| ( ( in @ SV362 @ SV274 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3328,plain,
! [SV63: $i,SV310: $i,SV275: $i,SV418: $i] :
( ( ( in @ SV418 @ SV275 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV418 ) @ SV63 )
= $false )
| ( ( ~ ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 ) )
= $true )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3329,plain,
! [SV311: $i,SV276: $i,SV63: $i,SV440: $i,SV419: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV419 @ SV440 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV440 @ SV276 ) )
= $true )
| ( ( in @ SV419 @ SV311 )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3330,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
| ~ ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 ) )
= $false )
| ( ( in @ SV420 @ SV311 )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3331,plain,
! [SV279: $i,SV66: $i] :
( ( ( is_well_founded_in @ SV66 @ SV279 )
= $false )
| ( ( is_antisymmetric_in @ SV66 @ SV279 )
= $false )
| ( ( is_reflexive_in @ SV66 @ SV279 )
= $false )
| ( ( is_transitive_in @ SV66 @ SV279 )
= $false )
| ( ( is_connected_in @ SV66 @ SV279 )
= $false )
| ( ( well_orders @ SV66 @ SV279 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3332,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3225]) ).
thf(3333,plain,
! [SV66: $i] :
( ( ( ~ ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
= $false )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3225]) ).
thf(3334,plain,
! [SV441: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV441 ) )
= $true )
| ( ( is_antisymmetric_in @ SV66 @ SV441 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3335,plain,
! [SV442: $i] :
( ( ( ~ ( relation @ SV442 ) )
= $true )
| ( ( ~ ( well_ordering @ SV442 )
| ( reflexive @ SV442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3336,plain,
! [SV443: $i] :
( ( ( ~ ( relation @ SV443 ) )
= $true )
| ( ( ~ ( well_ordering @ SV443 )
| ( transitive @ SV443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3337,plain,
! [SV402: $i] :
( ( ( well_ordering @ SV402 )
= $false )
| ( ( antisymmetric @ SV402 )
= $true )
| ( ( relation @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3338,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3339,plain,
! [SV175: $i,SV69: $i,SV403: $i] :
( ( ( relation @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
| ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3340,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3341,plain,
! [SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3235]) ).
thf(3342,plain,
! [SV175: $i,SV69: $i,SV444: $i] :
( ( ( ~ ( function @ SV444 )
| ~ ( relation @ SV444 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
| ( one_to_one @ SV444 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3343,plain,
! [SV71: $i,SV284: $i,SV445: $i,SV428: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV284 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV71 )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3344,plain,
! [SV284: $i,SV71: $i,SV429: $i,SV446: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV429 ) @ SV71 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV429 @ SV446 ) @ SV284 )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3345,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ! [SY4970: $i] :
( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SY4970 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4970 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3346,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3241]) ).
thf(3347,plain,
! [SV368: $i,SV182: $i,SV72: $i] :
( ( ( ! [SY4971: $i,SY4972: $i] :
( ! [SY4794: $i] :
( ~ ( in @ ( ordered_pair @ SY4971 @ SY4794 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY4794 @ SY4972 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SY4971 @ SY4972 ) @ SV368 ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3242]) ).
thf(3348,plain,
! [SV72: $i,SV182: $i,SV368: $i] :
( ( ( ! [SY4974: $i,SY4975: $i] :
( ~ ( in @ ( ordered_pair @ SY4974 @ SY4975 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4974 @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY4975 @ SY4974 @ SV368 @ SV182 @ SV72 ) @ SY4975 ) @ SV182 ) ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3349,plain,
! [SV74: $i,SV288: $i] :
( ( ( ( ( sK25_C @ SV288 @ SV74 )
!= ( sK26_SY4416 @ SV288 @ SV74 ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3350,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) ) )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3246]) ).
thf(3351,plain,
! [SV74: $i,SV370: $i,SV289: $i,SV389: $i] :
( ( ( in @ SV389 @ SV289 )
= $false )
| ( ( in @ SV370 @ SV289 )
= $false )
| ( ( SV370 = SV389 )
= $true )
| ( ( in @ ( ordered_pair @ SV370 @ SV389 ) @ SV74 )
= $true )
| ( ( in @ ( ordered_pair @ SV389 @ SV370 ) @ SV74 )
= $true )
| ( ( is_connected_in @ SV74 @ SV289 )
= $false )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3352,plain,
! [SV189: $i] :
( ( ( ( sK75_B @ SV189 )
= ( sK76_SY4442 @ SV189 ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3353,plain,
! [SV189: $i] :
( ( ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
| ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3354,plain,
! [SV136: $i,SV372: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_dom @ SV372 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) )
= $true )
| ( ( function @ SV372 )
= $false )
| ( ( relation @ SV372 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3355,plain,
! [SV136: $i,SV76: $i,SV407: $i] :
( ( ( relation @ SV407 )
= $false )
| ( ( function @ SV407 )
= $false )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
| ( in @ SV76 @ ( relation_dom @ SV407 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3356,plain,
! [SV136: $i,SV76: $i,SV408: $i] :
( ( ( relation @ SV408 )
= $false )
| ( ( function @ SV408 )
= $false )
| ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
| ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) ) )
= $true )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3357,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3254]) ).
thf(3358,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV290 @ SV77 ) @ ( sK13_SY4405 @ SV290 @ SV77 ) ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3255]) ).
thf(3359,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV291 ) )
= $true )
| ( ( ~ ( in @ SV390 @ SV291 ) )
= $true )
| ( ( ~ ( in @ SV394 @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3360,plain,
! [SV374: $i,SV346: $i,SV78: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SV447 @ SV346 ) )
= $true )
| ( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3361,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3258]) ).
thf(3362,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3258]) ).
thf(3363,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i] :
( ( ( ! [SY5021: $i] :
( ~ ( in @ SY5021 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SY5021 @ SV347 )
| ( SV448
!= ( apply @ SV78 @ SY5021 ) ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3364,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ SV375 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SV449
!= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) ) ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3365,plain,
! [SV79: $i,SV292: $i,SV318: $i] :
( ( ( ( sK46_D @ SV318 @ SV292 @ SV79 )
= SV292 )
= $false )
| ( ( in @ ( sK46_D @ SV318 @ SV292 @ SV79 ) @ SV318 )
= $true )
| ( ( SV318
= ( fiber @ SV79 @ SV292 ) )
= $true )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3366,plain,
! [SV319: $i,SV79: $i,SV293: $i,SV421: $i] :
( ( ( in @ ( ordered_pair @ SV421 @ SV293 ) @ SV79 )
= $false )
| ( ( SV421 = SV293 )
= $true )
| ( ( in @ SV421 @ SV319 )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3367,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV319 )
| ( SV459 != SV293 ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3368,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ SV319 )
| ( in @ ( ordered_pair @ SV460 @ SV293 ) @ SV79 ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3369,plain,
! [SV295: $i,SV80: $i,SV450: $i,SV431: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV80 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV295 )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3370,plain,
! [SV80: $i,SV295: $i,SV451: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV295 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV80 )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3371,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3270]) ).
thf(3372,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3373,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
| ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3272]) ).
thf(3374,plain,
! [SV323: $i,SV137: $i,SV452: $i,SV83: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV83 )
| ~ ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV137 )
| ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV323 ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3375,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ~ ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3376,plain,
! [SV83: $i,SV137: $i,SV323: $i] :
( ( ( ~ ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) )
= $false )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3377,plain,
! [SV396: $i,SV85: $i,SV433: $i] :
( ( ( SV433
= ( apply @ SV85 @ SV396 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV396 @ SV433 ) @ SV85 )
= $true )
| ( ( in @ SV396 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3378,plain,
! [SV85: $i,SV434: $i,SV397: $i] :
( ( ( in @ ( ordered_pair @ SV397 @ SV434 ) @ SV85 )
= $false )
| ( ( SV434
= ( apply @ SV85 @ SV397 ) )
= $true )
| ( ( in @ SV397 @ ( relation_dom @ SV85 ) )
= $false )
| ( ( function @ SV85 )
= $false )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3379,plain,
! [SV435: $i,SV86: $i,SV351: $i] :
( ( ( ( sK31_C @ SV351 @ SV86 )
= ( apply @ SV86 @ SV435 ) )
= $false )
| ( ( ~ ( in @ SV435 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3380,plain,
! [SV86: $i,SV351: $i] :
( ( ( ( sK31_C @ SV351 @ SV86 )
= ( apply @ SV86 @ ( sK32_SY4420 @ SV351 @ SV86 ) ) )
= $true )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3282]) ).
thf(3381,plain,
! [SV86: $i,SV351: $i] :
( ( ( in @ ( sK32_SY4420 @ SV351 @ SV86 ) @ ( relation_dom @ SV86 ) )
= $true )
| ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3283]) ).
thf(3382,plain,
! [SV352: $i,SV462: $i,SV86: $i,SV436: $i] :
( ( ( ( SV436
!= ( apply @ SV86 @ SV462 ) )
| ~ ( in @ SV462 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( in @ SV436 @ SV352 )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(3383,plain,
! [SV86: $i,SV352: $i,SV437: $i] :
( ( ( in @ SV437 @ SV352 )
= $false )
| ( ( ~ ( ( SV437
!= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) ) )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3384,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 ) )
= $true )
| ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3385,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3287]) ).
thf(3386,plain,
! [SV354: $i,SV380: $i,SV88: $i] :
( ( ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
| ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3387,plain,
! [SV381: $i,SV355: $i,SV88: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( relation_dom @ SV88 ) )
| ~ ( in @ ( apply @ SV88 @ SV453 ) @ SV355 ) )
= $true )
| ( ( in @ SV453 @ SV381 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3388,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ~ ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3290]) ).
thf(3389,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ~ ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) )
= $false )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3290]) ).
thf(3390,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3391,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3291]) ).
thf(3392,plain,
( ( ~ ( function @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3292]) ).
thf(3393,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3292]) ).
thf(3394,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3293]) ).
thf(3395,plain,
! [SV207: $i,SV89: $i] :
( ( ( ~ ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3293]) ).
thf(3396,plain,
! [SV207: $i,SV89: $i,SV454: $i] :
( ( ( ~ ( function @ SV454 )
| ~ ( relation @ SV454 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3397,plain,
! [SV207: $i,SV89: $i,SV409: $i] :
( ( ( relation @ SV409 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
| ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3398,plain,
! [SV382: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( well_founded_relation @ SV89 ) )
= $true )
| ( ( well_founded_relation @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
= $false )
| ( ( function @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3399,plain,
! [SV242: $i,SV211: $i,SV424: $i,SV410: $i] :
( ( ( SV410 = SV424 )
= $false )
| ( ( ~ ( in @ SV410 @ SV211 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV410 @ SV424 ) @ SV242 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3400,plain,
! [SV211: $i,SV242: $i,SV463: $i,SV455: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV242 )
| ( SV455 = SV463 ) )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3401,plain,
! [SV211: $i,SV242: $i,SV456: $i] :
( ( ( ! [SY5024: $i] :
~ ( in @ ( ordered_pair @ SV456 @ SY5024 ) @ SV242 ) )
= $true )
| ( ( in @ SV456 @ SV211 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3402,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
| ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3403,plain,
! [SV93: $i,SV138: $i,SV414: $i] :
( ( ( relation @ SV414 )
= $false )
| ( ( function @ SV414 )
= $false )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) )
| ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3404,plain,
! [SV93: $i,SV138: $i,SV415: $i] :
( ( ( relation @ SV415 )
= $false )
| ( ( function @ SV415 )
= $false )
| ( ( ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) )
| ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) ) )
= $true )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3405,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3406,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3308]) ).
thf(3407,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
| ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3309]) ).
thf(3408,plain,
! [SV327: $i,SV96: $i,SV464: $i,SV305: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV305 )
| ~ ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV96 )
| ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV327 ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3409,plain,
! [SV96: $i,SV305: $i,SV327: $i] :
( ( ( ~ ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3311]) ).
