TSTP Solution File: SEU248+2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU248+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 : n008.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 12:09:03 EDT 2022
% Result : Theorem 73.52s 73.69s
% Output : CNFRefutation 81.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 437
% Syntax : Number of formulae : 5323 (2214 unt; 172 typ; 0 def)
% Number of atoms : 47950 (16628 equ; 0 cnn)
% Maximal formula atoms : 15 ( 9 avg)
% Number of connectives : 106499 (18465 ~;18325 |;1065 &;67959 @)
% ( 196 <=>; 489 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 313 ( 313 >; 0 *; 0 +; 0 <<)
% Number of symbols : 175 ( 172 usr; 17 con; 0-5 aty)
% Number of variables : 15349 ( 0 ^15287 !; 62 ?;15349 :)
% 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_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_sK100_C,type,
sK100_C: $i > $i > $i ).
thf(tp_sK101_SY666,type,
sK101_SY666: $i > $i > $i ).
thf(tp_sK102_C,type,
sK102_C: $i > $i > $i ).
thf(tp_sK103_SY667,type,
sK103_SY667: $i > $i > $i ).
thf(tp_sK104_B,type,
sK104_B: $i > $i ).
thf(tp_sK105_C,type,
sK105_C: $i > $i > $i ).
thf(tp_sK106_C,type,
sK106_C: $i > $i > $i ).
thf(tp_sK107_SY668,type,
sK107_SY668: $i > $i > $i ).
thf(tp_sK108_B,type,
sK108_B: $i > $i ).
thf(tp_sK109_D,type,
sK109_D: $i > $i > $i > $i ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK110_SY671,type,
sK110_SY671: $i > $i > $i > $i ).
thf(tp_sK111_B,type,
sK111_B: $i > $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY611,type,
sK14_SY611: $i > $i > $i ).
thf(tp_sK15_SY613,type,
sK15_SY613: $i > $i > $i ).
thf(tp_sK16_F,type,
sK16_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK17_D,type,
sK17_D: $i > $i > $i > $i ).
thf(tp_sK18_SY614,type,
sK18_SY614: $i > $i > $i > $i ).
thf(tp_sK19_SY618,type,
sK19_SY618: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_SY619,type,
sK21_SY619: $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_SY620,type,
sK23_SY620: $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY621,type,
sK25_SY621: $i > $i > $i ).
thf(tp_sK26_D,type,
sK26_D: $i > $i > $i > $i ).
thf(tp_sK27_C,type,
sK27_C: $i > $i > $i ).
thf(tp_sK28_SY623,type,
sK28_SY623: $i > $i > $i ).
thf(tp_sK29_D,type,
sK29_D: $i > $i > $i > $i ).
thf(tp_sK2_SY609,type,
sK2_SY609: $i ).
thf(tp_sK30_C,type,
sK30_C: $i > $i > $i ).
thf(tp_sK31_SY625,type,
sK31_SY625: $i > $i > $i ).
thf(tp_sK32_D,type,
sK32_D: $i > $i > $i > $i ).
thf(tp_sK33_D,type,
sK33_D: $i > $i > $i > $i ).
thf(tp_sK34_C,type,
sK34_C: $i > $i > $i ).
thf(tp_sK35_SY627,type,
sK35_SY627: $i > $i > $i ).
thf(tp_sK36_C,type,
sK36_C: $i > $i > $i ).
thf(tp_sK37_SY628,type,
sK37_SY628: $i > $i > $i ).
thf(tp_sK38_D,type,
sK38_D: $i > $i > $i > $i ).
thf(tp_sK39_B,type,
sK39_B: $i > $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK40_SY629,type,
sK40_SY629: $i > $i ).
thf(tp_sK41_E,type,
sK41_E: $i > $i > $i > $i > $i ).
thf(tp_sK42_SY630,type,
sK42_SY630: $i > $i > $i > $i > $i ).
thf(tp_sK43_D,type,
sK43_D: $i > $i > $i > $i ).
thf(tp_sK44_SY633,type,
sK44_SY633: $i > $i > $i > $i ).
thf(tp_sK45_SY635,type,
sK45_SY635: $i > $i > $i > $i ).
thf(tp_sK46_D,type,
sK46_D: $i > $i > $i > $i ).
thf(tp_sK47_D,type,
sK47_D: $i > $i > $i > $i ).
thf(tp_sK48_B,type,
sK48_B: $i > $i ).
thf(tp_sK49_C,type,
sK49_C: $i > $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK50_D,type,
sK50_D: $i > $i > $i > $i ).
thf(tp_sK51_C,type,
sK51_C: $i > $i > $i ).
thf(tp_sK52_SY636,type,
sK52_SY636: $i > $i > $i ).
thf(tp_sK53_C,type,
sK53_C: $i > $i > $i ).
thf(tp_sK54_E,type,
sK54_E: $i > $i > $i > $i > $i ).
thf(tp_sK55_E,type,
sK55_E: $i > $i > $i > $i > $i ).
thf(tp_sK56_D,type,
sK56_D: $i > $i > $i > $i ).
thf(tp_sK57_SY639,type,
sK57_SY639: $i > $i > $i > $i ).
thf(tp_sK58_E,type,
sK58_E: $i > $i > $i > $i > $i ).
thf(tp_sK59_D,type,
sK59_D: $i > $i > $i > $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK60_SY641,type,
sK60_SY641: $i > $i > $i > $i ).
thf(tp_sK61_D,type,
sK61_D: $i > $i > $i > $i ).
thf(tp_sK62_E,type,
sK62_E: $i > $i > $i > $i > $i ).
thf(tp_sK63_D,type,
sK63_D: $i > $i > $i > $i ).
thf(tp_sK64_SY643,type,
sK64_SY643: $i > $i > $i > $i ).
thf(tp_sK65_D,type,
sK65_D: $i > $i > $i > $i ).
thf(tp_sK66_SY644,type,
sK66_SY644: $i > $i > $i > $i ).
thf(tp_sK67_C,type,
sK67_C: $i > $i > $i ).
thf(tp_sK68_SY645,type,
sK68_SY645: $i > $i > $i ).
thf(tp_sK69_D,type,
sK69_D: $i > $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK70_B,type,
sK70_B: $i > $i ).
thf(tp_sK71_SY646,type,
sK71_SY646: $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK73_SY647,type,
sK73_SY647: $i > $i > $i ).
thf(tp_sK74_C,type,
sK74_C: $i > $i > $i ).
thf(tp_sK75_C,type,
sK75_C: $i > $i > $i ).
thf(tp_sK76_C,type,
sK76_C: $i > $i > $i ).
thf(tp_sK77_C,type,
sK77_C: $i > $i > $i ).
thf(tp_sK78_D,type,
sK78_D: $i > $i > $i > $i ).
thf(tp_sK79_D,type,
sK79_D: $i > $i > $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK80_B,type,
sK80_B: $i > $i ).
thf(tp_sK81_C,type,
sK81_C: $i > $i > $i ).
thf(tp_sK82_B,type,
sK82_B: $i > $i ).
thf(tp_sK83_SY653,type,
sK83_SY653: $i > $i ).
thf(tp_sK84_B,type,
sK84_B: $i > $i ).
thf(tp_sK85_SY654,type,
sK85_SY654: $i > $i ).
thf(tp_sK86_SY656,type,
sK86_SY656: $i > $i ).
thf(tp_sK87_B,type,
sK87_B: $i > $i ).
thf(tp_sK88_SY659,type,
sK88_SY659: $i > $i > $i ).
thf(tp_sK89_A,type,
sK89_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK90_A,type,
sK90_A: $i ).
thf(tp_sK91_A,type,
sK91_A: $i ).
thf(tp_sK92_A,type,
sK92_A: $i ).
thf(tp_sK93_A,type,
sK93_A: $i ).
thf(tp_sK94_A,type,
sK94_A: $i ).
thf(tp_sK95_A,type,
sK95_A: $i ).
thf(tp_sK96_D,type,
sK96_D: $i > $i > $i > $i ).
thf(tp_sK97_C,type,
sK97_C: $i > $i > $i ).
thf(tp_sK98_SY665,type,
sK98_SY665: $i > $i > $i ).
thf(tp_sK99_C,type,
sK99_C: $i > $i > $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(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(23,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(24,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(26,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(27,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(28,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(29,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(30,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(32,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(33,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(34,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(35,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(36,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(39,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(44,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(46,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(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/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(50,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(51,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_ordinal1) ).
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/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(54,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(57,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(59,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(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/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(62,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(64,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(65,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(67,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_ordinal1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(70,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(71,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(73,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(81,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(86,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(95,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(97,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(109,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(116,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
thf(117,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
thf(118,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_connected_in @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
thf(119,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
thf(120,axiom,
! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(122,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(124,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(125,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(130,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_antisymmetric_in @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
thf(131,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(132,axiom,
! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(133,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(137,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_relat_1) ).
thf(138,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(143,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
thf(144,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
thf(145,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(146,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(147,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(148,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(150,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_reflexive_in @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
thf(151,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_1) ).
thf(152,axiom,
! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_enumset1) ).
thf(156,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
thf(157,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
thf(158,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(161,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(162,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(169,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(170,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(171,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(172,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(173,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(174,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(178,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_relat_1) ).
thf(181,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom @ ( relation_dom_restriction @ B @ A ) )
= ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_dom @ ( relation_dom_restriction @ C @ B ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_dom @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(190,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ A )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
thf(193,axiom,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( apply @ ( relation_dom_restriction @ C @ A ) @ B )
= ( apply @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(196,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(199,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(200,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(202,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(203,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(204,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(206,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ B )
& ( in @ A @ ( relation_rng @ B ) ) )
=> ( ( A
= ( apply @ B @ ( apply @ ( function_inverse @ B ) @ A ) ) )
& ( A
= ( apply @ ( relation_composition @ ( function_inverse @ B ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(207,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).
thf(208,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
thf(210,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( function_inverse @ A ) )
<=> ( ( ( relation_dom @ B )
= ( relation_rng @ A ) )
& ! [C: $i,D: $i] :
( ( ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( ( in @ C @ ( relation_rng @ A ) )
& ( D
= ( apply @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(211,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(216,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_rng @ B ) )
=> ( ( relation_rng @ ( relation_composition @ B @ A ) )
= ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(219,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ ( relation_rng @ A ) @ ( relation_dom @ B ) )
=> ( ( relation_dom @ ( relation_composition @ A @ B ) )
= ( relation_dom @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(221,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(222,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_relat_1) ).
thf(223,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
thf(226,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(227,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(233,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(235,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(236,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(237,axiom,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(241,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
<=> ( ordinal_subset @ ( succ @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_ordinal1) ).
thf(242,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(243,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
thf(245,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(248,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(249,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(250,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(251,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(253,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(254,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
thf(255,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
thf(257,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(260,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_wellord1) ).
thf(261,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(262,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_wellord1) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t178_relat_1) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ~ ( ( A != empty_set )
& ( subset @ A @ ( relation_rng @ B ) )
& ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
thf(268,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_composition @ A @ B ) )
= ( relation_image @ B @ ( relation_rng @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t160_relat_1) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
thf(270,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ ( relation_dom @ B ) )
=> ( subset @ A @ ( relation_inverse_image @ B @ ( relation_image @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_image @ B @ A )
= ( relation_image @ B @ ( set_intersection2 @ ( relation_dom @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_relat_1) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_relat_1) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t140_relat_1) ).
thf(277,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_rng @ ( relation_rng_restriction @ A @ B ) )
= ( set_intersection2 @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_relat_1) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_relat_1) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_relat_1) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(287,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(292,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(296,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
thf(297,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).
thf(298,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(299,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(300,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_wellord1) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(302,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(304,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(306,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l29_wellord1) ).
thf(307,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[306]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[307]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(310,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(311,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(313,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(314,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(316,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(319,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(321,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(324,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(325,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(326,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(327,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(328,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(329,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(330,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(331,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(332,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(333,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(335,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(339,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ ( union @ A ) )
& ( epsilon_connected @ ( union @ A ) )
& ( ordinal @ ( union @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
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] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(344,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(345,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(346,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(347,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(348,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(349,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(350,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(351,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(353,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(357,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(358,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(359,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(360,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(361,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(362,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(363,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)],[116]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(365,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)],[118]) ).
thf(366,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
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)],[124]) ).
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)],[125]) ).
thf(372,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(374,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)],[130]) ).
thf(375,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(376,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)],[133]) ).
thf(377,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(378,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(379,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(380,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(381,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(383,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(386,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)],[150]) ).
thf(387,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(388,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(389,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)],[156]) ).
thf(390,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)],[157]) ).
thf(391,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)],[158]) ).
thf(392,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)],[161]) ).
thf(393,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)],[162]) ).
thf(394,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)],[164]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(398,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(399,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(400,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(401,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(402,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(403,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(404,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(406,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(407,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(408,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(409,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(410,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)],[186]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(412,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)],[191]) ).
thf(413,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)],[192]) ).
thf(414,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)],[194]) ).
thf(415,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(416,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)],[197]) ).
thf(417,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(418,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( one_to_one @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(419,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)],[206]) ).
thf(420,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(421,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)],[208]) ).
thf(422,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(423,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)],[210]) ).
thf(424,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(425,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(426,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(429,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(430,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(432,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(435,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)],[238]) ).
thf(436,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(437,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
<=> ( ordinal_subset @ ( succ @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(438,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(439,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)],[244]) ).
thf(440,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(442,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)],[251]) ).
thf(443,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)],[252]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(445,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)],[255]) ).
thf(446,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)],[256]) ).
thf(447,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(448,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)],[264]) ).
thf(449,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)],[265]) ).
thf(450,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)],[267]) ).
thf(451,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)],[268]) ).
thf(452,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)],[269]) ).
thf(453,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)],[273]) ).
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)],[275]) ).
thf(455,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(456,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(457,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(458,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(459,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)],[289]) ).
thf(460,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(461,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(462,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
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)],[296]) ).
thf(464,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(465,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)],[300]) ).
thf(466,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(467,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(469,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(470,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(471,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(472,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(473,plain,
( ( ! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(474,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(475,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(476,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(477,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(478,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(479,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(480,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(481,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(482,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(483,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(484,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(485,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(486,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(487,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(488,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(489,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(490,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(492,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(494,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(495,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(496,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(497,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(498,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(500,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(502,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(503,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(504,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(506,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)],[131]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(508,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)],[137]) ).
thf(509,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)],[144]) ).
thf(510,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(511,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(512,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)],[151]) ).
thf(513,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)],[160]) ).
thf(514,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(515,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(518,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)],[182]) ).
thf(519,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(521,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)],[188]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(523,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(524,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(525,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(526,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(527,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(529,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(530,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)],[216]) ).
thf(531,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)],[219]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(533,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)],[221]) ).
thf(534,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)],[222]) ).
thf(535,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(537,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(540,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)],[235]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(542,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(543,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(544,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(546,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(547,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)],[248]) ).
thf(548,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(549,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(550,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(551,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)],[260]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(553,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)],[262]) ).
thf(554,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)],[263]) ).
thf(555,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(556,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(557,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)],[271]) ).
thf(558,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)],[272]) ).
thf(559,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(560,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)],[276]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(562,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(563,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)],[280]) ).
thf(564,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(565,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(566,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(567,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(568,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)],[285]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(572,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(573,plain,
( ( ! [SY609: $i] :
( ( relation @ SY609 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ SY609 ) ) @ ( relation_dom @ SY609 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(574,plain,
( ( ( relation @ sK2_SY609 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY609 ) ) @ ( relation_dom @ sK2_SY609 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[573]) ).
thf(575,plain,
( ( relation @ sK2_SY609 )
= $true ),
inference(standard_cnf,[status(thm)],[574]) ).
thf(576,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY609 ) ) @ ( relation_dom @ sK2_SY609 ) )
= $false ),
inference(standard_cnf,[status(thm)],[574]) ).
thf(577,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY609 ) ) @ ( relation_dom @ sK2_SY609 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[576]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(579,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY610: $i] :
( ~ ( in @ SY610 @ B )
| ~ ( in @ SY610 @ ( sK3_C @ B @ A ) ) )
& ( in @ ( sK3_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(580,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(581,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(582,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(583,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[314]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_C @ B @ A ) @ A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( in @ ( sK4_C @ B @ A ) @ A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[318]) ).
thf(586,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[320]) ).
thf(587,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[322]) ).
thf(588,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[323]) ).
thf(589,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[324]) ).
thf(590,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(591,plain,
( ( ~ ( empty @ sK5_A )
& ( epsilon_transitive @ sK5_A )
& ( epsilon_connected @ sK5_A )
& ( ordinal @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(592,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(593,plain,
( ( ! [A: $i] :
( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK7_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[328]) ).
thf(594,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)],[329]) ).
thf(595,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_combined,[status(esa)],[330]) ).
thf(596,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK10_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK10_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(597,plain,
( ( ( epsilon_connected @ sK11_A )
& ( epsilon_transitive @ sK11_A )
& ( ordinal @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(598,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[333]) ).
thf(599,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(600,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(601,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[336]) ).
thf(602,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[337]) ).
thf(603,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[338]) ).
thf(604,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[339]) ).
thf(605,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(606,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(607,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(608,plain,
( ( ! [A: $i] : ( element @ ( sK12_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[351]) ).
thf(609,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(610,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(611,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(612,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(613,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(614,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(615,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK13_C @ B @ A ) @ B )
& ( in @ ( sK14_SY611 @ B @ A ) @ B )
& ( in @ ( sK15_SY613 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY611 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK14_SY611 @ B @ A ) @ ( sK15_SY613 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK15_SY613 @ 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)],[359]) ).