thf(3410,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( ~ ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) )
= $false )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3311]) ).
thf(3411,plain,
! [SV97: $i,SV328: $i,SV306: $i,SV425: $i] :
( ( ( in @ SV425 @ SV306 )
= $false )
| ( ( in @ ( ordered_pair @ SV425 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
= $false )
| ( ( ~ ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 ) )
= $true )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3412,plain,
! [SV329: $i,SV307: $i,SV97: $i,SV426: $i,SV458: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV458 @ SV426 ) @ SV97 ) )
= $true )
| ( ( ~ ( in @ SV458 @ SV307 ) )
= $true )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3315]) ).
thf(3413,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 )
| ~ ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 ) )
= $false )
| ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3414,plain,
! [SV330: $i,SV308: $i,SV439: $i] :
( ( ( in @ SV439 @ SV308 )
= $false )
| ( ( ( apply @ SV330 @ SV439 )
= SV439 )
= $true )
| ( ( SV330
= ( identity_relation @ SV308 ) )
= $false )
| ( ( function @ SV330 )
= $false )
| ( ( relation @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3415,plain,
! [SV153: $i] :
( ( ( in @ ( sK19_B @ SV153 ) @ ( relation_dom @ SV153 ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3319]) ).
thf(3416,plain,
! [SV153: $i] :
( ( ( in @ ( sK20_SY4413 @ SV153 ) @ ( relation_dom @ SV153 ) )
= $true )
| ( ( one_to_one @ SV153 )
= $true )
| ( ( function @ SV153 )
= $false )
| ( ( relation @ SV153 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3320]) ).
thf(3417,plain,
! [SV392: $i,SV385: $i,SV154: $i] :
( ( ( ( apply @ SV154 @ SV385 )
= ( apply @ SV154 @ SV392 ) )
= $false )
| ( ( in @ SV385 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( in @ SV392 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( SV385 = SV392 )
= $true )
| ( ( one_to_one @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3418,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3419,plain,
! [SV60: $i,SV416: $i] :
( ( ( relation @ SV416 )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( ( SV416
!= ( function_inverse @ SV60 ) )
| ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3420,plain,
! [SV60: $i,SV417: $i] :
( ( ( relation @ SV417 )
= $false )
| ( ( function @ SV417 )
= $false )
| ( ( ( SV417
!= ( function_inverse @ SV60 ) )
| ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3421,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
| ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3422,plain,
! [SV274: $i,SV62: $i,SV387: $i,SV362: $i] :
( ( ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 )
= $false )
| ( ( in @ SV362 @ SV274 )
= $false )
| ( ( in @ SV387 @ SV274 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 ) )
= $true )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3423,plain,
! [SV418: $i,SV63: $i,SV275: $i,SV310: $i] :
( ( ( in @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV310 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK52_D @ SV310 @ SV275 @ SV63 ) @ SV418 ) @ SV63 )
= $false )
| ( ( in @ SV418 @ SV275 )
= $false )
| ( ( SV310
= ( relation_inverse_image @ SV63 @ SV275 ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3424,plain,
! [SV311: $i,SV276: $i,SV63: $i,SV440: $i,SV419: $i] :
( ( ( in @ ( ordered_pair @ SV419 @ SV440 ) @ SV63 )
= $false )
| ( ( ~ ( in @ SV440 @ SV276 ) )
= $true )
| ( ( in @ SV419 @ SV311 )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3425,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( in @ SV420 @ SV311 )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3330]) ).
thf(3426,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( ~ ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 ) )
= $false )
| ( ( in @ SV420 @ SV311 )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3330]) ).
thf(3427,plain,
! [SV66: $i] :
( ( ( ! [SY4542: $i] :
( ~ ( well_orders @ SV66 @ SY4542 )
| ( is_reflexive_in @ SV66 @ SY4542 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3332]) ).
thf(3428,plain,
! [SV66: $i] :
( ( ( ! [SY4543: $i] :
( ~ ( well_orders @ SV66 @ SY4543 )
| ( is_transitive_in @ SV66 @ SY4543 ) ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3333]) ).
thf(3429,plain,
! [SV441: $i,SV66: $i] :
( ( ( well_orders @ SV66 @ SV441 )
= $false )
| ( ( is_antisymmetric_in @ SV66 @ SV441 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3430,plain,
! [SV442: $i] :
( ( ( relation @ SV442 )
= $false )
| ( ( ~ ( well_ordering @ SV442 )
| ( reflexive @ SV442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3431,plain,
! [SV443: $i] :
( ( ( relation @ SV443 )
= $false )
| ( ( ~ ( well_ordering @ SV443 )
| ( transitive @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3432,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3338]) ).
thf(3433,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3338]) ).
thf(3434,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV403 ) )
= $true )
| ( ( ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3435,plain,
! [SV175: $i,SV69: $i] :
( ( ( ! [SY4784: $i] :
( ~ ( function @ SY4784 )
| ~ ( relation @ SY4784 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4784 )
| ( ( relation_dom @ SY4784 )
= ( relation_field @ SV69 ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3340]) ).
thf(3436,plain,
! [SV175: $i,SV69: $i] :
( ( ( ! [SY4785: $i] :
( ~ ( function @ SY4785 )
| ~ ( relation @ SY4785 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SY4785 )
| ( ( relation_rng @ SY4785 )
= ( relation_field @ SV175 ) ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3437,plain,
! [SV175: $i,SV69: $i,SV444: $i] :
( ( ( ~ ( function @ SV444 ) )
= $true )
| ( ( ~ ( relation @ SV444 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
| ( one_to_one @ SV444 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3438,plain,
! [SV71: $i,SV284: $i,SV445: $i,SV428: $i] :
( ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV284 )
= $false )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV71 )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3439,plain,
! [SV284: $i,SV71: $i,SV429: $i,SV446: $i] :
( ( ( in @ ( ordered_pair @ SV446 @ SV429 ) @ SV71 )
= $false )
| ( ( in @ ( ordered_pair @ SV429 @ SV446 ) @ SV284 )
= $true )
| ( ( SV284
= ( relation_inverse @ SV71 ) )
= $false )
| ( ( relation @ SV284 )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3440,plain,
! [SV465: $i,SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SV465 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SV465 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3441,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3442,plain,
! [SV368: $i,SV182: $i,SV72: $i,SV466: $i] :
( ( ( ! [SY5026: $i] :
( ! [SY5027: $i] :
( ~ ( in @ ( ordered_pair @ SV466 @ SY5027 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY5027 @ SY5026 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SV466 @ SY5026 ) @ SV368 ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3443,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV467: $i] :
( ( ( ! [SY5028: $i] :
( ~ ( in @ ( ordered_pair @ SV467 @ SY5028 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SY5028 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SY5028 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SY5028 ) @ SV182 ) ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3444,plain,
! [SV74: $i,SV288: $i] :
( ( ( ( sK25_C @ SV288 @ SV74 )
= ( sK26_SY4416 @ SV288 @ SV74 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3445,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
| ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3446,plain,
! [SV189: $i] :
( ( ( ~ ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3447,plain,
! [SV189: $i] :
( ( ( ~ ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) ) )
= $false )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3448,plain,
! [SV136: $i,SV76: $i,SV372: $i] :
( ( ( in @ ( apply @ SV372 @ SV76 ) @ ( relation_dom @ SV136 ) )
= $false )
| ( ( in @ SV76 @ ( relation_dom @ SV372 ) )
= $false )
| ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV372 @ SV136 ) ) )
= $true )
| ( ( function @ SV372 )
= $false )
| ( ( relation @ SV372 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3449,plain,
! [SV136: $i,SV407: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ SV407 ) )
= $true )
| ( ( function @ SV407 )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3450,plain,
! [SV136: $i,SV408: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) )
= $true )
| ( ( function @ SV408 )
= $false )
| ( ( relation @ SV408 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3451,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
| ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3452,plain,
! [SV77: $i,SV394: $i,SV390: $i,SV291: $i,SV373: $i] :
( ( ( in @ SV373 @ SV291 )
= $false )
| ( ( ~ ( in @ SV390 @ SV291 ) )
= $true )
| ( ( ~ ( in @ SV394 @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3453,plain,
! [SV374: $i,SV346: $i,SV78: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( relation_dom @ SV78 ) ) )
= $true )
| ( ( ~ ( in @ SV447 @ SV346 ) )
= $true )
| ( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3454,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3361]) ).
thf(3455,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
= ( apply @ SV78 @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) ) )
= $true )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3456,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SV468 @ SV347 )
| ( SV448
!= ( apply @ SV78 @ SV468 ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3457,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( in @ SV449 @ SV375 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SV449
!= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) ) ) )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3458,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ SV319 ) )
= $true )
| ( ( ( SV459 != SV293 ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3459,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV460 @ SV293 ) @ SV79 )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3368]) ).
thf(3460,plain,
! [SV295: $i,SV80: $i,SV450: $i,SV431: $i] :
( ( ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV80 )
= $false )
| ( ( in @ ( ordered_pair @ SV431 @ SV450 ) @ SV295 )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3461,plain,
! [SV80: $i,SV295: $i,SV451: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV295 )
= $false )
| ( ( in @ ( ordered_pair @ SV432 @ SV451 ) @ SV80 )
= $true )
| ( ( SV80 = SV295 )
= $false )
| ( ( relation @ SV295 )
= $false )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3462,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
= $false )
| ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 ) )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3463,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3464,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 )
= $true )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3465,plain,
! [SV323: $i,SV137: $i,SV452: $i,SV83: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV83 )
| ~ ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV137 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV323 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3466,plain,
! [SV137: $i,SV83: $i,SV323: $i] :
( ( ( ! [SY4930: $i,SY4931: $i] :
( ~ ( in @ ( ordered_pair @ SY4930 @ SY4931 ) @ SV323 )
| ( in @ SY4931 @ SV83 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3375]) ).
thf(3467,plain,
! [SV83: $i,SV137: $i,SV323: $i] :
( ( ( ! [SY4932: $i,SY4933: $i] :
( ~ ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV323 )
| ( in @ ( ordered_pair @ SY4932 @ SY4933 ) @ SV137 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3376]) ).
thf(3468,plain,
! [SV351: $i,SV86: $i,SV435: $i] :
( ( ( in @ SV435 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( ( sK31_C @ SV351 @ SV86 )
= ( apply @ SV86 @ SV435 ) )
= $false )
| ( ( ~ ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 ) )
= $true )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3469,plain,
! [SV352: $i,SV462: $i,SV86: $i,SV436: $i] :
( ( ( ( SV436
!= ( apply @ SV86 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ SV462 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( in @ SV436 @ SV352 )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3470,plain,
! [SV352: $i,SV86: $i,SV437: $i] :
( ( ( ( SV437
!= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) )
| ~ ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
= $false )
| ( ( in @ SV437 @ SV352 )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3471,plain,
! [SV354: $i,SV380: $i,SV88: $i] :
( ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
= $false )
| ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
= $false )
| ( ( ~ ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3472,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
= $true )
| ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3473,plain,
! [SV354: $i,SV380: $i,SV88: $i] :
( ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
= $true )
| ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 )
= $true )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3474,plain,
! [SV381: $i,SV355: $i,SV88: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV88 @ SV453 ) @ SV355 ) )
= $true )
| ( ( in @ SV453 @ SV381 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3475,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ! [SY4985: $i] :
( ~ ( in @ SY4985 @ SV381 )
| ( in @ SY4985 @ ( relation_dom @ SV88 ) ) ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3476,plain,
! [SV355: $i,SV88: $i,SV381: $i] :
( ( ( ! [SY4986: $i] :
( ~ ( in @ SY4986 @ SV381 )
| ( in @ ( apply @ SV88 @ SY4986 ) @ SV355 ) ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3389]) ).
thf(3477,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3390]) ).
thf(3478,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3391]) ).
thf(3479,plain,
( ( function @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3392]) ).
thf(3480,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3393]) ).
thf(3481,plain,
! [SV207: $i,SV89: $i] :
( ( ( ! [SY4811: $i] :
( ~ ( function @ SY4811 )
| ~ ( relation @ SY4811 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4811 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3394]) ).
thf(3482,plain,
! [SV207: $i,SV89: $i] :
( ( ( ! [SY4812: $i] :
( ~ ( function @ SY4812 )
| ~ ( relation @ SY4812 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SY4812 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3395]) ).
thf(3483,plain,
! [SV207: $i,SV89: $i,SV454: $i] :
( ( ( ~ ( function @ SV454 ) )
= $true )
| ( ( ~ ( relation @ SV454 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3484,plain,
! [SV409: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV409 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3485,plain,
! [SV382: $i,SV207: $i,SV89: $i] :
( ( ( well_founded_relation @ SV89 )
= $false )
| ( ( well_founded_relation @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV382 )
= $false )
| ( ( function @ SV382 )
= $false )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3486,plain,
! [SV242: $i,SV424: $i,SV211: $i,SV410: $i] :
( ( ( in @ SV410 @ SV211 )
= $false )
| ( ( SV410 = SV424 )
= $false )
| ( ( in @ ( ordered_pair @ SV410 @ SV424 ) @ SV242 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3487,plain,
! [SV211: $i,SV242: $i,SV463: $i,SV455: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV242 ) )
= $true )
| ( ( SV455 = SV463 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3488,plain,
! [SV211: $i,SV242: $i,SV469: $i,SV456: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV456 @ SV469 ) @ SV242 ) )
= $true )
| ( ( in @ SV456 @ SV211 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3489,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( ~ ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3490,plain,
! [SV93: $i,SV384: $i,SV138: $i] :
( ( ( ~ ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3491,plain,
! [SV93: $i,SV414: $i,SV138: $i] :
( ( ( ( SV138
!= ( relation_dom_restriction @ SV414 @ SV93 ) ) )
= $true )
| ( ( ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3492,plain,
! [SV93: $i,SV415: $i,SV138: $i] :
( ( ( ( SV138
!= ( relation_dom_restriction @ SV415 @ SV93 ) ) )
= $true )
| ( ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) )
= $true )
| ( ( function @ SV415 )
= $false )
| ( ( relation @ SV415 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3404]) ).
thf(3493,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
= $false )
| ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 ) )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3494,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3495,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 )
= $true )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3407]) ).
thf(3496,plain,
! [SV327: $i,SV96: $i,SV464: $i,SV305: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV305 )
| ~ ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV327 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3497,plain,
! [SV96: $i,SV305: $i,SV327: $i] :
( ( ( ! [SY4938: $i] :
( ! [SY4939: $i] :
~ ( in @ ( ordered_pair @ SY4938 @ SY4939 ) @ SV327 )
| ( in @ SY4938 @ SV305 ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3409]) ).
thf(3498,plain,
! [SV305: $i,SV96: $i,SV327: $i] :
( ( ( ! [SY4940: $i,SY4941: $i] :
( ~ ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV327 )
| ( in @ ( ordered_pair @ SY4940 @ SY4941 ) @ SV96 ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3410]) ).
thf(3499,plain,
! [SV425: $i,SV97: $i,SV306: $i,SV328: $i] :
( ( ( in @ ( sK55_D @ SV328 @ SV306 @ SV97 ) @ SV328 )
= $false )
| ( ( in @ ( ordered_pair @ SV425 @ ( sK55_D @ SV328 @ SV306 @ SV97 ) ) @ SV97 )
= $false )
| ( ( in @ SV425 @ SV306 )
= $false )
| ( ( SV328
= ( relation_image @ SV97 @ SV306 ) )
= $true )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3500,plain,
! [SV329: $i,SV307: $i,SV97: $i,SV426: $i,SV458: $i] :
( ( ( in @ ( ordered_pair @ SV458 @ SV426 ) @ SV97 )
= $false )
| ( ( ~ ( in @ SV458 @ SV307 ) )
= $true )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3501,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 ) )
= $false )
| ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3413]) ).
thf(3502,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 ) )
= $false )
| ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3413]) ).
thf(3503,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3504,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3505,plain,
! [SV60: $i,SV416: $i] :
( ( ( ( SV416
!= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3419]) ).
thf(3506,plain,
! [SV60: $i,SV417: $i] :
( ( ( ( SV417
!= ( function_inverse @ SV60 ) ) )
= $true )
| ( ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(3507,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3421]) ).
thf(3508,plain,
! [SV62: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 ) )
= $false )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3421]) ).
thf(3509,plain,
! [SV274: $i,SV62: $i,SV362: $i,SV387: $i] :
( ( ( in @ ( ordered_pair @ SV387 @ SV362 ) @ SV62 )
= $false )
| ( ( in @ SV387 @ SV274 )
= $false )
| ( ( in @ SV362 @ SV274 )
= $false )
| ( ( in @ ( ordered_pair @ SV362 @ SV387 ) @ SV62 )
= $false )
| ( ( SV362 = SV387 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV274 )
= $false )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3510,plain,
! [SV311: $i,SV63: $i,SV419: $i,SV276: $i,SV440: $i] :
( ( ( in @ SV440 @ SV276 )
= $false )
| ( ( in @ ( ordered_pair @ SV419 @ SV440 ) @ SV63 )
= $false )
| ( ( in @ SV419 @ SV311 )
= $true )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3511,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( in @ ( ordered_pair @ SV420 @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) ) @ SV63 )
= $true )
| ( ( in @ SV420 @ SV311 )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3425]) ).
thf(3512,plain,
! [SV63: $i,SV276: $i,SV311: $i,SV420: $i] :
( ( ( in @ ( sK51_E @ SV420 @ SV311 @ SV276 @ SV63 ) @ SV276 )
= $true )
| ( ( in @ SV420 @ SV311 )
= $false )
| ( ( SV311
= ( relation_inverse_image @ SV63 @ SV276 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3426]) ).
thf(3513,plain,
! [SV470: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV470 )
| ( is_reflexive_in @ SV66 @ SV470 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3514,plain,
! [SV471: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV471 )
| ( is_transitive_in @ SV66 @ SV471 ) )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3515,plain,
! [SV442: $i] :
( ( ( ~ ( well_ordering @ SV442 ) )
= $true )
| ( ( reflexive @ SV442 )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3430]) ).
thf(3516,plain,
! [SV443: $i] :
( ( ( ~ ( well_ordering @ SV443 ) )
= $true )
| ( ( transitive @ SV443 )
= $true )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(3517,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3432]) ).
thf(3518,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3433]) ).
thf(3519,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( ~ ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) ) )
= $true )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3520,plain,
! [SV175: $i,SV69: $i,SV472: $i] :
( ( ( ~ ( function @ SV472 )
| ~ ( relation @ SV472 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
| ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3521,plain,
! [SV175: $i,SV69: $i,SV473: $i] :
( ( ( ~ ( function @ SV473 )
| ~ ( relation @ SV473 )
| ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
| ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(3522,plain,
! [SV175: $i,SV69: $i,SV444: $i] :
( ( ( function @ SV444 )
= $false )
| ( ( ~ ( relation @ SV444 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
| ( one_to_one @ SV444 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3523,plain,
! [SV465: $i,SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SV465 ) @ SV72 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV465 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(3524,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3525,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3526,plain,
! [SV368: $i,SV182: $i,SV474: $i,SV72: $i,SV466: $i] :
( ( ( ! [SY5029: $i] :
( ~ ( in @ ( ordered_pair @ SV466 @ SY5029 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY5029 @ SV474 ) @ SV182 ) )
| ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(3527,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
| ~ ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(3528,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3445]) ).
thf(3529,plain,
! [SV74: $i,SV288: $i] :
( ( ( ~ ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 ) )
= $false )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3445]) ).
thf(3530,plain,
! [SV189: $i] :
( ( ( in @ ( sK75_B @ SV189 ) @ ( relation_field @ SV189 ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3446]) ).
thf(3531,plain,
! [SV189: $i] :
( ( ( in @ ( sK76_SY4442 @ SV189 ) @ ( relation_field @ SV189 ) )
= $true )
| ( ( connected @ SV189 )
= $true )
| ( ( relation @ SV189 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3447]) ).
thf(3532,plain,
! [SV136: $i,SV407: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV407 @ SV136 ) ) )
= $false )
| ( ( in @ SV76 @ ( relation_dom @ SV407 ) )
= $true )
| ( ( function @ SV407 )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(3533,plain,
! [SV136: $i,SV408: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_dom @ ( relation_composition @ SV408 @ SV136 ) ) )
= $false )
| ( ( in @ ( apply @ SV408 @ SV76 ) @ ( relation_dom @ SV136 ) )
= $true )
| ( ( function @ SV408 )
= $false )
| ( ( relation @ SV408 )
= $false )
| ( ( function @ SV136 )
= $false )
| ( ( relation @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(3534,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3451]) ).
thf(3535,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3451]) ).
thf(3536,plain,
! [SV77: $i,SV394: $i,SV373: $i,SV291: $i,SV390: $i] :
( ( ( in @ SV390 @ SV291 )
= $false )
| ( ( in @ SV373 @ SV291 )
= $false )
| ( ( ~ ( in @ SV394 @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3537,plain,
! [SV374: $i,SV346: $i,SV78: $i,SV447: $i] :
( ( ( in @ SV447 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( ~ ( in @ SV447 @ SV346 ) )
= $true )
| ( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3538,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3539,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ ( relation_dom @ SV78 ) )
| ~ ( in @ SV468 @ SV347 ) )
= $true )
| ( ( ( SV448
!= ( apply @ SV78 @ SV468 ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3540,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
| ( SV449
!= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3541,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV459: $i] :
( ( ( in @ SV459 @ SV319 )
= $false )
| ( ( ( SV459 != SV293 ) )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3542,plain,
! [SV79: $i,SV293: $i,SV319: $i,SV460: $i] :
( ( ( in @ SV460 @ SV319 )
= $false )
| ( ( in @ ( ordered_pair @ SV460 @ SV293 ) @ SV79 )
= $true )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3543,plain,
! [SV83: $i,SV137: $i,SV322: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV322 )
= $false )
| ( ( in @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) @ SV83 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK58_D @ SV322 @ SV137 @ SV83 ) @ ( sK59_SY4435 @ SV322 @ SV137 @ SV83 ) ) @ SV137 )
= $false )
| ( ( SV322
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $true )
| ( ( relation @ SV322 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3544,plain,
! [SV323: $i,SV137: $i,SV452: $i,SV83: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV83 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV137 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV323 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3465]) ).
thf(3545,plain,
! [SV137: $i,SV83: $i,SV323: $i,SV476: $i] :
( ( ( ! [SY5030: $i] :
( ~ ( in @ ( ordered_pair @ SV476 @ SY5030 ) @ SV323 )
| ( in @ SY5030 @ SV83 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(3546,plain,
! [SV83: $i,SV137: $i,SV323: $i,SV477: $i] :
( ( ( ! [SY5031: $i] :
( ~ ( in @ ( ordered_pair @ SV477 @ SY5031 ) @ SV323 )
| ( in @ ( ordered_pair @ SV477 @ SY5031 ) @ SV137 ) ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3547,plain,
! [SV435: $i,SV86: $i,SV351: $i] :
( ( ( in @ ( sK31_C @ SV351 @ SV86 ) @ SV351 )
= $false )
| ( ( ( sK31_C @ SV351 @ SV86 )
= ( apply @ SV86 @ SV435 ) )
= $false )
| ( ( in @ SV435 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( SV351
= ( relation_rng @ SV86 ) )
= $true )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3548,plain,
! [SV352: $i,SV462: $i,SV86: $i,SV436: $i] :
( ( ( SV436
= ( apply @ SV86 @ SV462 ) )
= $false )
| ( ( ~ ( in @ SV462 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( in @ SV436 @ SV352 )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3549,plain,
! [SV352: $i,SV86: $i,SV437: $i] :
( ( ( ( SV437
!= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) ) )
= $false )
| ( ( in @ SV437 @ SV352 )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3470]) ).