thf(616,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY617: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ SY617 ) @ A )
| ~ ( in @ ( ordered_pair @ SY617 @ ( sK18_SY614 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK18_SY614 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK19_SY618 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK19_SY618 @ C @ B @ A ) @ ( sK18_SY614 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK18_SY614 @ 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 @ ( sK16_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(617,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK20_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK21_SY619 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK20_B @ A ) )
= ( apply @ A @ ( sK21_SY619 @ A ) ) )
& ( ( sK20_B @ A )
!= ( sK21_SY619 @ 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)],[361]) ).
thf(618,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(619,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY620 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ B @ A ) @ ( sK22_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY620 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ B @ A ) @ ( sK22_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)],[363]) ).
thf(620,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(621,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK24_C @ B @ A )
!= ( sK25_SY621 @ B @ A ) )
& ( in @ ( sK24_C @ B @ A ) @ B )
& ( in @ ( sK25_SY621 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY621 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ B @ A ) @ ( sK24_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)],[365]) ).
thf(622,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(623,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(625,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY622: $i] :
~ ( in @ ( ordered_pair @ SY622 @ ( sK27_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK28_SY623 @ B @ A ) @ ( sK27_C @ B @ A ) ) @ A )
| ( in @ ( sK27_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 @ ( sK26_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(626,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY624: $i] :
( ( ( sK30_C @ B @ A )
!= ( apply @ A @ SY624 ) )
| ~ ( in @ SY624 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( ( sK30_C @ B @ A )
= ( apply @ A @ ( sK31_SY625 @ B @ A ) ) )
& ( in @ ( sK31_SY625 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK30_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 @ ( sK29_D @ C @ B @ A ) ) )
& ( in @ ( sK29_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(627,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK32_D @ C @ B @ A ) @ A )
| ( in @ ( sK32_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK32_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK32_D @ C @ B @ A ) @ A )
| ( in @ ( sK32_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK32_D @ C @ B @ A ) @ B )
| ( in @ ( sK32_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(628,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY626: $i] :
( ~ ( in @ ( sK34_C @ B @ A ) @ SY626 )
| ~ ( in @ SY626 @ A ) )
| ~ ( in @ ( sK34_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK34_C @ B @ A ) @ ( sK35_SY627 @ B @ A ) )
& ( in @ ( sK35_SY627 @ B @ A ) @ A ) )
| ( in @ ( sK34_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK33_D @ C @ B @ A ) )
& ( in @ ( sK33_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(629,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ B )
& ( in @ ( sK37_SY628 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY628 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK37_SY628 @ B @ A ) @ ( sK36_C @ B @ A ) ) @ A )
& ( ( sK36_C @ B @ A )
!= ( sK37_SY628 @ 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)],[374]) ).
thf(630,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(631,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)],[376]) ).
thf(632,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(633,plain,
( ( ! [A: $i] :
( ( ( ( sK39_B @ A )
!= ( sK40_SY629 @ A ) )
& ( in @ ( sK39_B @ A ) @ A )
& ( in @ ( sK40_SY629 @ A ) @ A )
& ~ ( in @ ( sK39_B @ A ) @ ( sK40_SY629 @ A ) )
& ~ ( in @ ( sK40_SY629 @ A ) @ ( sK39_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(634,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ A )
| ~ ( in @ SY632 @ B )
| ( ( sK43_D @ C @ B @ A )
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ~ ( in @ ( sK43_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK44_SY633 @ C @ B @ A ) @ A )
& ( in @ ( sK45_SY635 @ C @ B @ A ) @ B )
& ( ( sK43_D @ C @ B @ A )
= ( ordered_pair @ ( sK44_SY633 @ C @ B @ A ) @ ( sK45_SY635 @ C @ B @ A ) ) ) )
| ( in @ ( sK43_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK41_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK42_SY630 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK41_E @ D @ C @ B @ A ) @ ( sK42_SY630 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[379]) ).
thf(635,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ( in @ ( sK46_D @ C @ B @ A ) @ A )
| ( in @ ( sK46_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[380]) ).
thf(636,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
= A )
| ( ( sK47_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(637,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(638,plain,
( ( ! [A: $i] :
( ( in @ ( sK48_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(639,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK49_C @ B @ A )
!= A )
| ~ ( in @ ( sK49_C @ B @ A ) @ B ) )
& ( ( ( sK49_C @ B @ A )
= A )
| ( in @ ( sK49_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(640,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK52_SY636 @ B @ A ) @ A )
& ~ ( in @ ( sK51_C @ B @ A ) @ ( sK52_SY636 @ B @ A ) ) )
| ~ ( in @ ( sK51_C @ B @ A ) @ B ) )
& ( ! [SY637: $i] :
( ~ ( in @ SY637 @ A )
| ( in @ ( sK51_C @ B @ A ) @ SY637 ) )
| ( in @ ( sK51_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK50_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK50_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[385]) ).
thf(641,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK53_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK53_C @ B @ A ) @ ( sK53_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)],[386]) ).
thf(642,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
= C )
| ( ( sK54_E @ D @ C @ B @ A )
= A )
| ( ( sK54_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[388]) ).
thf(643,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ C @ B @ A ) @ SY638 ) @ A )
| ~ ( in @ SY638 @ B ) )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_D @ C @ B @ A ) @ ( sK57_SY639 @ C @ B @ A ) ) @ A )
& ( in @ ( sK57_SY639 @ C @ B @ A ) @ B ) )
| ( in @ ( sK56_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 @ ( sK55_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK55_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(644,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ SY640 @ ( sK59_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY640 @ B ) )
| ~ ( in @ ( sK59_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK60_SY641 @ C @ B @ A ) @ ( sK59_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK60_SY641 @ C @ B @ A ) @ B ) )
| ( in @ ( sK59_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 @ ( sK58_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK58_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[390]) ).
thf(645,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK61_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK61_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK61_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)],[391]) ).
thf(646,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY642: $i] :
( ~ ( in @ SY642 @ ( relation_dom @ A ) )
| ~ ( in @ SY642 @ B )
| ( ( sK63_D @ C @ B @ A )
!= ( apply @ A @ SY642 ) ) )
| ~ ( in @ ( sK63_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK64_SY643 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK64_SY643 @ C @ B @ A ) @ B )
& ( ( sK63_D @ C @ B @ A )
= ( apply @ A @ ( sK64_SY643 @ C @ B @ A ) ) ) )
| ( in @ ( sK63_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 @ ( sK62_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK62_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[392]) ).
thf(647,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK65_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK65_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ 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)],[393]) ).
thf(648,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK67_C @ B @ A )
!= ( sK68_SY645 @ B @ A ) )
| ~ ( in @ ( sK67_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ B @ A ) ) @ B ) )
& ( ( ( sK67_C @ B @ A )
= ( sK68_SY645 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK67_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ 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)],[394]) ).
thf(649,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[395]) ).
thf(650,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(651,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(652,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)],[401]) ).
thf(653,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[402]) ).
thf(654,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(655,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(656,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(657,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(659,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(660,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)],[410]) ).
thf(661,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[411]) ).
thf(662,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)],[412]) ).
thf(663,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)],[413]) ).
thf(664,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)],[414]) ).
thf(665,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK69_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK69_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK69_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)],[416]) ).
thf(666,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[417]) ).
thf(667,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[418]) ).
thf(668,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)],[419]) ).
thf(669,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK70_B @ A ) @ ( sK71_SY646 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[420]) ).
thf(670,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)],[421]) ).
thf(671,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[422]) ).
thf(672,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_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)],[423]) ).
thf(673,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[424]) ).
thf(674,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK74_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[425]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[427]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[428]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[429]) ).
thf(678,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK75_C @ B @ A ) @ A )
& ( in @ ( sK75_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[431]) ).
thf(679,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[432]) ).
thf(680,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[434]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK76_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK76_C @ B @ A ) )
!= ( sK76_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)],[435]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[436]) ).
thf(683,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal_subset @ ( succ @ A ) @ B ) )
& ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( ordinal_subset @ ( succ @ A ) @ B )
| ( in @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[437]) ).
thf(684,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK77_C @ B @ A ) )
& ! [SY648: $i] :
( ~ ( ordinal @ SY648 )
| ~ ( in @ SY648 @ A )
| ( ordinal_subset @ ( sK77_C @ B @ A ) @ SY648 ) )
& ( in @ ( sK77_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[438]) ).
thf(685,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)],[439]) ).
thf(686,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[440]) ).
thf(687,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[441]) ).
thf(688,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)],[442]) ).
thf(689,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)],[443]) ).
thf(690,plain,
( ( ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( proper_subset @ A @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[444]) ).
thf(691,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)],[445]) ).
thf(692,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)],[446]) ).
thf(693,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)],[448]) ).
thf(694,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)],[449]) ).
thf(695,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 @ ( sK78_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK78_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK78_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[450]) ).
thf(696,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)],[451]) ).
thf(697,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)],[452]) ).
thf(698,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)],[453]) ).
thf(699,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 @ ( sK79_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK79_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK79_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[454]) ).
thf(700,plain,
( ( ! [A: $i] :
( ! [SY649: $i] :
( ~ ( subset @ SY649 @ ( sK80_B @ A ) )
| ( are_equipotent @ SY649 @ ( sK80_B @ A ) )
| ( in @ SY649 @ ( sK80_B @ A ) ) )
& ! [SY650: $i] :
( ~ ( in @ SY650 @ ( sK80_B @ A ) )
| ( in @ ( powerset @ SY650 ) @ ( sK80_B @ A ) ) )
& ! [SY651: $i,SY652: $i] :
( ~ ( in @ SY651 @ ( sK80_B @ A ) )
| ~ ( subset @ SY652 @ SY651 )
| ( in @ SY652 @ ( sK80_B @ A ) ) )
& ( in @ A @ ( sK80_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[455]) ).
thf(701,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[456]) ).
thf(702,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[458]) ).
thf(703,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)],[459]) ).
thf(704,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK81_C @ B @ A ) @ A )
& ~ ( in @ ( sK81_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[460]) ).
thf(705,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[461]) ).
thf(706,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[462]) ).
thf(707,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK82_B @ A ) @ ( sK83_SY653 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK83_SY653 @ A ) @ ( sK82_B @ A ) ) @ A )
& ( ( sK82_B @ A )
!= ( sK83_SY653 @ 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(708,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[464]) ).
thf(709,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK84_B @ A ) @ ( sK85_SY654 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK85_SY654 @ A ) @ ( sK86_SY656 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK84_B @ A ) @ ( sK86_SY656 @ 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)],[465]) ).
thf(710,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[466]) ).
thf(711,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[467]) ).
thf(712,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[468]) ).
thf(713,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[469]) ).
thf(714,plain,
( ( ! [A: $i] :
( ! [SY657: $i] :
( ~ ( subset @ SY657 @ ( sK87_B @ A ) )
| ( are_equipotent @ SY657 @ ( sK87_B @ A ) )
| ( in @ SY657 @ ( sK87_B @ A ) ) )
& ! [SY658: $i] :
( ( ! [SY663: $i] :
( ~ ( subset @ SY663 @ SY658 )
| ( in @ SY663 @ ( sK88_SY659 @ SY658 @ A ) ) )
& ( in @ ( sK88_SY659 @ SY658 @ A ) @ ( sK87_B @ A ) ) )
| ~ ( in @ SY658 @ ( sK87_B @ A ) ) )
& ! [SY661: $i,SY662: $i] :
( ~ ( in @ SY661 @ ( sK87_B @ A ) )
| ~ ( subset @ SY662 @ SY661 )
| ( in @ SY662 @ ( sK87_B @ A ) ) )
& ( in @ A @ ( sK87_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[470]) ).
thf(715,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[471]) ).
thf(716,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[472]) ).
thf(717,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[473]) ).
thf(718,plain,
( ( ( relation @ sK89_A )
& ( relation_empty_yielding @ sK89_A )
& ( function @ sK89_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[474]) ).
thf(719,plain,
( ( ( relation @ sK90_A )
& ( relation_empty_yielding @ sK90_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[475]) ).
thf(720,plain,
( ( ( function @ sK91_A )
& ( relation @ sK91_A )
& ( one_to_one @ sK91_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[476]) ).
thf(721,plain,
( ( ~ ( empty @ sK92_A )
& ( relation @ sK92_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[477]) ).
thf(722,plain,
( ( ( empty @ sK93_A )
& ( relation @ sK93_A )
& ( function @ sK93_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[478]) ).
thf(723,plain,
( ( ( empty @ sK94_A )
& ( relation @ sK94_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[479]) ).
thf(724,plain,
( ( ( function @ sK95_A )
& ( relation @ sK95_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[480]) ).
thf(725,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[481]) ).
thf(726,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)],[482]) ).
thf(727,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[483]) ).
thf(728,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[484]) ).
thf(729,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[485]) ).
thf(730,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[486]) ).
thf(731,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)],[487]) ).
thf(732,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)],[489]) ).
thf(733,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[490]) ).
thf(734,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[491]) ).
thf(735,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[492]) ).
thf(736,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[493]) ).
thf(737,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)],[494]) ).
thf(738,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)],[495]) ).
thf(739,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[496]) ).
thf(740,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)],[497]) ).
thf(741,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[498]) ).
thf(742,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[499]) ).
thf(743,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[501]) ).
thf(744,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[502]) ).
thf(745,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[503]) ).
thf(746,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)],[504]) ).
thf(747,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[505]) ).
thf(748,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY664: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ B @ A ) @ SY664 ) @ A )
| ~ ( in @ ( sK97_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK97_C @ B @ A ) @ ( sK98_SY665 @ B @ A ) ) @ A )
| ( in @ ( sK97_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 @ ( sK96_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[506]) ).
thf(749,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK99_C @ B @ A ) @ A )
& ~ ( in @ ( sK99_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[507]) ).
thf(750,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK100_C @ B @ A ) @ ( sK101_SY666 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK100_C @ B @ A ) @ ( sK101_SY666 @ 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)],[508]) ).
thf(751,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ 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)],[509]) ).
thf(752,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK104_B @ A ) @ A )
& ~ ( subset @ ( sK104_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[510]) ).
thf(753,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK105_C @ B @ A ) @ B )
| ~ ( subset @ ( sK105_C @ B @ A ) @ A ) )
& ( ( in @ ( sK105_C @ B @ A ) @ B )
| ( subset @ ( sK105_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[511]) ).
thf(754,plain,
( ( ! [A: $i] :
( ( ! [SY669: $i,SY670: $i] :
( ( sK108_B @ A )
!= ( ordered_pair @ SY669 @ SY670 ) )
& ( in @ ( sK108_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK106_C @ B @ A ) @ ( sK107_SY668 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[512]) ).
thf(755,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK110_SY671 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK110_SY671 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ 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)],[513]) ).
thf(756,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[514]) ).
thf(757,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(758,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[516]) ).
thf(759,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(760,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)],[518]) ).
thf(761,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(762,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[520]) ).
thf(763,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)],[521]) ).
thf(764,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[523]) ).
thf(765,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[524]) ).
thf(766,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)],[525]) ).
thf(767,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)],[526]) ).
thf(768,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[527]) ).
thf(769,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[528]) ).
thf(770,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)],[530]) ).
thf(771,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)],[531]) ).
thf(772,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[532]) ).
thf(773,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)],[533]) ).
thf(774,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)],[534]) ).
thf(775,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[535]) ).
thf(776,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[536]) ).
thf(777,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[537]) ).
thf(778,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[538]) ).
thf(779,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[539]) ).
thf(780,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)],[540]) ).
thf(781,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[542]) ).
thf(782,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK111_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK111_B @ A ) )
| ~ ( subset @ ( sK111_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[543]) ).
thf(783,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[545]) ).
thf(784,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(785,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)],[547]) ).
thf(786,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[548]) ).
thf(787,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(788,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[550]) ).
thf(789,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)],[551]) ).
thf(790,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)],[553]) ).
thf(791,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)],[554]) ).
thf(792,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[555]) ).
thf(793,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[556]) ).
thf(794,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)],[557]) ).
thf(795,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)],[558]) ).
thf(796,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[559]) ).
thf(797,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)],[560]) ).
thf(798,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[561]) ).
thf(799,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[562]) ).
thf(800,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)],[563]) ).
thf(801,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[564]) ).
thf(802,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[565]) ).
thf(803,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[566]) ).
thf(804,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[567]) ).
thf(805,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)],[568]) ).
thf(806,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[569]) ).
thf(807,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[570]) ).
thf(808,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[571]) ).
thf(809,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[572]) ).
thf(810,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(811,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(812,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(813,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(814,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)],[805]) ).
thf(815,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(816,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(817,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(818,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(819,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)],[800]) ).
thf(820,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(821,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(822,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)],[797]) ).
thf(823,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ A ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(824,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)],[795]) ).
thf(825,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)],[794]) ).
thf(826,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(827,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(828,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)],[791]) ).
thf(829,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)],[790]) ).
thf(830,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(831,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)],[789]) ).
thf(832,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(833,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(834,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(835,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)],[785]) ).
thf(836,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(837,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(838,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(839,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK111_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK111_B @ A ) )
| ~ ( subset @ ( sK111_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(840,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(841,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(842,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)],[780]) ).
thf(843,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(844,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(845,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(846,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(847,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(848,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(849,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(850,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(851,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)],[771]) ).