thf(3550,plain,
! [SV86: $i,SV352: $i,SV437: $i] :
( ( ( ~ ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) ) )
= $false )
| ( ( in @ SV437 @ SV352 )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3470]) ).
thf(3551,plain,
! [SV88: $i,SV354: $i,SV380: $i] :
( ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ SV380 )
= $false )
| ( ( in @ ( sK57_D @ SV380 @ SV354 @ SV88 ) @ ( relation_dom @ SV88 ) )
= $false )
| ( ( in @ ( apply @ SV88 @ ( sK57_D @ SV380 @ SV354 @ SV88 ) ) @ SV354 )
= $false )
| ( ( SV380
= ( relation_inverse_image @ SV88 @ SV354 ) )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3552,plain,
! [SV381: $i,SV355: $i,SV88: $i,SV453: $i] :
( ( ( in @ SV453 @ ( relation_dom @ SV88 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV88 @ SV453 ) @ SV355 ) )
= $true )
| ( ( in @ SV453 @ SV381 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3553,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV381 )
| ( in @ SV478 @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3554,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV381 )
| ( in @ ( apply @ SV88 @ SV479 ) @ SV355 ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(3555,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3556,plain,
! [SV207: $i,SV89: $i,SV480: $i] :
( ( ( ~ ( function @ SV480 )
| ~ ( relation @ SV480 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3557,plain,
! [SV207: $i,SV89: $i,SV481: $i] :
( ( ( ~ ( function @ SV481 )
| ~ ( relation @ SV481 )
| ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(3558,plain,
! [SV207: $i,SV89: $i,SV454: $i] :
( ( ( function @ SV454 )
= $false )
| ( ( ~ ( relation @ SV454 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3559,plain,
! [SV409: $i,SV207: $i,SV89: $i] :
( ( ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
= $false )
| ( ( ~ ( antisymmetric @ SV89 )
| ( antisymmetric @ SV207 ) )
= $true )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3560,plain,
! [SV211: $i,SV242: $i,SV463: $i,SV455: $i] :
( ( ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV242 )
= $false )
| ( ( SV455 = SV463 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3561,plain,
! [SV211: $i,SV242: $i,SV469: $i,SV456: $i] :
( ( ( in @ ( ordered_pair @ SV456 @ SV469 ) @ SV242 )
= $false )
| ( ( in @ SV456 @ SV211 )
= $true )
| ( ( SV242
= ( identity_relation @ SV211 ) )
= $false )
| ( ( relation @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3562,plain,
! [SV93: $i,SV138: $i,SV384: $i] :
( ( ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
= $true )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3489]) ).
thf(3563,plain,
! [SV93: $i,SV384: $i,SV138: $i] :
( ( ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
!= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3490]) ).
thf(3564,plain,
! [SV93: $i,SV414: $i,SV138: $i] :
( ( ( SV138
= ( relation_dom_restriction @ SV414 @ SV93 ) )
= $false )
| ( ( ! [SY5005: $i] :
( ~ ( in @ SY5005 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SY5005 )
= ( apply @ SV414 @ SY5005 ) ) ) )
= $true )
| ( ( function @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3565,plain,
! [SV93: $i,SV415: $i,SV138: $i] :
( ( ( SV138
= ( relation_dom_restriction @ SV415 @ SV93 ) )
= $false )
| ( ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV415 ) @ SV93 ) )
= $true )
| ( ( function @ SV415 )
= $false )
| ( ( relation @ SV415 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3566,plain,
! [SV96: $i,SV304: $i,SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV326 )
= $false )
| ( ( in @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ SV304 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK63_D @ SV326 @ SV304 @ SV96 ) @ ( sK64_SY4438 @ SV326 @ SV304 @ SV96 ) ) @ SV96 )
= $false )
| ( ( SV326
= ( relation_dom_restriction @ SV96 @ SV304 ) )
= $true )
| ( ( relation @ SV326 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3567,plain,
! [SV327: $i,SV96: $i,SV464: $i,SV305: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ SV305 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV327 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(3568,plain,
! [SV96: $i,SV305: $i,SV327: $i,SV482: $i] :
( ( ( ! [SY5032: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SY5032 ) @ SV327 )
| ( in @ SV482 @ SV305 ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(3569,plain,
! [SV305: $i,SV96: $i,SV327: $i,SV483: $i] :
( ( ( ! [SY5033: $i] :
( ~ ( in @ ( ordered_pair @ SV483 @ SY5033 ) @ SV327 )
| ( in @ ( ordered_pair @ SV483 @ SY5033 ) @ SV96 ) ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(3570,plain,
! [SV329: $i,SV97: $i,SV426: $i,SV307: $i,SV458: $i] :
( ( ( in @ SV458 @ SV307 )
= $false )
| ( ( in @ ( ordered_pair @ SV458 @ SV426 ) @ SV97 )
= $false )
| ( ( in @ SV426 @ SV329 )
= $true )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3571,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( in @ ( ordered_pair @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV427 ) @ SV97 )
= $true )
| ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3501]) ).
thf(3572,plain,
! [SV97: $i,SV307: $i,SV329: $i,SV427: $i] :
( ( ( in @ ( sK54_E @ SV427 @ SV329 @ SV307 @ SV97 ) @ SV307 )
= $true )
| ( ( in @ SV427 @ SV329 )
= $false )
| ( ( SV329
= ( relation_image @ SV97 @ SV307 ) )
= $false )
| ( ( relation @ SV97 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3502]) ).
thf(3573,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3574,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3504]) ).
thf(3575,plain,
! [SV60: $i,SV416: $i] :
( ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) ) )
= $true )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3576,plain,
! [SV60: $i,SV417: $i] :
( ( ( SV417
= ( function_inverse @ SV60 ) )
= $false )
| ( ( ( relation_dom @ SV417 )
= ( relation_rng @ SV60 ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3577,plain,
! [SV62: $i,SV273: $i] :
( ( ( in @ ( sK33_C @ SV273 @ SV62 ) @ SV273 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3507]) ).
thf(3578,plain,
! [SV62: $i,SV273: $i] :
( ( ( in @ ( sK34_SY4421 @ SV273 @ SV62 ) @ SV273 )
= $true )
| ( ( is_antisymmetric_in @ SV62 @ SV273 )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3508]) ).
thf(3579,plain,
! [SV470: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV470 ) )
= $true )
| ( ( is_reflexive_in @ SV66 @ SV470 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3580,plain,
! [SV471: $i,SV66: $i] :
( ( ( ~ ( well_orders @ SV66 @ SV471 ) )
= $true )
| ( ( is_transitive_in @ SV66 @ SV471 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(3581,plain,
! [SV442: $i] :
( ( ( well_ordering @ SV442 )
= $false )
| ( ( reflexive @ SV442 )
= $true )
| ( ( relation @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3515]) ).
thf(3582,plain,
! [SV443: $i] :
( ( ( well_ordering @ SV443 )
= $false )
| ( ( transitive @ SV443 )
= $true )
| ( ( relation @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3583,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3584,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3585,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3586,plain,
! [SV175: $i,SV69: $i,SV472: $i] :
( ( ( ~ ( function @ SV472 )
| ~ ( relation @ SV472 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
| ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3587,plain,
! [SV175: $i,SV69: $i,SV473: $i] :
( ( ( ~ ( function @ SV473 )
| ~ ( relation @ SV473 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
| ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3588,plain,
! [SV175: $i,SV69: $i,SV444: $i] :
( ( ( relation @ SV444 )
= $false )
| ( ( function @ SV444 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
| ( one_to_one @ SV444 ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3589,plain,
! [SV465: $i,SV72: $i,SV182: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SV465 ) @ SV72 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV465 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3590,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) ) @ SV72 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3524]) ).
thf(3591,plain,
! [SV72: $i,SV182: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY4412 @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3592,plain,
! [SV368: $i,SV182: $i,SV474: $i,SV72: $i,SV466: $i] :
( ( ( ! [SY5029: $i] :
( ~ ( in @ ( ordered_pair @ SV466 @ SY5029 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SY5029 @ SV474 ) @ SV182 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3593,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3594,plain,
! [SV74: $i,SV288: $i] :
( ( ( in @ ( sK25_C @ SV288 @ SV74 ) @ SV288 )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3595,plain,
! [SV74: $i,SV288: $i] :
( ( ( in @ ( sK26_SY4416 @ SV288 @ SV74 ) @ SV288 )
= $true )
| ( ( is_connected_in @ SV74 @ SV288 )
= $true )
| ( ( relation @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3529]) ).
thf(3596,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) ) )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3534]) ).
thf(3597,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( sK14_SY4407 @ SV290 @ SV77 ) @ SV290 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3598,plain,
! [SV77: $i,SV390: $i,SV373: $i,SV291: $i,SV394: $i] :
( ( ( in @ SV394 @ SV291 )
= $false )
| ( ( in @ SV373 @ SV291 )
= $false )
| ( ( in @ SV390 @ SV291 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3599,plain,
! [SV374: $i,SV78: $i,SV346: $i,SV447: $i] :
( ( ( in @ SV447 @ SV346 )
= $false )
| ( ( in @ SV447 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
!= ( apply @ SV78 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3600,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3538]) ).
thf(3601,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( ~ ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 ) )
= $false )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3538]) ).
thf(3602,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ ( relation_dom @ SV78 ) ) )
= $true )
| ( ( ~ ( in @ SV468 @ SV347 ) )
= $true )
| ( ( ( SV448
!= ( apply @ SV78 @ SV468 ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3603,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3604,plain,
! [SV347: $i,SV375: $i,SV78: $i,SV449: $i] :
( ( ( ( SV449
!= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3540]) ).
thf(3605,plain,
! [SV79: $i,SV319: $i,SV293: $i,SV459: $i] :
( ( ( SV459 = SV293 )
= $false )
| ( ( in @ SV459 @ SV319 )
= $false )
| ( ( SV319
= ( fiber @ SV79 @ SV293 ) )
= $false )
| ( ( relation @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3606,plain,
! [SV323: $i,SV137: $i,SV452: $i,SV83: $i,SV461: $i] :
( ( ( in @ SV461 @ SV83 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV137 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV323 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(3607,plain,
! [SV137: $i,SV83: $i,SV323: $i,SV484: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV484 ) @ SV323 )
| ( in @ SV484 @ SV83 ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(3608,plain,
! [SV83: $i,SV137: $i,SV323: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV323 )
| ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV137 ) )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(3609,plain,
! [SV352: $i,SV436: $i,SV86: $i,SV462: $i] :
( ( ( in @ SV462 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( SV436
= ( apply @ SV86 @ SV462 ) )
= $false )
| ( ( in @ SV436 @ SV352 )
= $true )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3610,plain,
! [SV352: $i,SV86: $i,SV437: $i] :
( ( ( SV437
= ( apply @ SV86 @ ( sK30_D @ SV437 @ SV352 @ SV86 ) ) )
= $true )
| ( ( in @ SV437 @ SV352 )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3611,plain,
! [SV86: $i,SV352: $i,SV437: $i] :
( ( ( in @ ( sK30_D @ SV437 @ SV352 @ SV86 ) @ ( relation_dom @ SV86 ) )
= $true )
| ( ( in @ SV437 @ SV352 )
= $false )
| ( ( SV352
= ( relation_rng @ SV86 ) )
= $false )
| ( ( function @ SV86 )
= $false )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3550]) ).
thf(3612,plain,
! [SV381: $i,SV355: $i,SV453: $i,SV88: $i] :
( ( ( in @ ( apply @ SV88 @ SV453 ) @ SV355 )
= $false )
| ( ( in @ SV453 @ ( relation_dom @ SV88 ) )
= $false )
| ( ( in @ SV453 @ SV381 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3613,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV381 ) )
= $true )
| ( ( in @ SV478 @ ( relation_dom @ SV88 ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3614,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV381 ) )
= $true )
| ( ( in @ ( apply @ SV88 @ SV479 ) @ SV355 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3615,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3555]) ).
thf(3616,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3555]) ).
thf(3617,plain,
! [SV207: $i,SV89: $i,SV480: $i] :
( ( ( ~ ( function @ SV480 )
| ~ ( relation @ SV480 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3618,plain,
! [SV207: $i,SV89: $i,SV481: $i] :
( ( ( ~ ( function @ SV481 )
| ~ ( relation @ SV481 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3557]) ).
thf(3619,plain,
! [SV207: $i,SV89: $i,SV454: $i] :
( ( ( relation @ SV454 )
= $false )
| ( ( function @ SV454 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
| ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3620,plain,
! [SV409: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( antisymmetric @ SV89 ) )
= $true )
| ( ( antisymmetric @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3621,plain,
! [SV93: $i,SV384: $i,SV138: $i] :
( ( ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
= $false )
| ( ( in @ ( sK67_D @ SV384 @ SV138 @ SV93 ) @ ( relation_dom @ SV138 ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3622,plain,
! [SV93: $i,SV384: $i,SV138: $i] :
( ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV138 )
!= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3623,plain,
! [SV93: $i,SV414: $i,SV138: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( relation_dom @ SV138 ) )
| ( ( apply @ SV138 @ SV486 )
= ( apply @ SV414 @ SV486 ) ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV414 @ SV93 ) )
= $false )
| ( ( function @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(3624,plain,
! [SV327: $i,SV96: $i,SV464: $i,SV305: $i,SV457: $i] :
( ( ( in @ SV457 @ SV305 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV96 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV327 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3625,plain,
! [SV96: $i,SV305: $i,SV327: $i,SV482: $i] :
( ( ( ! [SY5032: $i] :
~ ( in @ ( ordered_pair @ SV482 @ SY5032 ) @ SV327 ) )
= $true )
| ( ( in @ SV482 @ SV305 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(3626,plain,
! [SV305: $i,SV96: $i,SV327: $i,SV487: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV327 )
| ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV96 ) )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3627,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3628,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3629,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
| ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3630,plain,
! [SV470: $i,SV66: $i] :
( ( ( well_orders @ SV66 @ SV470 )
= $false )
| ( ( is_reflexive_in @ SV66 @ SV470 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3631,plain,
! [SV471: $i,SV66: $i] :
( ( ( well_orders @ SV66 @ SV471 )
= $false )
| ( ( is_transitive_in @ SV66 @ SV471 )
= $true )
| ( ( relation @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3580]) ).
thf(3632,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3633,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3634,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3635,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3636,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3585]) ).
thf(3637,plain,
! [SV175: $i,SV69: $i,SV472: $i] :
( ( ( ~ ( function @ SV472 ) )
= $true )
| ( ( ~ ( relation @ SV472 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
| ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(3638,plain,
! [SV175: $i,SV69: $i,SV473: $i] :
( ( ( ~ ( function @ SV473 ) )
= $true )
| ( ( ~ ( relation @ SV473 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
| ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3639,plain,
! [SV444: $i,SV175: $i,SV69: $i] :
( ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV444 ) )
= $true )
| ( ( one_to_one @ SV444 )
= $true )
| ( ( function @ SV444 )
= $false )
| ( ( relation @ SV444 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3640,plain,
! [SV72: $i,SV182: $i,SV367: $i,SV465: $i] :
( ( ( in @ ( ordered_pair @ SV465 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SV465 ) @ SV72 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 ) )
= $true )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3641,plain,
! [SV368: $i,SV182: $i,SV474: $i,SV72: $i,SV488: $i,SV466: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV466 @ SV488 ) @ SV72 )
| ~ ( in @ ( ordered_pair @ SV488 @ SV474 ) @ SV182 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(3642,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 ) ) )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3643,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
| ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3596]) ).
thf(3644,plain,
! [SV394: $i,SV291: $i,SV77: $i,SV390: $i,SV373: $i] :
( ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 )
= $false )
| ( ( in @ SV390 @ SV291 )
= $false )
| ( ( in @ SV373 @ SV291 )
= $false )
| ( ( in @ SV394 @ SV291 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3598]) ).
thf(3645,plain,
! [SV447: $i,SV78: $i,SV346: $i,SV374: $i] :
( ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
= ( apply @ SV78 @ SV447 ) )
= $false )
| ( ( in @ SV447 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( in @ SV447 @ SV346 )
= $false )
| ( ( ~ ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 ) )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3646,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ ( relation_dom @ SV78 ) )
= $true )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3600]) ).
thf(3647,plain,
! [SV78: $i,SV346: $i,SV374: $i] :
( ( ( in @ ( sK62_SY4437 @ SV374 @ SV346 @ SV78 ) @ SV346 )
= $true )
| ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $true )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3601]) ).
thf(3648,plain,
! [SV375: $i,SV448: $i,SV347: $i,SV78: $i,SV468: $i] :
( ( ( in @ SV468 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( ~ ( in @ SV468 @ SV347 ) )
= $true )
| ( ( ( SV448
!= ( apply @ SV78 @ SV468 ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3602]) ).
thf(3649,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) ) )
= $true )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3603]) ).
thf(3650,plain,
! [SV347: $i,SV375: $i,SV78: $i,SV449: $i] :
( ( ( SV449
= ( apply @ SV78 @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) ) )
= $true )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(3651,plain,
! [SV323: $i,SV83: $i,SV137: $i,SV461: $i,SV452: $i] :
( ( ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV137 )
= $false )
| ( ( in @ SV461 @ SV83 )
= $false )
| ( ( in @ ( ordered_pair @ SV452 @ SV461 ) @ SV323 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3652,plain,
! [SV137: $i,SV83: $i,SV323: $i,SV484: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ SV484 ) @ SV323 ) )
= $true )
| ( ( in @ SV484 @ SV83 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3653,plain,
! [SV83: $i,SV137: $i,SV323: $i,SV485: $i,SV477: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV323 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV137 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3608]) ).
thf(3654,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV478: $i] :
( ( ( in @ SV478 @ SV381 )
= $false )
| ( ( in @ SV478 @ ( relation_dom @ SV88 ) )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3655,plain,
! [SV355: $i,SV88: $i,SV381: $i,SV479: $i] :
( ( ( in @ SV479 @ SV381 )
= $false )
| ( ( in @ ( apply @ SV88 @ SV479 ) @ SV355 )
= $true )
| ( ( SV381
= ( relation_inverse_image @ SV88 @ SV355 ) )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3656,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3615]) ).
thf(3657,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3616]) ).
thf(3658,plain,
! [SV207: $i,SV89: $i,SV480: $i] :
( ( ( ~ ( function @ SV480 ) )
= $true )
| ( ( ~ ( relation @ SV480 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(3659,plain,
! [SV207: $i,SV89: $i,SV481: $i] :
( ( ( ~ ( function @ SV481 ) )
= $true )
| ( ( ~ ( relation @ SV481 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3618]) ).
thf(3660,plain,
! [SV454: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV454 ) )
= $true )
| ( ( ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( function @ SV454 )
= $false )
| ( ( relation @ SV454 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(3661,plain,
! [SV409: $i,SV207: $i,SV89: $i] :
( ( ( antisymmetric @ SV89 )
= $false )
| ( ( antisymmetric @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV409 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3620]) ).
thf(3662,plain,
! [SV93: $i,SV384: $i,SV138: $i] :
( ( ( ( relation_dom @ SV138 )
= ( set_intersection2 @ ( relation_dom @ SV384 ) @ SV93 ) )
= $false )
| ( ( ( apply @ SV138 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) )
= ( apply @ SV384 @ ( sK67_D @ SV384 @ SV138 @ SV93 ) ) )
= $false )
| ( ( SV138
= ( relation_dom_restriction @ SV384 @ SV93 ) )
= $true )
| ( ( function @ SV384 )
= $false )
| ( ( relation @ SV384 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3622]) ).
thf(3663,plain,
! [SV93: $i,SV414: $i,SV138: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( relation_dom @ SV138 ) ) )
= $true )
| ( ( ( apply @ SV138 @ SV486 )
= ( apply @ SV414 @ SV486 ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV414 @ SV93 ) )
= $false )
| ( ( function @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(3664,plain,
! [SV327: $i,SV305: $i,SV96: $i,SV464: $i,SV457: $i] :
( ( ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV96 )
= $false )
| ( ( in @ SV457 @ SV305 )
= $false )
| ( ( in @ ( ordered_pair @ SV457 @ SV464 ) @ SV327 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3665,plain,
! [SV96: $i,SV305: $i,SV327: $i,SV489: $i,SV482: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV482 @ SV489 ) @ SV327 ) )
= $true )
| ( ( in @ SV482 @ SV305 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(3666,plain,
! [SV305: $i,SV96: $i,SV327: $i,SV487: $i,SV483: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV327 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV96 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3667,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3668,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3669,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3670,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3628]) ).
thf(3671,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3629]) ).
thf(3672,plain,
! [SV416: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3629]) ).
thf(3673,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3674,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3675,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3634]) ).
thf(3676,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ! [SY4994: $i,SY4995: $i] :
( ~ ( in @ SY4994 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY4995 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SY4994 ) @ ( apply @ SV403 @ SY4995 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SY4994 @ SY4995 ) @ SV69 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3635]) ).
thf(3677,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(3678,plain,
! [SV175: $i,SV69: $i,SV472: $i] :
( ( ( function @ SV472 )
= $false )
| ( ( ~ ( relation @ SV472 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
| ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3679,plain,
! [SV175: $i,SV69: $i,SV473: $i] :
( ( ( function @ SV473 )
= $false )
| ( ( ~ ( relation @ SV473 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
| ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3638]) ).
thf(3680,plain,
! [SV444: $i,SV175: $i,SV69: $i] :
( ( ( relation_isomorphism @ SV69 @ SV175 @ SV444 )
= $false )
| ( ( one_to_one @ SV444 )
= $true )
| ( ( function @ SV444 )
= $false )
| ( ( relation @ SV444 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3681,plain,
! [SV465: $i,SV72: $i,SV182: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV367 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV367 @ SV182 @ SV72 ) @ SV465 ) @ SV72 )
= $false )
| ( ( in @ ( ordered_pair @ SV465 @ ( sK17_SY4408 @ SV367 @ SV182 @ SV72 ) ) @ SV182 )
= $false )
| ( ( SV367
= ( relation_composition @ SV72 @ SV182 ) )
= $true )
| ( ( relation @ SV367 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3640]) ).
thf(3682,plain,
! [SV368: $i,SV182: $i,SV474: $i,SV72: $i,SV488: $i,SV466: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV466 @ SV488 ) @ SV72 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV488 @ SV474 ) @ SV182 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3641]) ).
thf(3683,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
| ~ ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3684,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3685,plain,
! [SV77: $i,SV290: $i] :
( ( ( ~ ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 ) )
= $false )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3686,plain,
! [SV373: $i,SV291: $i,SV77: $i,SV394: $i,SV390: $i] :
( ( ( in @ ( ordered_pair @ SV390 @ SV394 ) @ SV77 )
= $false )
| ( ( in @ SV394 @ SV291 )
= $false )
| ( ( in @ SV373 @ SV291 )
= $false )
| ( ( in @ SV390 @ SV291 )
= $false )
| ( ( in @ ( ordered_pair @ SV373 @ SV390 ) @ SV77 )
= $false )
| ( ( in @ ( ordered_pair @ SV373 @ SV394 ) @ SV77 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV291 )
= $false )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3644]) ).