thf(852,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)],[770]) ).
thf(853,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(854,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(855,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(856,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)],[767]) ).
thf(857,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)],[766]) ).
thf(858,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(859,plain,
( ( ! [A: $i] :
( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ! [A: $i] :
( ( relation_rng @ ( identity_relation @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(860,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(861,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)],[763]) ).
thf(862,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(863,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(864,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)],[760]) ).
thf(865,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(866,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(867,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(868,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(869,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK110_SY671 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK110_SY671 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK109_D @ C @ B @ A ) @ ( sK110_SY671 @ 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)],[755]) ).
thf(870,plain,
( ( ! [A: $i] :
( ( ! [SY669: $i,SY670: $i] :
( ( sK108_B @ A )
!= ( ordered_pair @ SY669 @ SY670 ) )
& ( in @ ( sK108_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK106_C @ B @ A ) @ ( sK107_SY668 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(871,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK105_C @ B @ A ) @ B )
| ~ ( subset @ ( sK105_C @ B @ A ) @ A ) )
& ( ( in @ ( sK105_C @ B @ A ) @ B )
| ( subset @ ( sK105_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(872,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK104_B @ A ) @ A )
& ~ ( subset @ ( sK104_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(873,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK102_C @ B @ A ) @ ( sK103_SY667 @ 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)],[751]) ).
thf(874,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK100_C @ B @ A ) @ ( sK101_SY666 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK100_C @ B @ A ) @ ( sK101_SY666 @ 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)],[750]) ).
thf(875,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK99_C @ B @ A ) @ A )
& ~ ( in @ ( sK99_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(876,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY664: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ B @ A ) @ SY664 ) @ A )
| ~ ( in @ ( sK97_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK97_C @ B @ A ) @ ( sK98_SY665 @ B @ A ) ) @ A )
| ( in @ ( sK97_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 @ ( sK96_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(877,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(878,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)],[746]) ).
thf(879,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(880,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(881,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(882,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(883,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(884,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(885,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)],[740]) ).
thf(886,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(887,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)],[738]) ).
thf(888,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)],[737]) ).
thf(889,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(890,plain,
( ( ! [A: $i] : ( function @ ( identity_relation @ A ) )
& ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(891,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(892,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(893,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)],[732]) ).
thf(894,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(895,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)],[731]) ).
thf(896,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(897,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(898,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(899,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(900,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)],[726]) ).
thf(901,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(902,plain,
( ( ( function @ sK95_A )
& ( relation @ sK95_A ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(903,plain,
( ( ( empty @ sK94_A )
& ( relation @ sK94_A ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(904,plain,
( ( ( empty @ sK93_A )
& ( relation @ sK93_A )
& ( function @ sK93_A ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(905,plain,
( ( ~ ( empty @ sK92_A )
& ( relation @ sK92_A ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(906,plain,
( ( ( function @ sK91_A )
& ( relation @ sK91_A )
& ( one_to_one @ sK91_A ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(907,plain,
( ( ( relation @ sK90_A )
& ( relation_empty_yielding @ sK90_A ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(908,plain,
( ( ( relation @ sK89_A )
& ( relation_empty_yielding @ sK89_A )
& ( function @ sK89_A ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(909,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( ordinal_subset @ A @ B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ~ ( subset @ A @ B )
| ( ordinal_subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(910,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(911,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(912,plain,
( ( ! [A: $i] :
( ! [SY657: $i] :
( ~ ( subset @ SY657 @ ( sK87_B @ A ) )
| ( are_equipotent @ SY657 @ ( sK87_B @ A ) )
| ( in @ SY657 @ ( sK87_B @ A ) ) )
& ! [SY658: $i] :
( ( ! [SY663: $i] :
( ~ ( subset @ SY663 @ SY658 )
| ( in @ SY663 @ ( sK88_SY659 @ SY658 @ A ) ) )
& ( in @ ( sK88_SY659 @ SY658 @ A ) @ ( sK87_B @ A ) ) )
| ~ ( in @ SY658 @ ( sK87_B @ A ) ) )
& ! [SY661: $i,SY662: $i] :
( ~ ( in @ SY661 @ ( sK87_B @ A ) )
| ~ ( subset @ SY662 @ SY661 )
| ( in @ SY662 @ ( sK87_B @ A ) ) )
& ( in @ A @ ( sK87_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(913,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(914,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(915,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(916,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(917,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK84_B @ A ) @ ( sK85_SY654 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK85_SY654 @ A ) @ ( sK86_SY656 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK84_B @ A ) @ ( sK86_SY656 @ 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)],[709]) ).
thf(918,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(919,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK82_B @ A ) @ ( sK83_SY653 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK83_SY653 @ A ) @ ( sK82_B @ A ) ) @ A )
& ( ( sK82_B @ A )
!= ( sK83_SY653 @ 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)],[707]) ).
thf(920,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(921,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(922,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK81_C @ B @ A ) @ A )
& ~ ( in @ ( sK81_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(923,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)],[703]) ).
thf(924,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(925,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(926,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(927,plain,
( ( ! [A: $i] :
( ! [SY649: $i] :
( ~ ( subset @ SY649 @ ( sK80_B @ A ) )
| ( are_equipotent @ SY649 @ ( sK80_B @ A ) )
| ( in @ SY649 @ ( sK80_B @ A ) ) )
& ! [SY650: $i] :
( ~ ( in @ SY650 @ ( sK80_B @ A ) )
| ( in @ ( powerset @ SY650 ) @ ( sK80_B @ A ) ) )
& ! [SY651: $i,SY652: $i] :
( ~ ( in @ SY651 @ ( sK80_B @ A ) )
| ~ ( subset @ SY652 @ SY651 )
| ( in @ SY652 @ ( sK80_B @ A ) ) )
& ( in @ A @ ( sK80_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(928,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 @ ( sK79_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK79_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK79_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(929,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( subset @ ( relation_image @ B @ ( relation_inverse_image @ B @ A ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(930,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)],[697]) ).
thf(931,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)],[696]) ).
thf(932,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 @ ( sK78_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK78_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK78_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(933,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)],[694]) ).
thf(934,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)],[693]) ).
thf(935,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(936,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)],[692]) ).
thf(937,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)],[691]) ).
thf(938,plain,
( ( ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( proper_subset @ A @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(939,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)],[689]) ).
thf(940,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)],[688]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(942,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(943,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)],[685]) ).
thf(944,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ( ( ordinal @ ( sK77_C @ B @ A ) )
& ! [SY648: $i] :
( ~ ( ordinal @ SY648 )
| ~ ( in @ SY648 @ A )
| ( ordinal_subset @ ( sK77_C @ B @ A ) @ SY648 ) )
& ( in @ ( sK77_C @ B @ A ) @ A ) )
| ( A = empty_set )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(945,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal_subset @ ( succ @ A ) @ B ) )
& ! [B: $i] :
( ~ ( ordinal @ B )
| ~ ( ordinal_subset @ ( succ @ A ) @ B )
| ( in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(946,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(947,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( in @ ( sK76_C @ B @ A ) @ A )
& ( ( apply @ B @ ( sK76_C @ B @ A ) )
!= ( sK76_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)],[681]) ).
thf(948,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ A )
| ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(949,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(950,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(951,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK75_C @ B @ A ) @ A )
& ( in @ ( sK75_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(952,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(953,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(954,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(955,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(956,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(957,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK74_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(958,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(959,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ! [B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK73_SY647 @ B @ A )
= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_C @ B @ A ) @ ( relation_rng @ A ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK72_C @ B @ A )
= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) ) )
& ( ( ( sK72_C @ B @ A )
!= ( apply @ A @ ( sK73_SY647 @ B @ A ) ) )
| ~ ( in @ ( sK73_SY647 @ B @ A ) @ ( relation_dom @ A ) )
| ( ( sK73_SY647 @ B @ A )
!= ( apply @ B @ ( sK72_C @ B @ A ) ) )
| ~ ( in @ ( sK72_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)],[672]) ).
thf(960,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(961,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)],[670]) ).
thf(962,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK70_B @ A ) @ ( sK71_SY646 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(963,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)],[668]) ).
thf(964,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( one_to_one @ ( function_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(965,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(966,plain,
( ( ! [A: $i,B: $i] :
( ~ ( function @ B )
| ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( in @ ( sK69_D @ C @ B @ A ) @ ( relation_dom @ B ) )
& ( ( apply @ B @ ( sK69_D @ C @ B @ A ) )
!= ( apply @ C @ ( sK69_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)],[665]) ).
thf(967,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(968,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)],[664]) ).
thf(969,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)],[663]) ).
thf(970,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)],[662]) ).
thf(971,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(972,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)],[660]) ).
thf(973,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(974,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( relation_dom_restriction @ B @ A )
= ( relation_composition @ ( identity_relation @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(975,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(976,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(977,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(978,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(979,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(980,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(981,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)],[652]) ).
thf(982,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(983,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(984,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(985,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(986,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(987,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ A )
| ~ ( ordinal @ B )
| ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(988,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK67_C @ B @ A )
!= ( sK68_SY645 @ B @ A ) )
| ~ ( in @ ( sK67_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ B @ A ) ) @ B ) )
& ( ( ( sK67_C @ B @ A )
= ( sK68_SY645 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK67_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK67_C @ B @ A ) @ ( sK68_SY645 @ 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)],[648]) ).
thf(989,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK65_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK65_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK65_D @ C @ B @ A ) @ ( sK66_SY644 @ 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)],[647]) ).
thf(990,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY642: $i] :
( ~ ( in @ SY642 @ ( relation_dom @ A ) )
| ~ ( in @ SY642 @ B )
| ( ( sK63_D @ C @ B @ A )
!= ( apply @ A @ SY642 ) ) )
| ~ ( in @ ( sK63_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK64_SY643 @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK64_SY643 @ C @ B @ A ) @ B )
& ( ( sK63_D @ C @ B @ A )
= ( apply @ A @ ( sK64_SY643 @ C @ B @ A ) ) ) )
| ( in @ ( sK63_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 @ ( sK62_E @ D @ C @ B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK62_E @ D @ C @ B @ A ) @ B )
& ( D
= ( apply @ A @ ( sK62_E @ D @ C @ B @ A ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(991,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ~ ( in @ ( apply @ A @ ( sK61_D @ C @ B @ A ) ) @ B )
| ~ ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ A ) )
| ( in @ ( sK61_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( apply @ A @ ( sK61_D @ C @ B @ A ) ) @ B )
| ( in @ ( sK61_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)],[645]) ).
thf(992,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ ( ordered_pair @ SY640 @ ( sK59_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY640 @ B ) )
| ~ ( in @ ( sK59_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK60_SY641 @ C @ B @ A ) @ ( sK59_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK60_SY641 @ C @ B @ A ) @ B ) )
| ( in @ ( sK59_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 @ ( sK58_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK58_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(993,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY638: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ C @ B @ A ) @ SY638 ) @ A )
| ~ ( in @ SY638 @ B ) )
| ~ ( in @ ( sK56_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK56_D @ C @ B @ A ) @ ( sK57_SY639 @ C @ B @ A ) ) @ A )
& ( in @ ( sK57_SY639 @ C @ B @ A ) @ B ) )
| ( in @ ( sK56_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 @ ( sK55_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK55_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(994,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK54_E @ D @ C @ B @ A ) @ D )
| ( ( sK54_E @ D @ C @ B @ A )
= C )
| ( ( sK54_E @ D @ C @ B @ A )
= A )
| ( ( sK54_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(995,plain,
( ( ! [A: $i] :
( ( succ @ A )
= ( set_union2 @ A @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(996,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK53_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK53_C @ B @ A ) @ ( sK53_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)],[641]) ).
thf(997,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK52_SY636 @ B @ A ) @ A )
& ~ ( in @ ( sK51_C @ B @ A ) @ ( sK52_SY636 @ B @ A ) ) )
| ~ ( in @ ( sK51_C @ B @ A ) @ B ) )
& ( ! [SY637: $i] :
( ~ ( in @ SY637 @ A )
| ( in @ ( sK51_C @ B @ A ) @ SY637 ) )
| ( in @ ( sK51_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK50_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK50_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(998,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK49_C @ B @ A )
!= A )
| ~ ( in @ ( sK49_C @ B @ A ) @ B ) )
& ( ( ( sK49_C @ B @ A )
= A )
| ( in @ ( sK49_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(999,plain,
( ( ! [A: $i] :
( ( in @ ( sK48_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1000,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1001,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK47_D @ C @ B @ A ) @ C )
| ( ( sK47_D @ C @ B @ A )
= A )
| ( ( sK47_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1002,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK46_D @ C @ B @ A ) @ C )
| ( in @ ( sK46_D @ C @ B @ A ) @ A )
| ( in @ ( sK46_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1003,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY631 @ A )
| ~ ( in @ SY632 @ B )
| ( ( sK43_D @ C @ B @ A )
!= ( ordered_pair @ SY631 @ SY632 ) ) )
| ~ ( in @ ( sK43_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK44_SY633 @ C @ B @ A ) @ A )
& ( in @ ( sK45_SY635 @ C @ B @ A ) @ B )
& ( ( sK43_D @ C @ B @ A )
= ( ordered_pair @ ( sK44_SY633 @ C @ B @ A ) @ ( sK45_SY635 @ C @ B @ A ) ) ) )
| ( in @ ( sK43_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK41_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK42_SY630 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK41_E @ D @ C @ B @ A ) @ ( sK42_SY630 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1004,plain,
( ( ! [A: $i] :
( ( ( ( sK39_B @ A )
!= ( sK40_SY629 @ A ) )
& ( in @ ( sK39_B @ A ) @ A )
& ( in @ ( sK40_SY629 @ A ) @ A )
& ~ ( in @ ( sK39_B @ A ) @ ( sK40_SY629 @ A ) )
& ~ ( in @ ( sK40_SY629 @ A ) @ ( sK39_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1005,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ A )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK38_D @ C @ B @ A ) @ B )
| ( in @ ( sK38_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1006,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)],[631]) ).
thf(1007,plain,
( ( ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ~ ( epsilon_transitive @ A )
| ( ordinal @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ A ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1008,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ B )
& ( in @ ( sK37_SY628 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK37_SY628 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK37_SY628 @ B @ A ) @ ( sK36_C @ B @ A ) ) @ A )
& ( ( sK36_C @ B @ A )
!= ( sK37_SY628 @ 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)],[629]) ).
thf(1009,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY626: $i] :
( ~ ( in @ ( sK34_C @ B @ A ) @ SY626 )
| ~ ( in @ SY626 @ A ) )
| ~ ( in @ ( sK34_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK34_C @ B @ A ) @ ( sK35_SY627 @ B @ A ) )
& ( in @ ( sK35_SY627 @ B @ A ) @ A ) )
| ( in @ ( sK34_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK33_D @ C @ B @ A ) )
& ( in @ ( sK33_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1010,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK32_D @ C @ B @ A ) @ A )
| ( in @ ( sK32_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK32_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK32_D @ C @ B @ A ) @ A )
| ( in @ ( sK32_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK32_D @ C @ B @ A ) @ B )
| ( in @ ( sK32_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1011,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY624: $i] :
( ( ( sK30_C @ B @ A )
!= ( apply @ A @ SY624 ) )
| ~ ( in @ SY624 @ ( relation_dom @ A ) ) )
| ~ ( in @ ( sK30_C @ B @ A ) @ B ) )
& ( ( ( ( sK30_C @ B @ A )
= ( apply @ A @ ( sK31_SY625 @ B @ A ) ) )
& ( in @ ( sK31_SY625 @ B @ A ) @ ( relation_dom @ A ) ) )
| ( in @ ( sK30_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 @ ( sK29_D @ C @ B @ A ) ) )
& ( in @ ( sK29_D @ C @ B @ A ) @ ( relation_dom @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(1012,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY622: $i] :
~ ( in @ ( ordered_pair @ SY622 @ ( sK27_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK27_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK28_SY623 @ B @ A ) @ ( sK27_C @ B @ A ) ) @ A )
| ( in @ ( sK27_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 @ ( sK26_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(1013,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1014,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(1015,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1016,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_field @ A )
= ( set_union2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1017,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK24_C @ B @ A )
!= ( sK25_SY621 @ B @ A ) )
& ( in @ ( sK24_C @ B @ A ) @ B )
& ( in @ ( sK25_SY621 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY621 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ B @ A ) @ ( sK24_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)],[621]) ).
thf(1018,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1019,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY620 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ B @ A ) @ ( sK22_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY620 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ B @ A ) @ ( sK22_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)],[619]) ).
thf(1020,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1021,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ( in @ ( sK20_B @ A ) @ ( relation_dom @ A ) )
& ( in @ ( sK21_SY619 @ A ) @ ( relation_dom @ A ) )
& ( ( apply @ A @ ( sK20_B @ A ) )
= ( apply @ A @ ( sK21_SY619 @ A ) ) )
& ( ( sK20_B @ A )
!= ( sK21_SY619 @ 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)],[617]) ).
thf(1022,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY617: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ SY617 ) @ A )
| ~ ( in @ ( ordered_pair @ SY617 @ ( sK18_SY614 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK18_SY614 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK19_SY618 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK19_SY618 @ C @ B @ A ) @ ( sK18_SY614 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK17_D @ C @ B @ A ) @ ( sK18_SY614 @ 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 @ ( sK16_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK16_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1023,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK13_C @ B @ A ) @ B )
& ( in @ ( sK14_SY611 @ B @ A ) @ B )
& ( in @ ( sK15_SY613 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK14_SY611 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK14_SY611 @ B @ A ) @ ( sK15_SY613 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK13_C @ B @ A ) @ ( sK15_SY613 @ 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)],[615]) ).
thf(1024,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ~ ( one_to_one @ A )
| ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1025,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(1026,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(1027,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(1028,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1029,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(1030,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(1031,plain,
( ( ! [A: $i] : ( element @ ( sK12_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1032,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(1033,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(1034,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(1035,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(1036,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(1037,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)],[345]) ).
thf(1038,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(1039,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(1040,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)],[606]) ).
thf(1041,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(1042,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(1043,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_connected @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( epsilon_transitive @ ( union @ A ) ) )
& ! [A: $i] :
( ~ ( ordinal @ A )
| ( ordinal @ ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(1044,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(1045,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(1046,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1047,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(1048,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1049,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1050,plain,
( ( ( epsilon_connected @ sK11_A )
& ( epsilon_transitive @ sK11_A )
& ( ordinal @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(1051,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK10_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK10_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(1052,plain,
( ( empty @ sK9_A )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1053,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)],[594]) ).
thf(1054,plain,
( ( ! [A: $i] :
( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK7_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1055,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1056,plain,
( ( ~ ( empty @ sK5_A )
& ( epsilon_transitive @ sK5_A )
& ( epsilon_connected @ sK5_A )
& ( ordinal @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1057,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1058,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1059,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ A @ A ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1060,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1061,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(1062,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(1063,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(1064,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(1065,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK4_C @ B @ A ) @ A )
| ~ ( in @ ( sK4_C @ B @ A ) @ B ) )
& ( ( in @ ( sK4_C @ B @ A ) @ A )
| ( in @ ( sK4_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1066,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(1067,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(1068,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1069,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(1070,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(1071,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(1072,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY610: $i] :
( ~ ( in @ SY610 @ B )
| ~ ( in @ SY610 @ ( sK3_C @ B @ A ) ) )
& ( in @ ( sK3_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1073,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1074,plain,
( ( relation @ sK2_SY609 )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1075,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY609 ) ) @ ( relation_dom @ sK2_SY609 ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1076,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK74_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(1077,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)],[895]) ).
thf(1078,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)],[961]) ).
thf(1079,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1080,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SX1 @ SX0 )
!= ( sK25_SY621 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK25_SY621 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY621 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SX1 @ SX0 ) @ ( sK24_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)],[1017]) ).
thf(1081,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK59_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK59_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SX2 @ SX1 @ SX0 ) @ ( sK59_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK60_SY641 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK59_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 @ ( sK58_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK58_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[992]) ).
thf(1082,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)],[1040]) ).
thf(1083,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK37_SY628 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK37_SY628 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SX1 @ SX0 ) @ ( sK36_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK36_C @ SX1 @ SX0 )
!= ( sK37_SY628 @ 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)],[1008]) ).
thf(1084,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK108_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK108_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK106_C @ SX1 @ SX0 ) @ ( sK107_SY668 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(1085,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK109_D @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY671 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK109_D @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY671 @ 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)],[869]) ).
thf(1086,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1087,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(1088,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK87_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK87_B @ SX0 ) )
| ( in @ SX1 @ ( sK87_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK88_SY659 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK88_SY659 @ SX1 @ SX0 ) @ ( sK87_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK87_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK87_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK87_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK87_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(1089,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(1090,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1002]) ).
thf(1091,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK97_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SX1 @ SX0 ) @ ( sK98_SY665 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK97_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 @ ( sK96_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(1092,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SX1 @ SX0 ) @ ( sK53_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)],[996]) ).
thf(1093,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK76_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK76_C @ SX1 @ SX0 ) )
!= ( sK76_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)],[947]) ).
thf(1094,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK10_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK10_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1051]) ).
thf(1095,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK14_SY611 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK15_SY613 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY611 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SX1 @ SX0 ) @ ( sK15_SY613 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SX1 @ SX0 ) @ ( sK15_SY613 @ 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)],[1023]) ).
thf(1096,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[818]) ).
thf(1097,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(1098,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY620 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SX1 @ SX0 ) @ ( sK22_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY620 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SX1 @ SX0 ) @ ( sK22_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)],[1019]) ).
thf(1099,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1100,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK4_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(1102,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)],[885]) ).
thf(1103,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK91_A )
| ~ ( relation @ sK91_A ) )
| ~ ( one_to_one @ sK91_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1104,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK43_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK45_SY635 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK43_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK44_SY633 @ SX2 @ SX1 @ SX0 ) @ ( sK45_SY635 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK42_SY630 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK41_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK42_SY630 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1003]) ).
thf(1105,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1020]) ).
thf(1106,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK48_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1107,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(1108,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(1109,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)],[1037]) ).
thf(1110,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1111,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)],[963]) ).
thf(1112,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( ( sK63_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX3 ) ) )
| ~ ( in @ ( sK63_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK64_SY643 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK63_D @ SX2 @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK64_SY643 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK63_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 @ ( sK62_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK62_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( apply @ SX0 @ ( sK62_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(1113,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)],[856]) ).
thf(1114,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK21_SY619 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK20_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK21_SY619 @ SX0 ) ) ) )
| ~ ( ( ( sK20_B @ SX0 )
!= ( sK21_SY619 @ 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)],[1021]) ).
thf(1115,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[844]) ).
thf(1116,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK83_SY653 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK82_B @ SX0 )
!= ( sK83_SY653 @ 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)],[919]) ).
thf(1117,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK32_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1010]) ).
thf(1118,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY627 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK35_SY627 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK33_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(1119,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)],[970]) ).
thf(1120,plain,
( ( ~ ( ~ ( empty @ sK94_A )
| ~ ( relation @ sK94_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(1121,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK49_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK49_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[998]) ).
thf(1122,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1123,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[843]) ).
thf(1124,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ( ( sK72_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SX1 @ SX0 )
= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ( ( sK73_SY647 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK72_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) )
| ( ( sK73_SY647 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK72_C @ SX1 @ SX0 ) @ ( relation_rng @ SX0 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK72_C @ SX1 @ SX0 )
= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) ) )
| ~ ( ( ( sK72_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) )
| ~ ( ( ( sK72_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK73_SY647 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK73_SY647 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( ( sK73_SY647 @ SX1 @ SX0 )
!= ( apply @ SX1 @ ( sK72_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK72_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)],[959]) ).
thf(1125,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)],[1053]) ).
thf(1126,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)],[842]) ).
thf(1127,plain,
( ( ~ ( ~ ( relation @ sK90_A )
| ~ ( relation_empty_yielding @ sK90_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1128,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( in @ SX0 @ SX1 )
| ( ordinal_subset @ ( succ @ SX0 ) @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ ( succ @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1129,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 @ ( sK78_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK78_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK78_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[932]) ).
thf(1130,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1131,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)],[835]) ).
thf(1132,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(1133,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)],[857]) ).
thf(1134,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(1135,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1136,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(1137,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)],[933]) ).
thf(1138,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)],[943]) ).
thf(1139,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1140,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1141,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)],[923]) ).
thf(1142,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( sK3_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(1143,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)],[936]) ).
thf(1144,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK80_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK80_B @ SX0 ) )
| ( in @ SX1 @ ( sK80_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK80_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK80_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK80_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK80_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK80_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(1145,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK104_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK104_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1146,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)],[972]) ).
thf(1147,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK93_A )
| ~ ( relation @ sK93_A ) )
| ~ ( function @ sK93_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1148,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( apply @ SX0 @ ( sK61_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) )
| ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( apply @ SX0 @ ( sK61_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( sK61_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)],[991]) ).
thf(1149,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1150,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)],[1006]) ).
thf(1151,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK11_A )
| ~ ( epsilon_transitive @ sK11_A ) )
| ~ ( ordinal @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1050]) ).
thf(1152,plain,
( ( ~ ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1153,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)],[861]) ).
thf(1154,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1032]) ).
thf(1155,plain,
( ( ~ ( ~ ~ ( empty @ sK92_A )
| ~ ( relation @ sK92_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1156,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(1157,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK18_SY614 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY614 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ ( sK19_SY618 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY614 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY614 @ 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 @ ( sK16_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1022]) ).
thf(1158,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK27_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK27_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SX1 @ SX0 ) @ ( sK27_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK27_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 @ ( sK26_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1012]) ).
thf(1159,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK54_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( SX4 = SX2 )
| ( SX4 = SX0 )
| ( SX4 = SX1 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX2 )
| ( in @ SX4 @ SX3 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX0 )
| ( in @ SX4 @ SX3 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SX1 )
| ( in @ SX4 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1160,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)],[887]) ).
thf(1161,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[997]) ).
thf(1162,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK47_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK47_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK47_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK47_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK47_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1163,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK85_SY654 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK86_SY656 @ 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)],[917]) ).
thf(1164,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1165,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)],[937]) ).
thf(1166,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[868]) ).
thf(1167,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)],[878]) ).
thf(1168,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[853]) ).
thf(1169,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(1170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( ~ ( ordinal @ ( sK77_C @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( ordinal @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( ordinal_subset @ ( sK77_C @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK77_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX0 = empty_set )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1172,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK7_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK7_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1054]) ).
thf(1173,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[983]) ).
thf(1174,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SX1 @ SX0 ) @ ( sK103_SY667 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SX1 @ SX0 ) @ ( sK103_SY667 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SX1 @ SX0 ) @ ( sK103_SY667 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK102_C @ SX1 @ SX0 ) @ ( sK103_SY667 @ 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)],[873]) ).
thf(1175,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)],[888]) ).
thf(1176,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ( ( sK30_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ SX2 ) )