thf(3687,plain,
! [SV447: $i,SV78: $i,SV346: $i,SV374: $i] :
( ( ( in @ ( sK61_D @ SV374 @ SV346 @ SV78 ) @ SV374 )
= $false )
| ( ( in @ SV447 @ SV346 )
= $false )
| ( ( in @ SV447 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( ( sK61_D @ SV374 @ SV346 @ SV78 )
= ( apply @ SV78 @ SV447 ) )
= $false )
| ( ( SV374
= ( relation_image @ SV78 @ SV346 ) )
= $true )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3688,plain,
! [SV375: $i,SV448: $i,SV78: $i,SV347: $i,SV468: $i] :
( ( ( in @ SV468 @ SV347 )
= $false )
| ( ( in @ SV468 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( ( SV448
!= ( apply @ SV78 @ SV468 ) ) )
= $true )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3689,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
| ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(3690,plain,
! [SV137: $i,SV83: $i,SV323: $i,SV484: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ SV484 ) @ SV323 )
= $false )
| ( ( in @ SV484 @ SV83 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3691,plain,
! [SV83: $i,SV137: $i,SV323: $i,SV485: $i,SV477: $i] :
( ( ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV323 )
= $false )
| ( ( in @ ( ordered_pair @ SV477 @ SV485 ) @ SV137 )
= $true )
| ( ( SV323
= ( relation_rng_restriction @ SV83 @ SV137 ) )
= $false )
| ( ( relation @ SV323 )
= $false )
| ( ( relation @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(3692,plain,
! [SV207: $i,SV89: $i,SV480: $i] :
( ( ( function @ SV480 )
= $false )
| ( ( ~ ( relation @ SV480 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3693,plain,
! [SV207: $i,SV89: $i,SV481: $i] :
( ( ( function @ SV481 )
= $false )
| ( ( ~ ( relation @ SV481 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3694,plain,
! [SV454: $i,SV207: $i,SV89: $i] :
( ( ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
= $false )
| ( ( ~ ( connected @ SV89 )
| ( connected @ SV207 ) )
= $true )
| ( ( function @ SV454 )
= $false )
| ( ( relation @ SV454 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3695,plain,
! [SV93: $i,SV414: $i,SV138: $i,SV486: $i] :
( ( ( in @ SV486 @ ( relation_dom @ SV138 ) )
= $false )
| ( ( ( apply @ SV138 @ SV486 )
= ( apply @ SV414 @ SV486 ) )
= $true )
| ( ( SV138
= ( relation_dom_restriction @ SV414 @ SV93 ) )
= $false )
| ( ( function @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( function @ SV138 )
= $false )
| ( ( relation @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3696,plain,
! [SV96: $i,SV305: $i,SV327: $i,SV489: $i,SV482: $i] :
( ( ( in @ ( ordered_pair @ SV482 @ SV489 ) @ SV327 )
= $false )
| ( ( in @ SV482 @ SV305 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3697,plain,
! [SV305: $i,SV96: $i,SV327: $i,SV487: $i,SV483: $i] :
( ( ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV327 )
= $false )
| ( ( in @ ( ordered_pair @ SV483 @ SV487 ) @ SV96 )
= $true )
| ( ( SV327
= ( relation_dom_restriction @ SV96 @ SV305 ) )
= $false )
| ( ( relation @ SV327 )
= $false )
| ( ( relation @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3666]) ).
thf(3698,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3667]) ).
thf(3699,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3668]) ).
thf(3700,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(3701,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(3702,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3671]) ).
thf(3703,plain,
! [SV416: $i,SV60: $i] :
( ( ( ~ ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3672]) ).
thf(3704,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3705,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
| ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(3706,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(3707,plain,
! [SV175: $i,SV403: $i,SV69: $i,SV490: $i] :
( ( ( ! [SY5034: $i] :
( ~ ( in @ SV490 @ ( relation_field @ SV69 ) )
| ~ ( in @ SY5034 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SY5034 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SV490 @ SY5034 ) @ SV69 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(3708,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
| ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(3709,plain,
! [SV175: $i,SV69: $i,SV472: $i] :
( ( ( relation @ SV472 )
= $false )
| ( ( function @ SV472 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
| ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3710,plain,
! [SV175: $i,SV69: $i,SV473: $i] :
( ( ( relation @ SV473 )
= $false )
| ( ( function @ SV473 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
| ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) ) )
= $true )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3711,plain,
! [SV368: $i,SV182: $i,SV474: $i,SV72: $i,SV488: $i,SV466: $i] :
( ( ( in @ ( ordered_pair @ SV466 @ SV488 ) @ SV72 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV488 @ SV474 ) @ SV182 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(3712,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3713,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV467: $i,SV475: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3683]) ).
thf(3714,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( sK12_C @ SV290 @ SV77 ) @ SV290 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3684]) ).
thf(3715,plain,
! [SV77: $i,SV290: $i] :
( ( ( in @ ( sK13_SY4405 @ SV290 @ SV77 ) @ SV290 )
= $true )
| ( ( is_transitive_in @ SV77 @ SV290 )
= $true )
| ( ( relation @ SV77 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3685]) ).
thf(3716,plain,
! [SV375: $i,SV347: $i,SV468: $i,SV78: $i,SV448: $i] :
( ( ( SV448
= ( apply @ SV78 @ SV468 ) )
= $false )
| ( ( in @ SV468 @ ( relation_dom @ SV78 ) )
= $false )
| ( ( in @ SV468 @ SV347 )
= $false )
| ( ( in @ SV448 @ SV375 )
= $true )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(3717,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3689]) ).
thf(3718,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 ) )
= $false )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3689]) ).
thf(3719,plain,
! [SV207: $i,SV89: $i,SV480: $i] :
( ( ( relation @ SV480 )
= $false )
| ( ( function @ SV480 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
| ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3692]) ).
thf(3720,plain,
! [SV207: $i,SV89: $i,SV481: $i] :
( ( ( relation @ SV481 )
= $false )
| ( ( function @ SV481 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
| ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(3721,plain,
! [SV454: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( connected @ SV89 ) )
= $true )
| ( ( connected @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
= $false )
| ( ( function @ SV454 )
= $false )
| ( ( relation @ SV454 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(3722,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3723,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(3724,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3725,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3726,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) )
| ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3727,plain,
! [SV416: $i,SV60: $i] :
( ( ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) )
| ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3728,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3729,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3730,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ~ ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3705]) ).
thf(3731,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3706]) ).
thf(3732,plain,
! [SV175: $i,SV403: $i,SV491: $i,SV69: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_field @ SV69 ) )
| ~ ( in @ SV491 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 )
| ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(3733,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3708]) ).
thf(3734,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ~ ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3708]) ).
thf(3735,plain,
! [SV472: $i,SV175: $i,SV69: $i] :
( ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV472 ) )
= $true )
| ( ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) )
= $true )
| ( ( function @ SV472 )
= $false )
| ( ( relation @ SV472 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3736,plain,
! [SV473: $i,SV175: $i,SV69: $i] :
( ( ( ~ ( relation_isomorphism @ SV69 @ SV175 @ SV473 ) )
= $true )
| ( ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) )
= $true )
| ( ( function @ SV473 )
= $false )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(3737,plain,
! [SV368: $i,SV72: $i,SV466: $i,SV182: $i,SV474: $i,SV488: $i] :
( ( ( in @ ( ordered_pair @ SV488 @ SV474 ) @ SV182 )
= $false )
| ( ( in @ ( ordered_pair @ SV466 @ SV488 ) @ SV72 )
= $false )
| ( ( in @ ( ordered_pair @ SV466 @ SV474 ) @ SV368 )
= $true )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3738,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV475: $i,SV467: $i] :
( ( ( in @ ( ordered_pair @ SV467 @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) ) @ SV72 )
= $true )
| ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3712]) ).
thf(3739,plain,
! [SV72: $i,SV182: $i,SV368: $i,SV467: $i,SV475: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_F @ SV475 @ SV467 @ SV368 @ SV182 @ SV72 ) @ SV475 ) @ SV182 )
= $true )
| ( ( in @ ( ordered_pair @ SV467 @ SV475 ) @ SV368 )
= $false )
| ( ( SV368
= ( relation_composition @ SV72 @ SV182 ) )
= $false )
| ( ( relation @ SV368 )
= $false )
| ( ( relation @ SV182 )
= $false )
| ( ( relation @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3740,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ ( relation_dom @ SV78 ) )
= $true )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3717]) ).
thf(3741,plain,
! [SV78: $i,SV347: $i,SV375: $i,SV449: $i] :
( ( ( in @ ( sK60_E @ SV449 @ SV375 @ SV347 @ SV78 ) @ SV347 )
= $true )
| ( ( in @ SV449 @ SV375 )
= $false )
| ( ( SV375
= ( relation_image @ SV78 @ SV347 ) )
= $false )
| ( ( function @ SV78 )
= $false )
| ( ( relation @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3742,plain,
! [SV480: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV480 ) )
= $true )
| ( ( ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( function @ SV480 )
= $false )
| ( ( relation @ SV480 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3719]) ).
thf(3743,plain,
! [SV481: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( relation_isomorphism @ SV89 @ SV207 @ SV481 ) )
= $true )
| ( ( ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( function @ SV481 )
= $false )
| ( ( relation @ SV481 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(3744,plain,
! [SV454: $i,SV207: $i,SV89: $i] :
( ( ( connected @ SV89 )
= $false )
| ( ( connected @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV454 )
= $false )
| ( ( function @ SV454 )
= $false )
| ( ( relation @ SV454 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3745,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3746,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3722]) ).
thf(3747,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3723]) ).
thf(3748,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3723]) ).
thf(3749,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3750,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3724]) ).
thf(3751,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(3752,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3753,plain,
! [SV60: $i,SV416: $i] :
( ( ( ~ ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3726]) ).
thf(3754,plain,
! [SV416: $i,SV60: $i] :
( ( ( ~ ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3755,plain,
! [SV416: $i,SV60: $i] :
( ( ( ~ ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) )
= $false )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3756,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(3757,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3758,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
| ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 ) )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3730]) ).
thf(3759,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(3760,plain,
! [SV175: $i,SV403: $i,SV491: $i,SV69: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_field @ SV69 ) )
| ~ ( in @ SV491 @ ( relation_field @ SV69 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(3761,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3733]) ).
thf(3762,plain,
! [SV175: $i,SV403: $i,SV69: $i] :
( ( ( ! [SY5000: $i,SY5001: $i] :
( ~ ( in @ ( ordered_pair @ SY5000 @ SY5001 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SY5000 ) @ ( apply @ SV403 @ SY5001 ) ) @ SV175 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3734]) ).
thf(3763,plain,
! [SV472: $i,SV175: $i,SV69: $i] :
( ( ( relation_isomorphism @ SV69 @ SV175 @ SV472 )
= $false )
| ( ( ( relation_dom @ SV472 )
= ( relation_field @ SV69 ) )
= $true )
| ( ( function @ SV472 )
= $false )
| ( ( relation @ SV472 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3764,plain,
! [SV473: $i,SV175: $i,SV69: $i] :
( ( ( relation_isomorphism @ SV69 @ SV175 @ SV473 )
= $false )
| ( ( ( relation_rng @ SV473 )
= ( relation_field @ SV175 ) )
= $true )
| ( ( function @ SV473 )
= $false )
| ( ( relation @ SV473 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3765,plain,
! [SV480: $i,SV207: $i,SV89: $i] :
( ( ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
= $false )
| ( ( ~ ( reflexive @ SV89 )
| ( reflexive @ SV207 ) )
= $true )
| ( ( function @ SV480 )
= $false )
| ( ( relation @ SV480 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3766,plain,
! [SV481: $i,SV207: $i,SV89: $i] :
( ( ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
= $false )
| ( ( ~ ( transitive @ SV89 )
| ( transitive @ SV207 ) )
= $true )
| ( ( function @ SV481 )
= $false )
| ( ( relation @ SV481 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3767,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3745]) ).