| ~ ( in @ SX2 @ ( relation_dom @ SX0 ) ) )
| ~ ( in @ ( sK30_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ( ( sK30_C @ SX1 @ SX0 )
!= ( apply @ SX0 @ ( sK31_SY625 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK31_SY625 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( in @ ( sK30_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 @ ( sK29_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK29_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(1177,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK111_B @ SX0 ) @ SX0 )
| ~ ( ~ ( ordinal @ ( sK111_B @ SX0 ) )
| ~ ( subset @ ( sK111_B @ SX0 ) @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(1178,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( in @ ( sK69_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( ( ( apply @ SX1 @ ( sK69_D @ SX2 @ SX1 @ SX0 ) )
!= ( apply @ SX2 @ ( sK69_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)],[966]) ).
thf(1179,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK89_A )
| ~ ( relation_empty_yielding @ sK89_A ) )
| ~ ( function @ sK89_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1180,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= ( sK40_SY629 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK40_SY629 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK39_B @ SX0 ) @ ( sK40_SY629 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SX0 ) @ ( sK39_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1004]) ).
thf(1181,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY644 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY644 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY644 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY644 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK65_D @ SX2 @ SX1 @ SX0 ) @ ( sK66_SY644 @ 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)],[989]) ).
thf(1182,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1183,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)],[981]) ).
thf(1184,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)],[814]) ).
thf(1185,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)],[900]) ).
thf(1186,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 @ ( sK79_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK79_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1187,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SX1 @ SX0 ) @ ( sK101_SY666 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SX1 @ SX0 ) @ ( sK101_SY666 @ 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)],[874]) ).
thf(1188,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(1189,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK38_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1005]) ).
thf(1190,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1191,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[921]) ).
thf(1192,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
| ~ ( epsilon_connected @ sK5_A ) )
| ~ ( ordinal @ sK5_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1056]) ).
thf(1193,plain,
( ( ~ ( ~ ( function @ sK95_A )
| ~ ( relation @ sK95_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1194,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK81_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK81_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1195,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)],[893]) ).
thf(1196,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SX2 @ SX1 @ SX0 ) @ ( sK57_SY639 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK57_SY639 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK56_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 @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK55_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[993]) ).
thf(1197,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
!= ( sK68_SY645 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
= ( sK68_SY645 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ 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)],[988]) ).
thf(1198,plain,
! [SV1: $i] :
( ( ! [SY672: $i] :
( ~ ( in @ SV1 @ SY672 )
| ( subset @ SV1 @ ( union @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1199,plain,
! [SV2: $i] :
( ( ! [SY673: $i] :
( ~ ( relation @ SY673 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SY673 ) ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1200,plain,
! [SV3: $i] :
( ( ! [SY674: $i] :
( ~ ( relation @ SY674 )
| ( subset @ ( relation_rng_restriction @ SV3 @ SY674 ) @ SY674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1201,plain,
! [SV4: $i] :
( ( ! [SY675: $i] :
( ~ ( relation @ SY675 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SY675 ) ) @ ( relation_rng @ SY675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1202,plain,
! [SV5: $i] :
( ( ! [SY676: $i] :
( ~ ( relation @ SY676 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SY676 ) )
= ( set_intersection2 @ ( relation_rng @ SY676 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1203,plain,
! [SV6: $i] :
( ( ! [SY677: $i,SY678: $i,SY679: $i] :
( ~ ( subset @ SV6 @ SY677 )
| ~ ( subset @ SY678 @ SY679 )
| ( subset @ ( cartesian_product2 @ SV6 @ SY678 ) @ ( cartesian_product2 @ SY677 @ SY679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1204,plain,
! [SV7: $i] :
( ( ! [SY680: $i] :
( ~ ( subset @ SV7 @ SY680 )
| ( ( set_union2 @ SV7 @ SY680 )
= SY680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1205,plain,
! [SV8: $i] :
( ( ! [SY681: $i,SY682: $i] :
( ~ ( relation @ SY682 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV8 @ SY682 ) @ SY681 )
= ( relation_rng_restriction @ SV8 @ ( relation_dom_restriction @ SY682 @ SY681 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1206,plain,
! [SV9: $i] :
( ( ! [SY683: $i] :
( ~ ( relation @ SY683 )
| ( subset @ ( relation_image @ SY683 @ SV9 ) @ ( relation_rng @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1207,plain,
! [SV10: $i] :
( ( ! [SY684: $i] :
( ~ ( relation @ SY684 )
| ( ( relation_image @ SY684 @ SV10 )
= ( relation_image @ SY684 @ ( set_intersection2 @ ( relation_dom @ SY684 ) @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1208,plain,
! [SV11: $i] :
( ( ! [SY685: $i] :
( ~ ( relation @ SY685 )
| ~ ( subset @ SV11 @ ( relation_dom @ SY685 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SY685 @ ( relation_image @ SY685 @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1209,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( ( relation_image @ SV12 @ ( relation_dom @ SV12 ) )
= ( relation_rng @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1210,plain,
! [SV13: $i] :
( ( ! [SY686: $i] :
( ~ ( relation @ SY686 )
| ( subset @ ( relation_inverse_image @ SY686 @ SV13 ) @ ( relation_dom @ SY686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1211,plain,
! [SV14: $i] :
( ( ! [SY687: $i,SY688: $i] :
( ~ ( relation @ SY688 )
| ~ ( subset @ SV14 @ SY687 )
| ( subset @ ( relation_inverse_image @ SY688 @ SV14 ) @ ( relation_inverse_image @ SY688 @ SY687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1212,plain,
! [SV15: $i] :
( ( ! [SY689: $i] :
( ~ ( relation @ SY689 )
| ( ( relation_restriction @ SY689 @ SV15 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV15 @ SY689 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1213,plain,
! [SV16: $i] :
( ( ! [SY690: $i] : ( subset @ ( set_intersection2 @ SV16 @ SY690 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1214,plain,
! [SV17: $i] :
( ( ! [SY691: $i] :
( ~ ( relation @ SY691 )
| ( ( relation_restriction @ SY691 @ SV17 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SY691 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1215,plain,
! [SV18: $i] :
( ( ! [SY692: $i,SY693: $i] :
( ~ ( subset @ SV18 @ SY692 )
| ~ ( subset @ SV18 @ SY693 )
| ( subset @ SV18 @ ( set_intersection2 @ SY692 @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1216,plain,
! [SV19: $i] :
( ( ! [SY694: $i,SY695: $i] :
( ~ ( subset @ SV19 @ SY694 )
| ~ ( subset @ SY694 @ SY695 )
| ( subset @ SV19 @ SY695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1217,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1218,plain,
! [SV21: $i] :
( ( ! [SY696: $i] :
( ~ ( subset @ SV21 @ SY696 )
| ! [SY697: $i] : ( subset @ ( set_intersection2 @ SV21 @ SY697 ) @ ( set_intersection2 @ SY696 @ SY697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1219,plain,
! [SV22: $i] :
( ( ! [SY698: $i] :
( ~ ( subset @ SV22 @ SY698 )
| ( ( set_intersection2 @ SV22 @ SY698 )
= SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1220,plain,
! [SV23: $i] :
( ( subset @ empty_set @ SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1221,plain,
! [SV24: $i] :
( ( ! [SY699: $i] :
( ~ ( subset @ SV24 @ SY699 )
| ! [SY700: $i] : ( subset @ ( set_difference @ SV24 @ SY700 ) @ ( set_difference @ SY699 @ SY700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1222,plain,
! [SV25: $i] :
( ( ! [SY701: $i] : ( subset @ ( set_difference @ SV25 @ SY701 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1223,plain,
! [SV26: $i] :
( ( ~ ( subset @ SV26 @ empty_set )
| ( SV26 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1224,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ! [SY702: $i] :
( ~ ( relation @ SY702 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SY702 ) ) @ ( relation_dom @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1225,plain,
! [SV28: $i] :
( ( ~ ( relation @ SV28 )
| ! [SY703: $i] :
( ~ ( relation @ SY703 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SY703 ) ) @ ( relation_rng @ SY703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1226,plain,
! [SV29: $i] :
( ( ! [SY704: $i] :
( ~ ( subset @ SV29 @ SY704 )
| ( SY704
= ( set_union2 @ SV29 @ ( set_difference @ SY704 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1227,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SY705 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SY705 ) )
= ( relation_dom @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1228,plain,
! [SV31: $i] :
( ( ~ ( relation @ SV31 )
| ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SY706 ) )
| ( ( relation_rng @ ( relation_composition @ SY706 @ SV31 ) )
= ( relation_rng @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1229,plain,
! [SV32: $i] :
( ( ! [SY707: $i] :
( ~ ( proper_subset @ SY707 @ SV32 )
| ~ ( subset @ SV32 @ SY707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1230,plain,
! [SV33: $i] :
( ( ! [SY708: $i,SY709: $i] :
( ~ ( disjoint @ SY708 @ SY709 )
| ~ ( subset @ SV33 @ SY708 )
| ( disjoint @ SV33 @ SY709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1231,plain,
! [SV34: $i] :
( ( ! [SY710: $i] :
( ~ ( subset @ ( singleton @ SV34 ) @ ( singleton @ SY710 ) )
| ( SV34 = SY710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1232,plain,
! [SV35: $i] :
( ( ! [SY711: $i] : ( subset @ SV35 @ ( set_union2 @ SV35 @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1233,plain,
! [SV36: $i] :
( ( ! [SY712: $i] :
( ~ ( relation @ SY712 )
| ( subset @ ( relation_dom_restriction @ SY712 @ SV36 ) @ SY712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1234,plain,
! [SV37: $i] :
( ( ! [SY713: $i,SY714: $i] :
( ~ ( subset @ SV37 @ SY713 )
| ~ ( subset @ SY714 @ SY713 )
| ( subset @ ( set_union2 @ SV37 @ SY714 ) @ SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1235,plain,
! [SV38: $i] :
( ( ! [SY715: $i] :
( ~ ( relation @ SY715 )
| ( ( relation_dom @ ( relation_dom_restriction @ SY715 @ SV38 ) )
= ( set_intersection2 @ ( relation_dom @ SY715 ) @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1236,plain,
! [SV39: $i] :
( ( ! [SY716: $i] :
( ~ ( in @ SV39 @ SY716 )
| ( subset @ SV39 @ ( union @ SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1237,plain,
! [SV40: $i] :
( ( ! [SY717: $i] :
( ~ ( relation @ SY717 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY717 @ SV40 ) ) @ ( relation_rng @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1238,plain,
! [SV41: $i] :
( ( ~ ( empty @ SV41 )
| ( relation @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1239,plain,
! [SV42: $i] :
( ( ~ ( relation @ SV42 )
| ! [SY718: $i] : ( relation @ ( relation_restriction @ SV42 @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1240,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ( relation @ ( relation_inverse @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1241,plain,
! [SV44: $i] :
( ( ! [SY719: $i] :
( ~ ( relation @ SV44 )
| ~ ( relation @ SY719 )
| ( relation @ ( relation_composition @ SV44 @ SY719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1242,plain,
! [SV45: $i] :
( ( relation @ ( identity_relation @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1243,plain,
! [SV46: $i] :
( ( ~ ( relation @ SV46 )
| ! [SY720: $i] : ( relation @ ( relation_dom_restriction @ SV46 @ SY720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1244,plain,
! [SV47: $i] :
( ( ! [SY721: $i] :
( ~ ( relation @ SY721 )
| ( relation @ ( relation_rng_restriction @ SV47 @ SY721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1245,plain,
! [SV48: $i] :
( ( ! [SY722: $i] :
( ~ ( relation @ SV48 )
| ~ ( relation @ SY722 )
| ( relation @ ( set_intersection2 @ SV48 @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1246,plain,
! [SV49: $i] :
( ( ! [SY723: $i] :
( ~ ( relation @ SV49 )
| ~ ( relation @ SY723 )
| ( relation @ ( set_union2 @ SV49 @ SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1247,plain,
! [SV50: $i] :
( ( ! [SY724: $i] :
( ~ ( relation @ SV50 )
| ~ ( relation @ SY724 )
| ( relation @ ( set_difference @ SV50 @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1248,plain,
! [SV51: $i] :
( ( ( empty @ SV51 )
| ~ ( relation @ SV51 )
| ~ ( empty @ ( relation_dom @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1249,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
| ~ ( relation @ SV52 )
| ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1250,plain,
! [SV53: $i] :
( ( ~ ( relation @ SV53 )
| ( ( relation_inverse @ ( relation_inverse @ SV53 ) )
= SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1251,plain,
! [SV54: $i] :
( ( subset @ SV54 @ SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1252,plain,
! [SV55: $i] :
( ( ( ( singleton @ SV55 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1253,plain,
! [SV56: $i] :
( ( ! [SY725: $i] :
( ~ ( in @ SV56 @ SY725 )
| ( ( set_union2 @ ( singleton @ SV56 ) @ SY725 )
= SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1254,plain,
! [SV57: $i] :
( ( ! [SY726: $i] :
( ~ ( disjoint @ ( singleton @ SV57 ) @ SY726 )
| ~ ( in @ SV57 @ SY726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1255,plain,
! [SV58: $i] :
( ( ! [SY727: $i] :
( ( in @ SV58 @ SY727 )
| ( disjoint @ ( singleton @ SV58 ) @ SY727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1256,plain,
! [SV59: $i] :
( ( ! [SY728: $i] :
( ~ ( element @ SY728 @ ( powerset @ SV59 ) )
| ! [SY729: $i] :
( ~ ( in @ SY729 @ SY728 )
| ( in @ SY729 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1257,plain,
! [SV60: $i] :
( ( ! [SY730: $i] :
( ~ ( subset @ SV60 @ SY730 )
| ! [SY731: $i] :
( ( in @ SY731 @ SV60 )
| ( subset @ SV60 @ ( set_difference @ SY730 @ ( singleton @ SY731 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1258,plain,
! [SV61: $i] :
( ( in @ SV61 @ ( succ @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1259,plain,
! [SV62: $i] :
( ( ! [SY732: $i,SY733: $i,SY734: $i] :
( ( SV62 = SY734 )
| ( SV62 = SY733 )
| ( ( unordered_pair @ SV62 @ SY732 )
!= ( unordered_pair @ SY733 @ SY734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1260,plain,
! [SV63: $i] :
( ( ! [SY735: $i] :
( ~ ( function @ SY735 )
| ~ ( relation @ SY735 )
| ( subset @ ( relation_image @ SY735 @ ( relation_inverse_image @ SY735 @ SV63 ) ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1261,plain,
! [SV64: $i] :
( ( ! [SY736: $i] :
( ~ ( function @ SY736 )
| ~ ( relation @ SY736 )
| ~ ( subset @ SV64 @ ( relation_rng @ SY736 ) )
| ( ( relation_image @ SY736 @ ( relation_inverse_image @ SY736 @ SV64 ) )
= SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1262,plain,
! [SV65: $i] :
( ( ~ ( relation @ SV65 )
| ! [SY737: $i] :
( ~ ( relation @ SY737 )
| ( ( relation_rng @ ( relation_composition @ SV65 @ SY737 ) )
= ( relation_image @ SY737 @ ( relation_rng @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1263,plain,
! [SV66: $i] :
( ( ! [SY738: $i] :
( ~ ( relation @ SY738 )
| ( SV66 = empty_set )
| ~ ( subset @ SV66 @ ( relation_rng @ SY738 ) )
| ( ( relation_inverse_image @ SY738 @ SV66 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1264,plain,
! [SV67: $i] :
( ( ~ ( epsilon_transitive @ SV67 )
| ! [SY739: $i] :
( ~ ( ordinal @ SY739 )
| ~ ( proper_subset @ SV67 @ SY739 )
| ( in @ SV67 @ SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1265,plain,
! [SV68: $i] :
( ( ! [SY740: $i] :
( ~ ( function @ SY740 )
| ~ ( relation @ SY740 )
| ! [SY741: $i] :
( ~ ( function @ SY741 )
| ~ ( relation @ SY741 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY741 @ SY740 ) ) )
| ( ( apply @ ( relation_composition @ SY741 @ SY740 ) @ SV68 )
= ( apply @ SY740 @ ( apply @ SY741 @ SV68 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1266,plain,
! [SV69: $i] :
( ( ! [SY742: $i] :
( ~ ( function @ SY742 )
| ~ ( relation @ SY742 )
| ! [SY743: $i] :
( ~ ( function @ SY743 )
| ~ ( relation @ SY743 )
| ~ ( in @ SV69 @ ( relation_dom @ SY742 ) )
| ( ( apply @ ( relation_composition @ SY742 @ SY743 ) @ SV69 )
= ( apply @ SY743 @ ( apply @ SY742 @ SV69 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1267,plain,
! [SV70: $i] :
( ( ! [SY744: $i] :
( ~ ( ordinal @ SY744 )
| ~ ( in @ SV70 @ SY744 )
| ( ordinal @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1268,plain,
! [SV71: $i] :
( ( ~ ( ordinal @ SV71 )
| ! [SY745: $i] :
( ~ ( ordinal @ SY745 )
| ( in @ SV71 @ SY745 )
| ( SV71 = SY745 )
| ( in @ SY745 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1269,plain,
! [SV72: $i] :
( ( ! [SY746: $i] :
( ~ ( in @ SY746 @ SV72 )
| ( ( apply @ ( identity_relation @ SV72 ) @ SY746 )
= SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1270,plain,
! [SV73: $i] :
( ( ! [SY747: $i] :
( ( set_union2 @ SV73 @ ( set_difference @ SY747 @ SV73 ) )
= ( set_union2 @ SV73 @ SY747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1271,plain,
! [SV74: $i] :
( ( ! [SY748: $i,SY749: $i] :
( ~ ( in @ SV74 @ SY748 )
| ~ ( in @ SY748 @ SY749 )
| ~ ( in @ SY749 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1272,plain,
! [SV75: $i] :
( ( ! [SY750: $i] :
( ( set_difference @ ( set_union2 @ SV75 @ SY750 ) @ SY750 )
= ( set_difference @ SV75 @ SY750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1273,plain,
! [SV76: $i] :
( ( ! [SY751: $i] :
( ~ ( element @ SY751 @ ( powerset @ ( powerset @ SV76 ) ) )
| ( SY751 = empty_set )
| ( ( complements_of_subsets @ SV76 @ SY751 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1274,plain,
! [SV77: $i] :
( ( ! [SY752: $i] :
( ~ ( in @ SV77 @ SY752 )
| ( ( set_union2 @ ( singleton @ SV77 ) @ SY752 )
= SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1275,plain,
! [SV78: $i] :
( ( ! [SY753: $i] :
( ( set_difference @ SV78 @ ( set_difference @ SV78 @ SY753 ) )
= ( set_intersection2 @ SV78 @ SY753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1276,plain,
! [SV79: $i] :
( ( ( SV79 = empty_set )
| ! [SY754: $i] :
( ~ ( element @ SY754 @ ( powerset @ SV79 ) )
| ! [SY755: $i] :
( ~ ( element @ SY755 @ SV79 )
| ( in @ SY755 @ SY754 )
| ( in @ SY755 @ ( subset_complement @ SV79 @ SY754 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1277,plain,
! [SV80: $i] :
( ( ! [SY756: $i,SY757: $i] :
( ~ ( element @ SY757 @ ( powerset @ SV80 ) )
| ~ ( in @ SY756 @ ( subset_complement @ SV80 @ SY757 ) )
| ~ ( in @ SY756 @ SY757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1278,plain,
! [SV81: $i] :
( ( ~ ( relation @ SV81 )
| ( in @ ( ordered_pair @ ( sK70_B @ SV81 ) @ ( sK71_SY646 @ SV81 ) ) @ SV81 )
| ( SV81 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1279,plain,
! [SV82: $i] :
( ( ~ ( function @ SV82 )
| ~ ( relation @ SV82 )
| ~ ( one_to_one @ SV82 )
| ( one_to_one @ ( function_inverse @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1280,plain,
! [SV83: $i] :
( ( ( unordered_pair @ SV83 @ SV83 )
= ( singleton @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1281,plain,
! [SV84: $i] :
( ( ! [SY758: $i,SY759: $i] :
( ~ ( function @ SY759 )
| ~ ( relation @ SY759 )
| ~ ( in @ SY758 @ ( relation_dom @ ( relation_dom_restriction @ SY759 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY759 @ SV84 ) @ SY758 )
= ( apply @ SY759 @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1282,plain,
! [SV85: $i] :
( ( ! [SY760: $i,SY761: $i] :
( ~ ( function @ SY761 )
| ~ ( relation @ SY761 )
| ~ ( in @ SY760 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SY761 @ SV85 ) @ SY760 )
= ( apply @ SY761 @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1283,plain,
! [SV86: $i] :
( ( ! [SY762: $i] :
( ! [SY763: $i] :
( ( singleton @ SV86 )
!= ( unordered_pair @ SY762 @ SY763 ) )
| ( SV86 = SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1284,plain,
! [SV87: $i] :
( ( ! [SY764: $i] :
( ~ ( relation @ SY764 )
| ( ( relation_dom_restriction @ SY764 @ SV87 )
= ( relation_composition @ ( identity_relation @ SV87 ) @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1285,plain,
! [SV88: $i] :
( ( ( union @ ( powerset @ SV88 ) )
= SV88 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1286,plain,
! [SV89: $i] :
( ( ! [SY765: $i,SY766: $i] :
( ( ( singleton @ SV89 )
!= ( unordered_pair @ SY765 @ SY766 ) )
| ( SY765 = SY766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1287,plain,
! [SV90: $i] :
( ( ! [SY767: $i] :
( ~ ( in @ SV90 @ SY767 )
| ~ ( in @ SY767 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1288,plain,
! [SV91: $i] :
( ( ! [SY768: $i] :
( ~ ( proper_subset @ SV91 @ SY768 )
| ~ ( proper_subset @ SY768 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1289,plain,
! [SV92: $i] :
( ( ~ ( empty @ SV92 )
| ( function @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1290,plain,
! [SV93: $i] :
( ( ~ ( epsilon_connected @ SV93 )
| ~ ( epsilon_transitive @ SV93 )
| ( ordinal @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1291,plain,
! [SV94: $i] :
( ( ! [SY769: $i] :
( ( unordered_pair @ SV94 @ SY769 )
= ( unordered_pair @ SY769 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1292,plain,
! [SV95: $i] :
( ( ! [SY770: $i] :
( ( set_union2 @ SV95 @ SY770 )
= ( set_union2 @ SY770 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1293,plain,
! [SV96: $i] :
( ( ! [SY771: $i] :
( ( set_intersection2 @ SV96 @ SY771 )
= ( set_intersection2 @ SY771 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1294,plain,
! [SV97: $i] :
( ( ! [SY772: $i] :
( ~ ( ordinal @ SV97 )
| ~ ( ordinal @ SY772 )
| ( ordinal_subset @ SV97 @ SY772 )
| ( ordinal_subset @ SY772 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1295,plain,
! [SV98: $i] :
( ( ( succ @ SV98 )
= ( set_union2 @ SV98 @ ( singleton @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1296,plain,
! [SV99: $i] :
( ( ! [SY773: $i] :
( ~ ( element @ SY773 @ ( powerset @ SV99 ) )
| ( ( subset_complement @ SV99 @ SY773 )
= ( set_difference @ SV99 @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1297,plain,
! [SV100: $i] :
( ( ! [SY774: $i] :
( ( ordered_pair @ SV100 @ SY774 )
= ( unordered_pair @ ( unordered_pair @ SV100 @ SY774 ) @ ( singleton @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1298,plain,
! [SV101: $i] :
( ( ~ ( relation @ SV101 )
| ( ( relation_field @ SV101 )
= ( set_union2 @ ( relation_dom @ SV101 ) @ ( relation_rng @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1299,plain,
! [SV102: $i] :
( ( ~ ( relation @ SV102 )
| ! [SY775: $i] :
( ( relation_restriction @ SV102 @ SY775 )
= ( set_intersection2 @ SV102 @ ( cartesian_product2 @ SY775 @ SY775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1300,plain,
! [SV103: $i] :
( ( ~ ( function @ SV103 )
| ~ ( relation @ SV103 )
| ~ ( one_to_one @ SV103 )
| ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1301,plain,
! [SV104: $i] :
( ( element @ ( cast_to_subset @ SV104 ) @ ( powerset @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1302,plain,
! [SV105: $i] :
( ( ! [SY776: $i] :
( ~ ( element @ SY776 @ ( powerset @ SV105 ) )
| ( element @ ( subset_complement @ SV105 @ SY776 ) @ ( powerset @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1303,plain,
! [SV106: $i] :
( ( ! [SY777: $i] :
( ~ ( element @ SY777 @ ( powerset @ ( powerset @ SV106 ) ) )
| ( element @ ( union_of_subsets @ SV106 @ SY777 ) @ ( powerset @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1304,plain,
! [SV107: $i] :
( ( ! [SY778: $i] :
( ~ ( element @ SY778 @ ( powerset @ ( powerset @ SV107 ) ) )
| ( element @ ( meet_of_subsets @ SV107 @ SY778 ) @ ( powerset @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1305,plain,
! [SV108: $i] :
( ( ! [SY779: $i,SY780: $i] :
( ~ ( element @ SY779 @ ( powerset @ SV108 ) )
| ~ ( element @ SY780 @ ( powerset @ SV108 ) )
| ( element @ ( subset_difference @ SV108 @ SY779 @ SY780 ) @ ( powerset @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1306,plain,
! [SV109: $i] :
( ( ! [SY781: $i] :
( ~ ( element @ SY781 @ ( powerset @ ( powerset @ SV109 ) ) )
| ( element @ ( complements_of_subsets @ SV109 @ SY781 ) @ ( powerset @ ( powerset @ SV109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1307,plain,
! [SV110: $i] :
( ( element @ ( sK12_B @ SV110 ) @ SV110 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1308,plain,
! [SV111: $i] :
( ( ~ ( empty @ ( succ @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1309,plain,
! [SV112: $i] :
( ( ~ ( empty @ ( powerset @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1310,plain,
! [SV113: $i] :
( ( ! [SY782: $i] :
~ ( empty @ ( ordered_pair @ SV113 @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1311,plain,
! [SV114: $i] :
( ( ~ ( empty @ ( singleton @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1312,plain,
! [SV115: $i] :
( ( ( empty @ SV115 )
| ! [SY783: $i] :
~ ( empty @ ( set_union2 @ SV115 @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1313,plain,
! [SV116: $i] :
( ( ! [SY784: $i] :
~ ( empty @ ( unordered_pair @ SV116 @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1314,plain,
! [SV117: $i] :
( ( ( empty @ SV117 )
| ! [SY785: $i] :
~ ( empty @ ( set_union2 @ SY785 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1315,plain,
! [SV118: $i] :
( ( ! [SY786: $i] :
( ( empty @ SV118 )
| ( empty @ SY786 )
| ~ ( empty @ ( cartesian_product2 @ SV118 @ SY786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1316,plain,
! [SV119: $i] :
( ( ( set_union2 @ SV119 @ SV119 )
= SV119 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1317,plain,
! [SV120: $i] :
( ( ( set_intersection2 @ SV120 @ SV120 )
= SV120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1318,plain,
! [SV121: $i] :
( ( ! [SY787: $i] :
( ~ ( element @ SY787 @ ( powerset @ SV121 ) )
| ( ( subset_complement @ SV121 @ ( subset_complement @ SV121 @ SY787 ) )
= SY787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1319,plain,
! [SV122: $i] :
( ( ! [SY788: $i] :
( ~ ( element @ SY788 @ ( powerset @ ( powerset @ SV122 ) ) )
| ( ( complements_of_subsets @ SV122 @ ( complements_of_subsets @ SV122 @ SY788 ) )
= SY788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1320,plain,
! [SV123: $i] :
( ( ~ ( proper_subset @ SV123 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1321,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1322,plain,
! [SV124: $i] :
( ( ! [SY789: $i] :
( ~ ( element @ SY789 @ ( powerset @ ( powerset @ SV124 ) ) )
| ( ( union_of_subsets @ SV124 @ SY789 )
= ( union @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1323,plain,
! [SV125: $i] :
( ( ! [SY790: $i,SY791: $i] :
( ~ ( element @ SY790 @ ( powerset @ SV125 ) )
| ~ ( element @ SY791 @ ( powerset @ SV125 ) )
| ( ( subset_difference @ SV125 @ SY790 @ SY791 )
= ( set_difference @ SY790 @ SY791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1324,plain,
! [SV126: $i] :
( ( ~ ( ordinal @ SV126 )
| ! [B: $i] :
~ ( ordinal @ B )
| ( ordinal_subset @ SV126 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1325,plain,
! [SV127: $i] :
( ( ! [SY793: $i] :
( ~ ( disjoint @ SV127 @ SY793 )
| ( disjoint @ SY793 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1326,plain,
! [SV128: $i] :
( ( ( set_union2 @ SV128 @ empty_set )
= SV128 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1327,plain,
! [SV129: $i] :
( ( ! [SY794: $i] :
( ~ ( in @ SV129 @ SY794 )
| ( element @ SV129 @ SY794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1328,plain,
! [SV130: $i] :
( ( ( set_intersection2 @ SV130 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1329,plain,
! [SV131: $i] :
( ( ! [SY795: $i] :
( ~ ( element @ SV131 @ SY795 )
| ( empty @ SY795 )
| ( in @ SV131 @ SY795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1330,plain,
! [SV132: $i] :
( ( ( set_difference @ SV132 @ empty_set )
= SV132 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1331,plain,
! [SV133: $i] :
( ( ( set_difference @ empty_set @ SV133 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1332,plain,
! [SV134: $i] :
( ( ! [SY796: $i,SY797: $i] :
( ~ ( element @ SY796 @ ( powerset @ SY797 ) )
| ~ ( in @ SV134 @ SY796 )
| ( element @ SV134 @ SY797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1333,plain,
! [SV135: $i] :
( ( ! [SY798: $i,SY799: $i] :
( ~ ( element @ SY798 @ ( powerset @ SY799 ) )
| ~ ( in @ SV135 @ SY798 )
| ~ ( empty @ SY799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1334,plain,
! [SV136: $i] :
( ( ~ ( empty @ SV136 )
| ( SV136 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1335,plain,
! [SV137: $i] :
( ( ! [SY800: $i] :
( ~ ( empty @ SY800 )
| ~ ( in @ SV137 @ SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1336,plain,
! [SV138: $i] :
( ( ! [SY801: $i] :
( ( SV138 = SY801 )
| ~ ( empty @ SV138 )
| ~ ( empty @ SY801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1337,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY609 ) ) @ ( relation_dom @ sK2_SY609 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1338,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK74_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1339,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)],[1077]) ).
thf(1340,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)],[1078]) ).
thf(1341,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1342,plain,
! [SV139: $i] :
( ( ~ ( relation @ SV139 )
| ~ ( ~ ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) )
| ~ ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1343,plain,
! [SV140: $i] :
( ( ~ ( relation @ SV140 )
| ~ ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) )
| ~ ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1344,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)],[1082]) ).
thf(1345,plain,
! [SV141: $i] :
( ( ~ ( relation @ SV141 )
| ~ ( ~ ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) )
| ~ ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1346,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK108_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK108_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK106_C @ SX1 @ SX0 ) @ ( sK107_SY668 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1347,plain,
! [SV142: $i] :
( ( ! [SY818: $i] :
( ~ ( relation @ SY818 )
| ~ ( ~ ! [SY819: $i] :
( ~ ( relation @ SY819 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY819 @ SY818 @ SV142 ) @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) ) @ SY818 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY819 @ SY818 @ SV142 ) @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) ) @ SY819 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY819 @ SY818 @ SV142 ) @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) ) @ SY819 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY819 @ SY818 @ SV142 ) @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) ) @ SY818 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY819 @ SY818 @ SV142 ) @ ( sK110_SY671 @ SY819 @ SY818 @ SV142 ) ) @ SY819 ) ) ) )
| ( SY819
= ( relation_rng_restriction @ SV142 @ SY818 ) ) )
| ~ ! [SY820: $i] :
( ~ ( relation @ SY820 )
| ( SY820
!= ( relation_rng_restriction @ SV142 @ SY818 ) )
| ~ ( ~ ! [SY821: $i,SY822: $i] :
( ~ ( in @ SY822 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SY818 )
| ( in @ ( ordered_pair @ SY821 @ SY822 ) @ SY820 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY820 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY820 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY818 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1348,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1349,plain,
! [SV143: $i] :
( ( ! [SY827: $i] :
~ ( ~ ! [SY828: $i,SY829: $i] :
( ~ ( in @ SV143 @ SY828 )
| ~ ( in @ SY827 @ SY829 )
| ( in @ ( ordered_pair @ SV143 @ SY827 ) @ ( cartesian_product2 @ SY828 @ SY829 ) ) )
| ~ ~ ( ~ ! [SY830: $i] :
( ! [SY831: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SY827 ) @ ( cartesian_product2 @ SY830 @ SY831 ) )
| ( in @ SV143 @ SY830 ) )
| ~ ! [SY832: $i,SY833: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SY827 ) @ ( cartesian_product2 @ SY832 @ SY833 ) )
| ( in @ SY827 @ SY833 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1350,plain,
! [SV144: $i] :
( ( ~ ( ~ ! [SY834: $i] :
( ~ ( subset @ SY834 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SY834 @ ( sK87_B @ SV144 ) )
| ( in @ SY834 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1351,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1352,plain,
! [SV145: $i] :
( ( ~ ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV145 @ SY839 ) ) )
| ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV145 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV145 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV145 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1353,plain,
! [SV146: $i] :
( ( ~ ( relation @ SV146 )
| ~ ( ~ ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) )
| ~ ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1354,plain,
! [SV147: $i] :
( ( ~ ( relation @ SV147 )
| ~ ( ~ ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) )
| ~ ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1355,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK76_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK76_C @ SX1 @ SX0 ) )
!= ( sK76_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)],[1093]) ).
thf(1356,plain,
! [SV148: $i] :
( ( ( empty @ SV148 )
| ~ ( ~ ( element @ ( sK10_B @ SV148 ) @ ( powerset @ SV148 ) )
| ~ ~ ( empty @ ( sK10_B @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1357,plain,
! [SV149: $i] :
( ( ~ ( relation @ SV149 )
| ~ ( ~ ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) )
| ~ ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1358,plain,
! [SV150: $i] :
( ( ~ ( ~ ! [SY860: $i] :
( ~ ( subset @ SV150 @ SY860 )
| ! [SY861: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY861 ) @ ( cartesian_product2 @ SY860 @ SY861 ) ) )
| ~ ! [SY862: $i] :
( ~ ( subset @ SV150 @ SY862 )
| ! [SY863: $i] : ( subset @ ( cartesian_product2 @ SY863 @ SV150 ) @ ( cartesian_product2 @ SY863 @ SY862 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1359,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1360,plain,
! [SV151: $i] :
( ( ~ ( relation @ SV151 )
| ~ ( ~ ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) )
| ~ ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1361,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1362,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1363,plain,
! [SV152: $i] :
( ( ! [SY870: $i] :
( ~ ( ~ ( ~ ( in @ ( sK4_C @ SY870 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SY870 @ SV152 ) @ SY870 ) )
| ~ ( ( in @ ( sK4_C @ SY870 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SY870 @ SV152 ) @ SY870 ) ) )
| ( SV152 = SY870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1364,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)],[1102]) ).
thf(1365,plain,
( ( ~ ~ ( ~ ( function @ sK91_A )
| ~ ( relation @ sK91_A ) )
| ~ ( one_to_one @ sK91_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1366,plain,
! [SV153: $i] :
( ( ~ ( ~ ! [SY871: $i,SY872: $i] :
( ~ ( ~ ( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV153 )
| ~ ( in @ SY874 @ SY871 )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ~ ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) @ SY871 ) )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) ) )
| ( SY872
= ( cartesian_product2 @ SV153 @ SY871 ) ) )
| ~ ! [SY875: $i,SY876: $i] :
( ( SY876
!= ( cartesian_product2 @ SV153 @ SY875 ) )
| ~ ( ~ ! [SY877: $i] :
( ! [SY878: $i,SY879: $i] :
( ~ ( in @ SY878 @ SV153 )
| ~ ( in @ SY879 @ SY875 )
| ( SY877
!= ( ordered_pair @ SY878 @ SY879 ) ) )
| ( in @ SY877 @ SY876 ) )
| ~ ! [SY880: $i] :
( ~ ( in @ SY880 @ SY876 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) @ SY875 ) )
| ( SY880
!= ( ordered_pair @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1367,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1368,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK48_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1369,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1370,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1371,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)],[1109]) ).
thf(1372,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1373,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)],[1111]) ).
thf(1374,plain,
! [SV154: $i] :
( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 )
| ~ ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1375,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)],[1113]) ).
thf(1376,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK21_SY619 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK20_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK21_SY619 @ SX0 ) ) ) )
| ~ ( ( ( sK20_B @ SX0 )
!= ( sK21_SY619 @ 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)],[1114]) ).
thf(1377,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1378,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK83_SY653 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK82_B @ SX0 )
!= ( sK83_SY653 @ 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)],[1116]) ).
thf(1379,plain,
! [SV155: $i] :
( ( ~ ( ~ ! [SY889: $i,SY890: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) ) ) )
| ( SY890
= ( set_difference @ SV155 @ SY889 ) ) )
| ~ ! [SY891: $i,SY892: $i] :
( ( SY892
!= ( set_difference @ SV155 @ SY891 ) )
| ~ ( ~ ! [SY893: $i] :
( ~ ( in @ SY893 @ SV155 )
| ( in @ SY893 @ SY891 )
| ( in @ SY893 @ SY892 ) )
| ~ ~ ( ~ ! [SY894: $i] :
( ~ ( in @ SY894 @ SY892 )
| ( in @ SY894 @ SV155 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY892 )
| ~ ( in @ SX3 @ SY891 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY627 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK35_SY627 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK33_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1381,plain,
! [SV156: $i] :
( ( ! [SY896: $i] :
~ ( ~ ! [SY897: $i,SY898: $i] :
( ~ ( relation @ SY898 )
| ~ ( in @ SV156 @ SY897 )
| ~ ( in @ ( ordered_pair @ SV156 @ SY896 ) @ SY898 )
| ( in @ ( ordered_pair @ SV156 @ SY896 ) @ ( relation_composition @ ( identity_relation @ SY897 ) @ SY898 ) ) )
| ~ ~ ( ~ ! [SY899: $i,SY900: $i] :
( ~ ( relation @ SY900 )
| ~ ( in @ ( ordered_pair @ SV156 @ SY896 ) @ ( relation_composition @ ( identity_relation @ SY899 ) @ SY900 ) )
| ( in @ SV156 @ SY899 ) )
| ~ ! [SY901: $i,SY902: $i] :
( ~ ( relation @ SY902 )
| ~ ( in @ ( ordered_pair @ SV156 @ SY896 ) @ ( relation_composition @ ( identity_relation @ SY901 ) @ SY902 ) )
| ( in @ ( ordered_pair @ SV156 @ SY896 ) @ SY902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1382,plain,
( ( ~ ( empty @ sK94_A )
| ~ ( relation @ sK94_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK49_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK49_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1384,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1385,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1386,plain,
! [SV157: $i] :
( ( ~ ( function @ SV157 )
| ~ ( relation @ SV157 )
| ~ ( one_to_one @ SV157 )
| ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1387,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)],[1125]) ).
thf(1388,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)],[1126]) ).
thf(1389,plain,
( ( ~ ( relation @ sK90_A )
| ~ ( relation_empty_yielding @ sK90_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1390,plain,
! [SV158: $i] :
( ( ~ ( ordinal @ SV158 )
| ~ ( ~ ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) )
| ~ ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1391,plain,
! [SV159: $i] :
( ( ~ ( ~ ! [SY916: $i,SY917: $i] :
( ~ ( relation @ SY917 )
| ! [SY918: $i] :
( ~ ( in @ SY918 @ ( relation_rng @ SY917 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY918 ) @ SY917 )
| ~ ( in @ SY918 @ SY916 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SY917 @ SY916 ) ) )
| ~ ! [SY919: $i,SY920: $i] :
( ~ ( relation @ SY920 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SY920 @ SY919 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ ( relation_rng @ SY920 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SY920 @ SY919 @ SV159 ) ) @ SY920 ) )
| ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ SY919 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1392,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1393,plain,
! [SV160: $i] :
( ( ~ ( relation @ SV160 )
| ~ ( ~ ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) )
| ~ ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1394,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1395,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)],[1133]) ).