thf(3768,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3746]) ).
thf(3769,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(3770,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3748]) ).
thf(3771,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3772,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3773,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3774,plain,
! [SV60: $i,SV416: $i] :
( ( ( ! [SY5006: $i,SY5007: $i] :
( ( SY5007
!= ( apply @ SV416 @ SY5006 ) )
| ~ ( in @ SY5006 @ ( relation_rng @ SV60 ) )
| ( SY5006
= ( apply @ SV60 @ SY5007 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3752]) ).
thf(3775,plain,
! [SV60: $i,SV416: $i] :
( ( ( ! [SY5008: $i,SY5009: $i] :
( ( SY5009
!= ( apply @ SV416 @ SY5008 ) )
| ~ ( in @ SY5008 @ ( relation_rng @ SV60 ) )
| ( in @ SY5009 @ ( relation_dom @ SV60 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3753]) ).
thf(3776,plain,
! [SV416: $i,SV60: $i] :
( ( ( ! [SY5010: $i,SY5011: $i] :
( ( SY5010
!= ( apply @ SV60 @ SY5011 ) )
| ~ ( in @ SY5011 @ ( relation_dom @ SV60 ) )
| ( SY5011
= ( apply @ SV416 @ SY5010 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3754]) ).
thf(3777,plain,
! [SV416: $i,SV60: $i] :
( ( ( ! [SY4509: $i] :
( ! [SY4510: $i] :
( ( SY4509
!= ( apply @ SV60 @ SY4510 ) )
| ~ ( in @ SY4510 @ ( relation_dom @ SV60 ) ) )
| ( in @ SY4509 @ ( relation_rng @ SV60 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(3778,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3779,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3780,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) )
| ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3781,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3782,plain,
! [SV175: $i,SV403: $i,SV491: $i,SV69: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_field @ SV69 ) )
| ~ ( in @ SV491 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3760]) ).
thf(3783,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) )
| ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3784,plain,
! [SV175: $i,SV403: $i,SV69: $i,SV492: $i] :
( ( ( ! [SY5035: $i] :
( ~ ( in @ ( ordered_pair @ SV492 @ SY5035 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SV492 ) @ ( apply @ SV403 @ SY5035 ) ) @ SV175 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3785,plain,
! [SV480: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( reflexive @ SV89 ) )
= $true )
| ( ( reflexive @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
= $false )
| ( ( function @ SV480 )
= $false )
| ( ( relation @ SV480 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3786,plain,
! [SV481: $i,SV207: $i,SV89: $i] :
( ( ( ~ ( transitive @ SV89 ) )
= $true )
| ( ( transitive @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
= $false )
| ( ( function @ SV481 )
= $false )
| ( ( relation @ SV481 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3787,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(3788,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(3789,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
| ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3790,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3770]) ).
thf(3791,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(3792,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(3793,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3794,plain,
! [SV60: $i,SV493: $i,SV416: $i] :
( ( ( ! [SY5036: $i] :
( ( SY5036
!= ( apply @ SV416 @ SV493 ) )
| ~ ( in @ SV493 @ ( relation_rng @ SV60 ) )
| ( SV493
= ( apply @ SV60 @ SY5036 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(3795,plain,
! [SV60: $i,SV494: $i,SV416: $i] :
( ( ( ! [SY5037: $i] :
( ( SY5037
!= ( apply @ SV416 @ SV494 ) )
| ~ ( in @ SV494 @ ( relation_rng @ SV60 ) )
| ( in @ SY5037 @ ( relation_dom @ SV60 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(3796,plain,
! [SV416: $i,SV60: $i,SV495: $i] :
( ( ( ! [SY5038: $i] :
( ( SV495
!= ( apply @ SV60 @ SY5038 ) )
| ~ ( in @ SY5038 @ ( relation_dom @ SV60 ) )
| ( SY5038
= ( apply @ SV416 @ SV495 ) ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(3797,plain,
! [SV416: $i,SV60: $i,SV496: $i] :
( ( ( ! [SY5039: $i] :
( ( SV496
!= ( apply @ SV60 @ SY5039 ) )
| ~ ( in @ SY5039 @ ( relation_dom @ SV60 ) ) )
| ( in @ SV496 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(3798,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(3799,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(3800,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) )
| ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(3801,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3781]) ).
thf(3802,plain,
! [SV175: $i,SV403: $i,SV491: $i,SV69: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ SV491 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3782]) ).
thf(3803,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3783]) ).
thf(3804,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ~ ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3783]) ).
thf(3805,plain,
! [SV175: $i,SV403: $i,SV69: $i,SV497: $i,SV492: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV492 @ SV497 ) @ SV69 )
| ( in @ ( ordered_pair @ ( apply @ SV403 @ SV492 ) @ ( apply @ SV403 @ SV497 ) ) @ SV175 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(3806,plain,
! [SV480: $i,SV207: $i,SV89: $i] :
( ( ( reflexive @ SV89 )
= $false )
| ( ( reflexive @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV480 )
= $false )
| ( ( function @ SV480 )
= $false )
| ( ( relation @ SV480 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(3807,plain,
! [SV481: $i,SV207: $i,SV89: $i] :
( ( ( transitive @ SV89 )
= $false )
| ( ( transitive @ SV207 )
= $true )
| ( ( relation_isomorphism @ SV89 @ SV207 @ SV481 )
= $false )
| ( ( function @ SV481 )
= $false )
| ( ( relation @ SV481 )
= $false )
| ( ( relation @ SV207 )
= $false )
| ( ( relation @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3808,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3787]) ).
thf(3809,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3787]) ).
thf(3810,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(3811,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3812,plain,
! [SV60: $i,SV386: $i] :
( ( ( ~ ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3813,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3790]) ).
thf(3814,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3815,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK70_C @ SV386 @ SV60 )
!= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3816,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
!= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(3817,plain,
! [SV60: $i,SV493: $i,SV416: $i,SV498: $i] :
( ( ( ( SV498
!= ( apply @ SV416 @ SV493 ) )
| ~ ( in @ SV493 @ ( relation_rng @ SV60 ) )
| ( SV493
= ( apply @ SV60 @ SV498 ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(3818,plain,
! [SV60: $i,SV494: $i,SV416: $i,SV499: $i] :
( ( ( ( SV499
!= ( apply @ SV416 @ SV494 ) )
| ~ ( in @ SV494 @ ( relation_rng @ SV60 ) )
| ( in @ SV499 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(3819,plain,
! [SV416: $i,SV500: $i,SV60: $i,SV495: $i] :
( ( ( ( SV495
!= ( apply @ SV60 @ SV500 ) )
| ~ ( in @ SV500 @ ( relation_dom @ SV60 ) )
| ( SV500
= ( apply @ SV416 @ SV495 ) ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(3820,plain,
! [SV416: $i,SV60: $i,SV496: $i] :
( ( ( ! [SY5039: $i] :
( ( SV496
!= ( apply @ SV60 @ SY5039 ) )
| ~ ( in @ SY5039 @ ( relation_dom @ SV60 ) ) ) )
= $true )
| ( ( in @ SV496 @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(3821,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(3822,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3799]) ).
thf(3823,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( ( relation_dom @ SV366 )
!= ( relation_field @ SV69 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(3824,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( one_to_one @ SV366 )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3825,plain,
! [SV175: $i,SV403: $i,SV491: $i,SV69: $i,SV490: $i] :
( ( ( in @ SV490 @ ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( in @ SV491 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3826,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ! [SY4563: $i] :
( ! [SY4564: $i] :
~ ( in @ ( ordered_pair @ SY4563 @ SY4564 ) @ SV69 )
| ( in @ SY4563 @ ( relation_field @ SV69 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3803]) ).
thf(3827,plain,
! [SV403: $i,SV175: $i,SV69: $i] :
( ( ( ! [SY4565: $i,SY4566: $i] :
( ~ ( in @ ( ordered_pair @ SY4565 @ SY4566 ) @ SV69 )
| ( in @ SY4566 @ ( relation_field @ SV69 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3804]) ).
thf(3828,plain,
! [SV175: $i,SV403: $i,SV69: $i,SV497: $i,SV492: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV492 @ SV497 ) @ SV69 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV403 @ SV492 ) @ ( apply @ SV403 @ SV497 ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3805]) ).
thf(3829,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3808]) ).
thf(3830,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(3831,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3832,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3811]) ).
thf(3833,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
| ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3812]) ).
thf(3834,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(3835,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(3836,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(3837,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( ~ ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(3838,plain,
! [SV60: $i,SV493: $i,SV416: $i,SV498: $i] :
( ( ( ( SV498
!= ( apply @ SV416 @ SV493 ) )
| ~ ( in @ SV493 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV493
= ( apply @ SV60 @ SV498 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(3839,plain,
! [SV60: $i,SV494: $i,SV416: $i,SV499: $i] :
( ( ( ( SV499
!= ( apply @ SV416 @ SV494 ) )
| ~ ( in @ SV494 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( in @ SV499 @ ( relation_dom @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(3840,plain,
! [SV416: $i,SV500: $i,SV60: $i,SV495: $i] :
( ( ( ( SV495
!= ( apply @ SV60 @ SV500 ) )
| ~ ( in @ SV500 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( SV500
= ( apply @ SV416 @ SV495 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(3841,plain,
! [SV416: $i,SV501: $i,SV60: $i,SV496: $i] :
( ( ( ( SV496
!= ( apply @ SV60 @ SV501 ) )
| ~ ( in @ SV501 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ SV496 @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(3842,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3843,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3844,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( ( relation_rng @ SV366 )
!= ( relation_field @ SV175 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(3845,plain,
! [SV175: $i,SV403: $i,SV490: $i,SV69: $i,SV491: $i] :
( ( ( in @ SV491 @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ SV490 @ ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3846,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV502: $i] :
( ( ( ! [SY5040: $i] :
~ ( in @ ( ordered_pair @ SV502 @ SY5040 ) @ SV69 )
| ( in @ SV502 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(3847,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV503: $i] :
( ( ( ! [SY5041: $i] :
( ~ ( in @ ( ordered_pair @ SV503 @ SY5041 ) @ SV69 )
| ( in @ SY5041 @ ( relation_field @ SV69 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(3848,plain,
! [SV175: $i,SV403: $i,SV69: $i,SV497: $i,SV492: $i] :
( ( ( in @ ( ordered_pair @ SV492 @ SV497 ) @ SV69 )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV403 @ SV492 ) @ ( apply @ SV403 @ SV497 ) ) @ SV175 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(3849,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3829]) ).
thf(3850,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(3851,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3852,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(3853,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(3854,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(3855,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3835]) ).
thf(3856,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(3857,plain,
! [SV60: $i,SV386: $i] :
( ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( ( relation_dom @ SV386 )
!= ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3858,plain,
! [SV60: $i,SV493: $i,SV416: $i,SV498: $i] :
( ( ( ( SV498
!= ( apply @ SV416 @ SV493 ) ) )
= $true )
| ( ( ~ ( in @ SV493 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV493
= ( apply @ SV60 @ SV498 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3838]) ).