thf(1396,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1397,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1398,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1399,plain,
! [SV161: $i] :
( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( relation @ SY924 )
| ~ ( in @ SV161 @ SY924 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SY923 @ SY923 ) )
| ( in @ SV161 @ ( relation_restriction @ SY924 @ SY923 ) ) )
| ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1400,plain,
! [SV162: $i] :
( ( ~ ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( relation @ SY930 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY929 ) @ SY930 )
| ( in @ SV162 @ ( relation_field @ SY930 ) ) )
| ~ ! [SY931: $i,SY932: $i] :
( ~ ( relation @ SY932 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY931 ) @ SY932 )
| ( in @ SY931 @ ( relation_field @ SY932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1401,plain,
! [SV163: $i] :
( ( ! [SY933: $i] :
~ ( ~ ! [SY934: $i] :
( ! [SY935: $i] :
( ( ordered_pair @ SV163 @ SY933 )
!= ( ordered_pair @ SY934 @ SY935 ) )
| ( SV163 = SY934 ) )
| ~ ! [SY936: $i,SY937: $i] :
( ( ( ordered_pair @ SV163 @ SY933 )
!= ( ordered_pair @ SY936 @ SY937 ) )
| ( SY933 = SY937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1402,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1403,plain,
! [SV164: $i] :
( ( ~ ( ~ ! [SY938: $i,SY939: $i] :
( ~ ( function @ SY939 )
| ~ ( relation @ SY939 )
| ~ ( in @ SY938 @ ( relation_dom @ SY939 ) )
| ~ ( in @ SY938 @ SV164 )
| ( in @ SY938 @ ( relation_dom @ ( relation_dom_restriction @ SY939 @ SV164 ) ) ) )
| ~ ~ ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) )
| ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1404,plain,
! [SV165: $i] :
( ( ! [SY944: $i] :
( ~ ( ~ ! [SY945: $i] :
( ~ ( in @ SY945 @ SY944 )
| ~ ( in @ SY945 @ ( sK3_C @ SY944 @ SV165 ) ) )
| ~ ( in @ ( sK3_C @ SY944 @ SV165 ) @ SY944 ) )
| ~ ( in @ SV165 @ SY944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1405,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY946: $i,SY947: $i] :
( ~ ( relation @ SY947 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY946 ) @ SY947 )
| ( in @ SV166 @ ( relation_dom @ SY947 ) ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( relation @ SY949 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY948 ) @ SY949 )
| ( in @ SY948 @ ( relation_rng @ SY949 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1406,plain,
! [SV167: $i] :
( ( ~ ( ~ ! [SY950: $i] :
( ~ ( subset @ SY950 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SY950 @ ( sK80_B @ SV167 ) )
| ( in @ SY950 @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1407,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK104_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK104_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1408,plain,
! [SV168: $i] :
( ( ~ ( ~ ! [SY954: $i,SY955: $i] :
( ~ ( function @ SY955 )
| ~ ( relation @ SY955 )
| ( SY954
!= ( apply @ SY955 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SY955 ) )
| ( in @ ( ordered_pair @ SV168 @ SY954 ) @ SY955 ) )
| ~ ~ ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) )
| ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1409,plain,
( ( ~ ~ ( ~ ( empty @ sK93_A )
| ~ ( relation @ sK93_A ) )
| ~ ( function @ sK93_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1410,plain,
! [SV169: $i] :
( ( ~ ( function @ SV169 )
| ~ ( relation @ SV169 )
| ~ ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1411,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1412,plain,
! [SV170: $i] :
( ( ~ ( function @ SV170 )
| ~ ( relation @ SV170 )
| ~ ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1413,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK11_A )
| ~ ( epsilon_transitive @ sK11_A ) )
| ~ ( ordinal @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1414,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) )
| ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1415,plain,
! [SV171: $i] :
( ( ~ ( ~ ! [SY975: $i,SY976: $i] :
( ~ ( relation @ SY976 )
| ~ ( in @ SV171 @ SY975 )
| ~ ( in @ SV171 @ ( relation_dom @ SY976 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY976 @ SY975 ) ) ) )
| ~ ~ ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) )
| ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1416,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1417,plain,
( ( ~ ~ ( empty @ sK92_A )
| ~ ( relation @ sK92_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1418,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1419,plain,
! [SV172: $i] :
( ( ~ ( relation @ SV172 )
| ! [SY981: $i] :
( ~ ( relation @ SY981 )
| ~ ( ~ ! [SY982: $i] :
( ~ ( relation @ SY982 )
| ~ ( ~ ( ! [SY983: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ SY983 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY983 @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) ) )
| ( SY982
= ( relation_composition @ SV172 @ SY981 ) ) )
| ~ ! [SY984: $i] :
( ~ ( relation @ SY984 )
| ( SY984
!= ( relation_composition @ SV172 @ SY981 ) )
| ~ ( ~ ! [SY985: $i,SY986: $i] :
( ! [SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY985 @ SY987 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY987 @ SY986 ) @ SY981 ) )
| ( in @ ( ordered_pair @ SY985 @ SY986 ) @ SY984 ) )
| ~ ! [SY988: $i,SY989: $i] :
( ~ ( in @ ( ordered_pair @ SY988 @ SY989 ) @ SY984 )
| ~ ( ~ ( in @ ( ordered_pair @ SY988 @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) @ SY989 ) @ SY981 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1420,plain,
! [SV173: $i] :
( ( ~ ( relation @ SV173 )
| ~ ( ~ ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) )
| ~ ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1421,plain,
! [SV174: $i] :
( ( ! [SY996: $i] :
~ ( ~ ! [SY997: $i,SY998: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 ) @ SY998 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
!= SY997 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 ) @ SY998 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 ) @ SY998 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
!= SY996 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 ) @ SY998 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
= SY997 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY998 @ SY997 @ SY996 @ SV174 )
= SY996 ) ) )
| ( SY998
= ( unordered_triple @ SV174 @ SY996 @ SY997 ) ) )
| ~ ! [SY999: $i,SY1000: $i] :
( ( SY1000
!= ( unordered_triple @ SV174 @ SY996 @ SY999 ) )
| ~ ( ~ ! [SY1001: $i] :
( ~ ( in @ SY1001 @ SY1000 )
| ( SY1001 = SY999 )
| ( SY1001 = SV174 )
| ( SY1001 = SY996 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY999 )
| ( in @ SX4 @ SY1000 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1000 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SY996 )
| ( in @ SX4 @ SY1000 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1422,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)],[1160]) ).
thf(1423,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1424,plain,
! [SV175: $i] :
( ( ~ ( ~ ! [SY1005: $i,SY1006: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SY1005 ) ) )
| ~ ( ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SV175 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SY1005 ) ) )
| ( SY1006
= ( unordered_pair @ SV175 @ SY1005 ) ) )
| ~ ! [SY1007: $i,SY1008: $i] :
( ( SY1008
!= ( unordered_pair @ SV175 @ SY1007 ) )
| ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SY1008 )
| ( SY1009 = SV175 )
| ( SY1009 = SY1007 ) )
| ~ ~ ( ~ ! [SY1010: $i] :
( ( SY1010 != SV175 )
| ( in @ SY1010 @ SY1008 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1007 )
| ( in @ SX3 @ SY1008 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1425,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK85_SY654 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK86_SY656 @ 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)],[1163]) ).
thf(1426,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1427,plain,
! [SV176: $i] :
( ( ! [SY1012: $i] :
( ~ ( function @ SY1012 )
| ~ ( relation @ SY1012 )
| ~ ( ~ ! [SY1013: $i] :
( ~ ( function @ SY1013 )
| ~ ( relation @ SY1013 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1013 ) )
| ~ ( in @ ( apply @ SY1013 @ SV176 ) @ ( relation_dom @ SY1012 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1013 @ SY1012 ) ) ) )
| ~ ~ ( ~ ! [SY1014: $i] :
( ~ ( function @ SY1014 )
| ~ ( relation @ SY1014 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1014 @ SY1012 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1014 ) ) )
| ~ ! [SY1015: $i] :
( ~ ( function @ SY1015 )
| ~ ( relation @ SY1015 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1015 @ SY1012 ) ) )
| ( in @ ( apply @ SY1015 @ SV176 ) @ ( relation_dom @ SY1012 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1428,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1429,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)],[1167]) ).
thf(1430,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1431,plain,
! [SV177: $i] :
( ( ~ ( ~ ! [SY1016: $i,SY1017: $i] :
( ~ ( in @ SV177 @ SY1017 )
| ~ ( in @ SY1016 @ SY1017 )
| ( subset @ ( unordered_pair @ SV177 @ SY1016 ) @ SY1017 ) )
| ~ ~ ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) )
| ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1432,plain,
! [SV178: $i] :
( ( ! [SY1022: $i] :
( ~ ( ordinal @ SY1022 )
| ~ ( ~ ( ordinal @ ( sK77_C @ SY1022 @ SV178 ) )
| ~ ~ ( ~ ! [SY1023: $i] :
( ~ ( ordinal @ SY1023 )
| ~ ( in @ SY1023 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SY1022 @ SV178 ) @ SY1023 ) )
| ~ ( in @ ( sK77_C @ SY1022 @ SV178 ) @ SV178 ) ) )
| ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1433,plain,
! [SV179: $i] :
( ( ! [SY1024: $i] :
( ~ ( element @ SY1024 @ ( powerset @ SV179 ) )
| ~ ( ~ ! [SY1025: $i] :
( ~ ( element @ SY1025 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SY1024 @ SY1025 )
| ( subset @ SY1024 @ ( subset_complement @ SV179 @ SY1025 ) ) )
| ~ ! [SY1026: $i] :
( ~ ( element @ SY1026 @ ( powerset @ SV179 ) )
| ~ ( subset @ SY1024 @ ( subset_complement @ SV179 @ SY1026 ) )
| ( disjoint @ SY1024 @ SY1026 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1434,plain,
! [SV180: $i] :
( ( ~ ( ~ ( element @ ( sK7_B @ SV180 ) @ ( powerset @ SV180 ) )
| ~ ( empty @ ( sK7_B @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1435,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1436,plain,
! [SV181: $i] :
( ( ~ ( relation @ SV181 )
| ~ ( ~ ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) )
| ~ ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1437,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)],[1175]) ).
thf(1438,plain,
! [SV182: $i] :
( ( ~ ( function @ SV182 )
| ~ ( relation @ SV182 )
| ~ ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1439,plain,
! [SV183: $i] :
( ( ~ ( ~ ( in @ ( sK111_B @ SV183 ) @ SV183 )
| ~ ( ~ ( ordinal @ ( sK111_B @ SV183 ) )
| ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) ) )
| ( ordinal @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1440,plain,
! [SV184: $i] :
( ( ! [SY1039: $i] :
( ~ ( function @ SY1039 )
| ~ ( relation @ SY1039 )
| ~ ( ~ ! [SY1040: $i] :
( ~ ( function @ SY1040 )
| ~ ( relation @ SY1040 )
| ~ ( ~ ( in @ ( sK69_D @ SY1040 @ SY1039 @ SV184 ) @ ( relation_dom @ SY1039 ) )
| ~ ( ( ( apply @ SY1039 @ ( sK69_D @ SY1040 @ SY1039 @ SV184 ) )
!= ( apply @ SY1040 @ ( sK69_D @ SY1040 @ SY1039 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SY1039 )
!= ( set_intersection2 @ ( relation_dom @ SY1040 ) @ SV184 ) )
| ( SY1039
= ( relation_dom_restriction @ SY1040 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1041: $i] :
( ~ ( function @ SY1041 )
| ~ ( relation @ SY1041 )
| ( SY1039
!= ( relation_dom_restriction @ SY1041 @ SV184 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SY1039 ) )
| ( ( apply @ SY1039 @ SX3 )
= ( apply @ SY1041 @ SX3 ) ) ) )
| ~ ! [SY1043: $i] :
( ~ ( function @ SY1043 )
| ~ ( relation @ SY1043 )
| ( SY1039
!= ( relation_dom_restriction @ SY1043 @ SV184 ) )
| ( ( relation_dom @ SY1039 )
= ( set_intersection2 @ ( relation_dom @ SY1043 ) @ SV184 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1441,plain,
( ( ~ ~ ( ~ ( relation @ sK89_A )
| ~ ( relation_empty_yielding @ sK89_A ) )
| ~ ( function @ sK89_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1442,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= ( sK40_SY629 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK40_SY629 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK39_B @ SX0 ) @ ( sK40_SY629 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SX0 ) @ ( sK39_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1443,plain,
! [SV185: $i] :
( ( ~ ( relation @ SV185 )
| ~ ( ~ ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) )
| ~ ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1444,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1445,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)],[1183]) ).
thf(1446,plain,
! [SV186: $i] :
( ( ~ ( ~ ! [SY1054: $i,SY1055: $i] :
( ~ ( relation @ SY1055 )
| ~ ( in @ SV186 @ SY1054 )
| ~ ( in @ SV186 @ ( relation_rng @ SY1055 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1054 @ SY1055 ) ) ) )
| ~ ~ ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) )
| ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1447,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)],[1185]) ).
thf(1448,plain,
! [SV187: $i] :
( ( ~ ( ~ ! [SY1060: $i,SY1061: $i] :
( ~ ( relation @ SY1061 )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( relation_dom @ SY1061 ) )
| ~ ( in @ ( ordered_pair @ SY1062 @ SV187 ) @ SY1061 )
| ~ ( in @ SY1062 @ SY1060 ) )
| ( in @ SV187 @ ( relation_image @ SY1061 @ SY1060 ) ) )
| ~ ! [SY1063: $i,SY1064: $i] :
( ~ ( relation @ SY1064 )
| ~ ( in @ SV187 @ ( relation_image @ SY1064 @ SY1063 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ ( relation_dom @ SY1064 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SV187 ) @ SY1064 ) )
| ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SY1063 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1449,plain,
! [SV188: $i] :
( ( ~ ( relation @ SV188 )
| ~ ( ~ ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) )
| ~ ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1450,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 )
| ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1451,plain,
! [SV189: $i] :
( ( ~ ( ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) ) ) )
| ( SY1070
= ( set_intersection2 @ SV189 @ SY1069 ) ) )
| ~ ! [SY1071: $i,SY1072: $i] :
( ( SY1072
!= ( set_intersection2 @ SV189 @ SY1071 ) )
| ~ ( ~ ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV189 )
| ~ ( in @ SY1073 @ SY1071 )
| ( in @ SY1073 @ SY1072 ) )
| ~ ~ ( ~ ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SY1072 )
| ( in @ SY1074 @ SV189 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1072 )
| ( in @ SX3 @ SY1071 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1452,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1453,plain,
! [SV190: $i] :
( ( ! [SY1076: $i] :
~ ( ~ ! [SY1077: $i,SY1078: $i] :
( ~ ( in @ SV190 @ SY1077 )
| ~ ( in @ SY1076 @ SY1078 )
| ( in @ ( ordered_pair @ SV190 @ SY1076 ) @ ( cartesian_product2 @ SY1077 @ SY1078 ) ) )
| ~ ~ ( ~ ! [SY1079: $i] :
( ! [SY1080: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SY1076 ) @ ( cartesian_product2 @ SY1079 @ SY1080 ) )
| ( in @ SV190 @ SY1079 ) )
| ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SY1076 ) @ ( cartesian_product2 @ SY1081 @ SY1082 ) )
| ( in @ SY1076 @ SY1082 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1454,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
| ~ ( epsilon_connected @ sK5_A ) )
| ~ ( ordinal @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1455,plain,
( ( ~ ( function @ sK95_A )
| ~ ( relation @ sK95_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1456,plain,
! [SV191: $i] :
( ( ! [SY1083: $i] :
( ~ ( ~ ( in @ ( sK81_C @ SY1083 @ SV191 ) @ SV191 )
| ~ ~ ( in @ ( sK81_C @ SY1083 @ SV191 ) @ SY1083 ) )
| ( element @ SV191 @ ( powerset @ SY1083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1457,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)],[1195]) ).
thf(1458,plain,
! [SV192: $i] :
( ( ~ ( relation @ SV192 )
| ~ ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) )
| ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1459,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
!= ( sK68_SY645 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
= ( sK68_SY645 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ 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)],[1197]) ).