thf(3859,plain,
! [SV60: $i,SV494: $i,SV416: $i,SV499: $i] :
( ( ( ( SV499
!= ( apply @ SV416 @ SV494 ) ) )
= $true )
| ( ( ~ ( in @ SV494 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( in @ SV499 @ ( relation_dom @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(3860,plain,
! [SV416: $i,SV500: $i,SV60: $i,SV495: $i] :
( ( ( ( SV495
!= ( apply @ SV60 @ SV500 ) ) )
= $true )
| ( ( ~ ( in @ SV500 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( SV500
= ( apply @ SV416 @ SV495 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(3861,plain,
! [SV416: $i,SV501: $i,SV60: $i,SV496: $i] :
( ( ( ( SV496
!= ( apply @ SV60 @ SV501 ) ) )
= $true )
| ( ( ~ ( in @ SV501 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ SV496 @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(3862,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(3863,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(3864,plain,
! [SV69: $i,SV175: $i,SV366: $i] :
( ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ~ ( one_to_one @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3865,plain,
! [SV69: $i,SV175: $i,SV491: $i,SV490: $i,SV403: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV403 @ SV490 ) @ ( apply @ SV403 @ SV491 ) ) @ SV175 )
= $false )
| ( ( in @ SV490 @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ SV491 @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV490 @ SV491 ) @ SV69 )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3866,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV502: $i] :
( ( ( ! [SY5040: $i] :
~ ( in @ ( ordered_pair @ SV502 @ SY5040 ) @ SV69 ) )
= $true )
| ( ( in @ SV502 @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(3867,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV504: $i,SV503: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV503 @ SV504 ) @ SV69 )
| ( in @ SV504 @ ( relation_field @ SV69 ) ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(3868,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3869,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(3870,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3851]) ).
thf(3871,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3872,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(3873,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $true )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3874,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3855]) ).
thf(3875,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $true )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3876,plain,
! [SV60: $i,SV386: $i] :
( ( ( ( relation_dom @ SV386 )
= ( relation_rng @ SV60 ) )
= $false )
| ( ( in @ ( sK71_SY4441 @ SV386 @ SV60 ) @ ( relation_dom @ SV60 ) )
= $false )
| ( ( ( sK70_C @ SV386 @ SV60 )
= ( apply @ SV60 @ ( sK71_SY4441 @ SV386 @ SV60 ) ) )
= $false )
| ( ( ( sK71_SY4441 @ SV386 @ SV60 )
= ( apply @ SV386 @ ( sK70_C @ SV386 @ SV60 ) ) )
= $false )
| ( ( in @ ( sK70_C @ SV386 @ SV60 ) @ ( relation_rng @ SV60 ) )
= $false )
| ( ( SV386
= ( function_inverse @ SV60 ) )
= $true )
| ( ( function @ SV386 )
= $false )
| ( ( relation @ SV386 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3857]) ).
thf(3877,plain,
! [SV60: $i,SV493: $i,SV416: $i,SV498: $i] :
( ( ( SV498
= ( apply @ SV416 @ SV493 ) )
= $false )
| ( ( ~ ( in @ SV493 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( SV493
= ( apply @ SV60 @ SV498 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(3878,plain,
! [SV60: $i,SV494: $i,SV416: $i,SV499: $i] :
( ( ( SV499
= ( apply @ SV416 @ SV494 ) )
= $false )
| ( ( ~ ( in @ SV494 @ ( relation_rng @ SV60 ) ) )
= $true )
| ( ( in @ SV499 @ ( relation_dom @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(3879,plain,
! [SV416: $i,SV500: $i,SV60: $i,SV495: $i] :
( ( ( SV495
= ( apply @ SV60 @ SV500 ) )
= $false )
| ( ( ~ ( in @ SV500 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( SV500
= ( apply @ SV416 @ SV495 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(3880,plain,
! [SV416: $i,SV501: $i,SV60: $i,SV496: $i] :
( ( ( SV496
= ( apply @ SV60 @ SV501 ) )
= $false )
| ( ( ~ ( in @ SV501 @ ( relation_dom @ SV60 ) ) )
= $true )
| ( ( in @ SV496 @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3861]) ).
thf(3881,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( one_to_one @ SV366 )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV366 @ ( sK21_D @ SV366 @ SV175 @ SV69 ) ) @ ( apply @ SV366 @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) ) @ SV175 )
= $false )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $false )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(3882,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( one_to_one @ SV366 )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(3883,plain,
! [SV175: $i,SV69: $i,SV366: $i] :
( ( ( one_to_one @ SV366 )
= $false )
| ( ( ( relation_dom @ SV366 )
= ( relation_field @ SV69 ) )
= $false )
| ( ( ( relation_rng @ SV366 )
= ( relation_field @ SV175 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK21_D @ SV366 @ SV175 @ SV69 ) @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) ) @ SV69 )
= $true )
| ( ( in @ ( sK22_SY4414 @ SV366 @ SV175 @ SV69 ) @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV366 )
= $true )
| ( ( function @ SV366 )
= $false )
| ( ( relation @ SV366 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(3884,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV505: $i,SV502: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV502 @ SV505 ) @ SV69 ) )
= $true )
| ( ( in @ SV502 @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(3885,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV504: $i,SV503: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV503 @ SV504 ) @ SV69 ) )
= $true )
| ( ( in @ SV504 @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(3886,plain,
! [SV416: $i,SV498: $i,SV60: $i,SV493: $i] :
( ( ( in @ SV493 @ ( relation_rng @ SV60 ) )
= $false )
| ( ( SV498
= ( apply @ SV416 @ SV493 ) )
= $false )
| ( ( SV493
= ( apply @ SV60 @ SV498 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(3887,plain,
! [SV416: $i,SV499: $i,SV60: $i,SV494: $i] :
( ( ( in @ SV494 @ ( relation_rng @ SV60 ) )
= $false )
| ( ( SV499
= ( apply @ SV416 @ SV494 ) )
= $false )
| ( ( in @ SV499 @ ( relation_dom @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(3888,plain,
! [SV416: $i,SV495: $i,SV60: $i,SV500: $i] :
( ( ( in @ SV500 @ ( relation_dom @ SV60 ) )
= $false )
| ( ( SV495
= ( apply @ SV60 @ SV500 ) )
= $false )
| ( ( SV500
= ( apply @ SV416 @ SV495 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(3889,plain,
! [SV416: $i,SV496: $i,SV60: $i,SV501: $i] :
( ( ( in @ SV501 @ ( relation_dom @ SV60 ) )
= $false )
| ( ( SV496
= ( apply @ SV60 @ SV501 ) )
= $false )
| ( ( in @ SV496 @ ( relation_rng @ SV60 ) )
= $true )
| ( ( SV416
= ( function_inverse @ SV60 ) )
= $false )
| ( ( function @ SV416 )
= $false )
| ( ( relation @ SV416 )
= $false )
| ( ( one_to_one @ SV60 )
= $false )
| ( ( function @ SV60 )
= $false )
| ( ( relation @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(3890,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV505: $i,SV502: $i] :
( ( ( in @ ( ordered_pair @ SV502 @ SV505 ) @ SV69 )
= $false )
| ( ( in @ SV502 @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(3891,plain,
! [SV403: $i,SV175: $i,SV69: $i,SV504: $i,SV503: $i] :
( ( ( in @ ( ordered_pair @ SV503 @ SV504 ) @ SV69 )
= $false )
| ( ( in @ SV504 @ ( relation_field @ SV69 ) )
= $true )
| ( ( relation_isomorphism @ SV69 @ SV175 @ SV403 )
= $false )
| ( ( function @ SV403 )
= $false )
| ( ( relation @ SV403 )
= $false )
| ( ( relation @ SV175 )
= $false )
| ( ( relation @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(3892,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[754,3891,3890,3889,3888,3887,3886,3883,3882,3881,3876,3875,3874,3873,3872,3871,3870,3869,3868,3865,3848,3824,3807,3806,3764,3763,3744,3741,3740,3739,3738,3737,3716,3715,3714,3697,3696,3695,3691,3690,3687,3686,3681,3680,3664,3662,3661,3657,3656,3655,3654,3651,3650,3647,3646,3631,3630,3621,3612,3611,3610,3609,3605,3597,3595,3594,3591,3590,3582,3581,3578,3577,3576,3572,3571,3570,3566,3565,3561,3560,3551,3547,3543,3542,3533,3532,3531,3530,3512,3511,3510,3509,3499,3495,3494,3486,3485,3480,3479,3478,3473,3472,3464,3463,3461,3460,3455,3448,3444,3439,3438,3429,3423,3417,3416,3415,3414,3381,3380,3378,3377,3366,3365,3358,3352,3351,3337,3331,3326,3317,3314,3313,3303,3302,3301,3297,3280,3279,3276,3275,3267,3263,3261,3250,3244,3237,3232,3231,3227,3221,3220,3208,3193,3192,3190,3186,3185,3179,3177,3171,3160,3159,3154,3153,3130,3128,3126,3122,3121,3111,3110,3109,3104,3100,3088,3086,3039,3036,3027,3024,3012,3006,2994,2993,2990,2980,2979,2969,2963,2961,2960,2942,2941,2937,2917,2916,2906,2905,2870,2869,2865,2864,2859,2852,2851,2847,2841,2840,2830,2829,2828,2818,2813,2811,2810,2809,2799,2798,2795,2786,2777,2775,2750,2749,2738,2729,2723,2707,2691,2682,2676,2636,2635,2624,2615,2603,2588,2577,2554,2529,2528,2514,2509,2508,2486,2485,2464,2463,2451,2450,2449,2448,2416,2389,2380,2379,2372,2371,2359,2358,2351,2349,2299,2278,2277,2276,2275,2247,2246,2243,2242,2218,2217,2208,2207,2177,2176,2150,2140,2139,2138,2137,2126,2125,2120,2119,2099,2098,2091,2090,2082,2081,2080,2077,2076,2066,2065,1931,1928,1921,1900,1899,1889,1888,1880,1878,1873,1872,1865,1864,1861,1860,1840,1839,1796,1795,1791,1790,1762,1761,1760,1759,1751,1750,1748,1747,1746,1745,1744,1742,1738,1736,1735,1584,1583,1560,1553,1505,1504,1471,1420,1419,1417,1415,1414,1413,1412,1411,1407,1391,1390,1387,1383,1381,1379,1378,1377,1376,1375,1370,1369,1363,1348,1344,1343,1339,1338,1336,1334,1329,1321,1310,1309,1279,1254,1232,1223,1219,1218,1217,1193,1185,891]) ).
thf(3893,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3892]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU261+2 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jun 19 14:12:59 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.21/0.48 .........
% 0.50/0.67
% 0.50/0.67 No.of.Axioms: 320
% 0.50/0.67
% 0.50/0.67 Length.of.Defs: 0
% 0.50/0.67
% 0.50/0.67 Contains.Choice.Funs: false
% 0.57/0.76 ....................
% 0.69/0.87 (rf:2,axioms:233,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:322,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.29/75.48 .....................ignored arguments false
% 75.48/75.66 .........
% 75.61/75.82 (rf:0,axioms:320,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:322,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.49/150.70 .......................................
% 150.81/150.99 (rf:2,axioms:233,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:322,loop_count:0,foatp_calls:0,translation:fof_full)........................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 225.23/225.54 ..............................
% 225.42/225.77 (rf:-1,axioms:143,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:322,loop_count:0,foatp_calls:0,translation:fof_full)...........................................................................................................................................................................................................................................................................................
% 227.38/228.05
% 227.38/228.05 ********************************
% 227.38/228.05 * All subproblems solved! *
% 227.38/228.05 ********************************
% 227.38/228.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:144,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3892,loop_count:0,foatp_calls:1,translation:fof_full)
% 232.43/232.78
% 232.43/232.78 %**** Beginning of derivation protocol ****
% 232.43/232.78 % SZS output start CNFRefutation
% See solution above
% 232.53/232.80
% 232.53/232.80 %**** End of derivation protocol ****
% 232.53/232.80 %**** no. of clauses in derivation: 3716 ****
% 232.53/232.80 %**** clause counter: 3892 ****
% 232.53/232.80
% 232.53/232.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:144,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3892,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------