thf(1460,plain,
! [SV193: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV193 )
| ( subset @ SV1 @ ( union @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1461,plain,
! [SV2: $i,SV194: $i] :
( ( ~ ( relation @ SV194 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV194 ) ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1462,plain,
! [SV3: $i,SV195: $i] :
( ( ~ ( relation @ SV195 )
| ( subset @ ( relation_rng_restriction @ SV3 @ SV195 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1463,plain,
! [SV4: $i,SV196: $i] :
( ( ~ ( relation @ SV196 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV196 ) ) @ ( relation_rng @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1464,plain,
! [SV5: $i,SV197: $i] :
( ( ~ ( relation @ SV197 )
| ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV197 ) )
= ( set_intersection2 @ ( relation_rng @ SV197 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1465,plain,
! [SV198: $i,SV6: $i] :
( ( ! [SY1092: $i,SY1093: $i] :
( ~ ( subset @ SV6 @ SV198 )
| ~ ( subset @ SY1092 @ SY1093 )
| ( subset @ ( cartesian_product2 @ SV6 @ SY1092 ) @ ( cartesian_product2 @ SV198 @ SY1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1466,plain,
! [SV199: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV199 )
| ( ( set_union2 @ SV7 @ SV199 )
= SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1467,plain,
! [SV200: $i,SV8: $i] :
( ( ! [SY1094: $i] :
( ~ ( relation @ SY1094 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV8 @ SY1094 ) @ SV200 )
= ( relation_rng_restriction @ SV8 @ ( relation_dom_restriction @ SY1094 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1468,plain,
! [SV9: $i,SV201: $i] :
( ( ~ ( relation @ SV201 )
| ( subset @ ( relation_image @ SV201 @ SV9 ) @ ( relation_rng @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1469,plain,
! [SV10: $i,SV202: $i] :
( ( ~ ( relation @ SV202 )
| ( ( relation_image @ SV202 @ SV10 )
= ( relation_image @ SV202 @ ( set_intersection2 @ ( relation_dom @ SV202 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1470,plain,
! [SV11: $i,SV203: $i] :
( ( ~ ( relation @ SV203 )
| ~ ( subset @ SV11 @ ( relation_dom @ SV203 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV203 @ ( relation_image @ SV203 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1471,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ( relation_image @ SV12 @ ( relation_dom @ SV12 ) )
= ( relation_rng @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1472,plain,
! [SV13: $i,SV204: $i] :
( ( ~ ( relation @ SV204 )
| ( subset @ ( relation_inverse_image @ SV204 @ SV13 ) @ ( relation_dom @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1473,plain,
! [SV205: $i,SV14: $i] :
( ( ! [SY1095: $i] :
( ~ ( relation @ SY1095 )
| ~ ( subset @ SV14 @ SV205 )
| ( subset @ ( relation_inverse_image @ SY1095 @ SV14 ) @ ( relation_inverse_image @ SY1095 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1474,plain,
! [SV15: $i,SV206: $i] :
( ( ~ ( relation @ SV206 )
| ( ( relation_restriction @ SV206 @ SV15 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV15 @ SV206 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1475,plain,
! [SV207: $i,SV16: $i] :
( ( subset @ ( set_intersection2 @ SV16 @ SV207 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1476,plain,
! [SV17: $i,SV208: $i] :
( ( ~ ( relation @ SV208 )
| ( ( relation_restriction @ SV208 @ SV17 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV208 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1477,plain,
! [SV209: $i,SV18: $i] :
( ( ! [SY1096: $i] :
( ~ ( subset @ SV18 @ SV209 )
| ~ ( subset @ SV18 @ SY1096 )
| ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SY1096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1478,plain,
! [SV210: $i,SV19: $i] :
( ( ! [SY1097: $i] :
( ~ ( subset @ SV19 @ SV210 )
| ~ ( subset @ SV210 @ SY1097 )
| ( subset @ SV19 @ SY1097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1479,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1480,plain,
! [SV211: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV211 )
| ! [SY1098: $i] : ( subset @ ( set_intersection2 @ SV21 @ SY1098 ) @ ( set_intersection2 @ SV211 @ SY1098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1481,plain,
! [SV212: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV212 )
| ( ( set_intersection2 @ SV22 @ SV212 )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1482,plain,
! [SV213: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV213 )
| ! [SY1099: $i] : ( subset @ ( set_difference @ SV24 @ SY1099 ) @ ( set_difference @ SV213 @ SY1099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1483,plain,
! [SV214: $i,SV25: $i] :
( ( subset @ ( set_difference @ SV25 @ SV214 ) @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1484,plain,
! [SV26: $i] :
( ( ( ~ ( subset @ SV26 @ empty_set ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1485,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ! [SY702: $i] :
( ~ ( relation @ SY702 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SY702 ) ) @ ( relation_dom @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1486,plain,
! [SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ! [SY703: $i] :
( ~ ( relation @ SY703 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SY703 ) ) @ ( relation_rng @ SY703 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1487,plain,
! [SV215: $i,SV29: $i] :
( ( ~ ( subset @ SV29 @ SV215 )
| ( SV215
= ( set_union2 @ SV29 @ ( set_difference @ SV215 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1488,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SY705 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SY705 ) )
= ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1489,plain,
! [SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SY706 ) )
| ( ( relation_rng @ ( relation_composition @ SY706 @ SV31 ) )
= ( relation_rng @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1490,plain,
! [SV32: $i,SV216: $i] :
( ( ~ ( proper_subset @ SV216 @ SV32 )
| ~ ( subset @ SV32 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1491,plain,
! [SV33: $i,SV217: $i] :
( ( ! [SY1100: $i] :
( ~ ( disjoint @ SV217 @ SY1100 )
| ~ ( subset @ SV33 @ SV217 )
| ( disjoint @ SV33 @ SY1100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1492,plain,
! [SV218: $i,SV34: $i] :
( ( ~ ( subset @ ( singleton @ SV34 ) @ ( singleton @ SV218 ) )
| ( SV34 = SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1493,plain,
! [SV219: $i,SV35: $i] :
( ( subset @ SV35 @ ( set_union2 @ SV35 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1494,plain,
! [SV36: $i,SV220: $i] :
( ( ~ ( relation @ SV220 )
| ( subset @ ( relation_dom_restriction @ SV220 @ SV36 ) @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1495,plain,
! [SV221: $i,SV37: $i] :
( ( ! [SY1101: $i] :
( ~ ( subset @ SV37 @ SV221 )
| ~ ( subset @ SY1101 @ SV221 )
| ( subset @ ( set_union2 @ SV37 @ SY1101 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1496,plain,
! [SV38: $i,SV222: $i] :
( ( ~ ( relation @ SV222 )
| ( ( relation_dom @ ( relation_dom_restriction @ SV222 @ SV38 ) )
= ( set_intersection2 @ ( relation_dom @ SV222 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1497,plain,
! [SV223: $i,SV39: $i] :
( ( ~ ( in @ SV39 @ SV223 )
| ( subset @ SV39 @ ( union @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1498,plain,
! [SV40: $i,SV224: $i] :
( ( ~ ( relation @ SV224 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV224 @ SV40 ) ) @ ( relation_rng @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1499,plain,
! [SV41: $i] :
( ( ( ~ ( empty @ SV41 ) )
= $true )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1500,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ! [SY718: $i] : ( relation @ ( relation_restriction @ SV42 @ SY718 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1501,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1502,plain,
! [SV225: $i,SV44: $i] :
( ( ~ ( relation @ SV44 )
| ~ ( relation @ SV225 )
| ( relation @ ( relation_composition @ SV44 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1503,plain,
! [SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ! [SY720: $i] : ( relation @ ( relation_dom_restriction @ SV46 @ SY720 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1504,plain,
! [SV47: $i,SV226: $i] :
( ( ~ ( relation @ SV226 )
| ( relation @ ( relation_rng_restriction @ SV47 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1505,plain,
! [SV227: $i,SV48: $i] :
( ( ~ ( relation @ SV48 )
| ~ ( relation @ SV227 )
| ( relation @ ( set_intersection2 @ SV48 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1506,plain,
! [SV228: $i,SV49: $i] :
( ( ~ ( relation @ SV49 )
| ~ ( relation @ SV228 )
| ( relation @ ( set_union2 @ SV49 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1507,plain,
! [SV229: $i,SV50: $i] :
( ( ~ ( relation @ SV50 )
| ~ ( relation @ SV229 )
| ( relation @ ( set_difference @ SV50 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1508,plain,
! [SV51: $i] :
( ( ( ( empty @ SV51 )
| ~ ( relation @ SV51 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1509,plain,
! [SV52: $i] :
( ( ( ( empty @ SV52 )
| ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1510,plain,
! [SV53: $i] :
( ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV53 ) )
= SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1511,plain,
! [SV55: $i] :
( ( ( singleton @ SV55 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1512,plain,
! [SV230: $i,SV56: $i] :
( ( ~ ( in @ SV56 @ SV230 )
| ( ( set_union2 @ ( singleton @ SV56 ) @ SV230 )
= SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1513,plain,
! [SV231: $i,SV57: $i] :
( ( ~ ( disjoint @ ( singleton @ SV57 ) @ SV231 )
| ~ ( in @ SV57 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1514,plain,
! [SV232: $i,SV58: $i] :
( ( ( in @ SV58 @ SV232 )
| ( disjoint @ ( singleton @ SV58 ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1515,plain,
! [SV59: $i,SV233: $i] :
( ( ~ ( element @ SV233 @ ( powerset @ SV59 ) )
| ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV233 )
| ( in @ SY1102 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1516,plain,
! [SV234: $i,SV60: $i] :
( ( ~ ( subset @ SV60 @ SV234 )
| ! [SY1103: $i] :
( ( in @ SY1103 @ SV60 )
| ( subset @ SV60 @ ( set_difference @ SV234 @ ( singleton @ SY1103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1517,plain,
! [SV235: $i,SV62: $i] :
( ( ! [SY1104: $i,SY1105: $i] :
( ( SV62 = SY1105 )
| ( SV62 = SY1104 )
| ( ( unordered_pair @ SV62 @ SV235 )
!= ( unordered_pair @ SY1104 @ SY1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1518,plain,
! [SV63: $i,SV236: $i] :
( ( ~ ( function @ SV236 )
| ~ ( relation @ SV236 )
| ( subset @ ( relation_image @ SV236 @ ( relation_inverse_image @ SV236 @ SV63 ) ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1519,plain,
! [SV64: $i,SV237: $i] :
( ( ~ ( function @ SV237 )
| ~ ( relation @ SV237 )
| ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) )
| ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1520,plain,
! [SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( ! [SY737: $i] :
( ~ ( relation @ SY737 )
| ( ( relation_rng @ ( relation_composition @ SV65 @ SY737 ) )
= ( relation_image @ SY737 @ ( relation_rng @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1521,plain,
! [SV66: $i,SV238: $i] :
( ( ~ ( relation @ SV238 )
| ( SV66 = empty_set )
| ~ ( subset @ SV66 @ ( relation_rng @ SV238 ) )
| ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1522,plain,
! [SV67: $i] :
( ( ( ~ ( epsilon_transitive @ SV67 ) )
= $true )
| ( ( ! [SY739: $i] :
( ~ ( ordinal @ SY739 )
| ~ ( proper_subset @ SV67 @ SY739 )
| ( in @ SV67 @ SY739 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1523,plain,
! [SV68: $i,SV239: $i] :
( ( ~ ( function @ SV239 )
| ~ ( relation @ SV239 )
| ! [SY1106: $i] :
( ~ ( function @ SY1106 )
| ~ ( relation @ SY1106 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY1106 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SY1106 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SY1106 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1524,plain,
! [SV69: $i,SV240: $i] :
( ( ~ ( function @ SV240 )
| ~ ( relation @ SV240 )
| ! [SY1107: $i] :
( ~ ( function @ SY1107 )
| ~ ( relation @ SY1107 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SY1107 ) @ SV69 )
= ( apply @ SY1107 @ ( apply @ SV240 @ SV69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1525,plain,
! [SV70: $i,SV241: $i] :
( ( ~ ( ordinal @ SV241 )
| ~ ( in @ SV70 @ SV241 )
| ( ordinal @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1526,plain,
! [SV71: $i] :
( ( ( ~ ( ordinal @ SV71 ) )
= $true )
| ( ( ! [SY745: $i] :
( ~ ( ordinal @ SY745 )
| ( in @ SV71 @ SY745 )
| ( SV71 = SY745 )
| ( in @ SY745 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1527,plain,
! [SV72: $i,SV242: $i] :
( ( ~ ( in @ SV242 @ SV72 )
| ( ( apply @ ( identity_relation @ SV72 ) @ SV242 )
= SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1528,plain,
! [SV243: $i,SV73: $i] :
( ( ( set_union2 @ SV73 @ ( set_difference @ SV243 @ SV73 ) )
= ( set_union2 @ SV73 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1529,plain,
! [SV244: $i,SV74: $i] :
( ( ! [SY1108: $i] :
( ~ ( in @ SV74 @ SV244 )
| ~ ( in @ SV244 @ SY1108 )
| ~ ( in @ SY1108 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1530,plain,
! [SV245: $i,SV75: $i] :
( ( ( set_difference @ ( set_union2 @ SV75 @ SV245 ) @ SV245 )
= ( set_difference @ SV75 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1531,plain,
! [SV76: $i,SV246: $i] :
( ( ~ ( element @ SV246 @ ( powerset @ ( powerset @ SV76 ) ) )
| ( SV246 = empty_set )
| ( ( complements_of_subsets @ SV76 @ SV246 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1532,plain,
! [SV247: $i,SV77: $i] :
( ( ~ ( in @ SV77 @ SV247 )
| ( ( set_union2 @ ( singleton @ SV77 ) @ SV247 )
= SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1533,plain,
! [SV248: $i,SV78: $i] :
( ( ( set_difference @ SV78 @ ( set_difference @ SV78 @ SV248 ) )
= ( set_intersection2 @ SV78 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1534,plain,
! [SV79: $i] :
( ( ( SV79 = empty_set )
= $true )
| ( ( ! [SY754: $i] :
( ~ ( element @ SY754 @ ( powerset @ SV79 ) )
| ! [SY755: $i] :
( ~ ( element @ SY755 @ SV79 )
| ( in @ SY755 @ SY754 )
| ( in @ SY755 @ ( subset_complement @ SV79 @ SY754 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1535,plain,
! [SV249: $i,SV80: $i] :
( ( ! [SY1109: $i] :
( ~ ( element @ SY1109 @ ( powerset @ SV80 ) )
| ~ ( in @ SV249 @ ( subset_complement @ SV80 @ SY1109 ) )
| ~ ( in @ SV249 @ SY1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1536,plain,
! [SV81: $i] :
( ( ( ~ ( relation @ SV81 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK70_B @ SV81 ) @ ( sK71_SY646 @ SV81 ) ) @ SV81 )
| ( SV81 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1537,plain,
! [SV82: $i] :
( ( ( ~ ( function @ SV82 )
| ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( one_to_one @ SV82 )
| ( one_to_one @ ( function_inverse @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1538,plain,
! [SV84: $i,SV250: $i] :
( ( ! [SY1110: $i] :
( ~ ( function @ SY1110 )
| ~ ( relation @ SY1110 )
| ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SY1110 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SY1110 @ SV84 ) @ SV250 )
= ( apply @ SY1110 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1539,plain,
! [SV85: $i,SV251: $i] :
( ( ! [SY1111: $i] :
( ~ ( function @ SY1111 )
| ~ ( relation @ SY1111 )
| ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SY1111 @ SV85 ) @ SV251 )
= ( apply @ SY1111 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1540,plain,
! [SV252: $i,SV86: $i] :
( ( ! [SY1112: $i] :
( ( singleton @ SV86 )
!= ( unordered_pair @ SV252 @ SY1112 ) )
| ( SV86 = SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1541,plain,
! [SV87: $i,SV253: $i] :
( ( ~ ( relation @ SV253 )
| ( ( relation_dom_restriction @ SV253 @ SV87 )
= ( relation_composition @ ( identity_relation @ SV87 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1542,plain,
! [SV254: $i,SV89: $i] :
( ( ! [SY1113: $i] :
( ( ( singleton @ SV89 )
!= ( unordered_pair @ SV254 @ SY1113 ) )
| ( SV254 = SY1113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1543,plain,
! [SV255: $i,SV90: $i] :
( ( ~ ( in @ SV90 @ SV255 )
| ~ ( in @ SV255 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1544,plain,
! [SV256: $i,SV91: $i] :
( ( ~ ( proper_subset @ SV91 @ SV256 )
| ~ ( proper_subset @ SV256 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1545,plain,
! [SV92: $i] :
( ( ( ~ ( empty @ SV92 ) )
= $true )
| ( ( function @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1546,plain,
! [SV93: $i] :
( ( ( ~ ( epsilon_connected @ SV93 )
| ~ ( epsilon_transitive @ SV93 ) )
= $true )
| ( ( ordinal @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1547,plain,
! [SV257: $i,SV94: $i] :
( ( ( unordered_pair @ SV94 @ SV257 )
= ( unordered_pair @ SV257 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1548,plain,
! [SV258: $i,SV95: $i] :
( ( ( set_union2 @ SV95 @ SV258 )
= ( set_union2 @ SV258 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1549,plain,
! [SV259: $i,SV96: $i] :
( ( ( set_intersection2 @ SV96 @ SV259 )
= ( set_intersection2 @ SV259 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1550,plain,
! [SV260: $i,SV97: $i] :
( ( ~ ( ordinal @ SV97 )
| ~ ( ordinal @ SV260 )
| ( ordinal_subset @ SV97 @ SV260 )
| ( ordinal_subset @ SV260 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1551,plain,
! [SV99: $i,SV261: $i] :
( ( ~ ( element @ SV261 @ ( powerset @ SV99 ) )
| ( ( subset_complement @ SV99 @ SV261 )
= ( set_difference @ SV99 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1552,plain,
! [SV262: $i,SV100: $i] :
( ( ( ordered_pair @ SV100 @ SV262 )
= ( unordered_pair @ ( unordered_pair @ SV100 @ SV262 ) @ ( singleton @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1553,plain,
! [SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( ( relation_field @ SV101 )
= ( set_union2 @ ( relation_dom @ SV101 ) @ ( relation_rng @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1554,plain,
! [SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ! [SY775: $i] :
( ( relation_restriction @ SV102 @ SY775 )
= ( set_intersection2 @ SV102 @ ( cartesian_product2 @ SY775 @ SY775 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1555,plain,
! [SV103: $i] :
( ( ( ~ ( function @ SV103 )
| ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( one_to_one @ SV103 )
| ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1556,plain,
! [SV105: $i,SV263: $i] :
( ( ~ ( element @ SV263 @ ( powerset @ SV105 ) )
| ( element @ ( subset_complement @ SV105 @ SV263 ) @ ( powerset @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1557,plain,
! [SV106: $i,SV264: $i] :
( ( ~ ( element @ SV264 @ ( powerset @ ( powerset @ SV106 ) ) )
| ( element @ ( union_of_subsets @ SV106 @ SV264 ) @ ( powerset @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1558,plain,
! [SV107: $i,SV265: $i] :
( ( ~ ( element @ SV265 @ ( powerset @ ( powerset @ SV107 ) ) )
| ( element @ ( meet_of_subsets @ SV107 @ SV265 ) @ ( powerset @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1559,plain,
! [SV108: $i,SV266: $i] :
( ( ! [SY1114: $i] :
( ~ ( element @ SV266 @ ( powerset @ SV108 ) )
| ~ ( element @ SY1114 @ ( powerset @ SV108 ) )
| ( element @ ( subset_difference @ SV108 @ SV266 @ SY1114 ) @ ( powerset @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1560,plain,
! [SV109: $i,SV267: $i] :
( ( ~ ( element @ SV267 @ ( powerset @ ( powerset @ SV109 ) ) )
| ( element @ ( complements_of_subsets @ SV109 @ SV267 ) @ ( powerset @ ( powerset @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1561,plain,
! [SV111: $i] :
( ( empty @ ( succ @ SV111 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1562,plain,
! [SV112: $i] :
( ( empty @ ( powerset @ SV112 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1563,plain,
! [SV268: $i,SV113: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV113 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1564,plain,
! [SV114: $i] :
( ( empty @ ( singleton @ SV114 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1565,plain,
! [SV115: $i] :
( ( ( empty @ SV115 )
= $true )
| ( ( ! [SY783: $i] :
~ ( empty @ ( set_union2 @ SV115 @ SY783 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1566,plain,
! [SV269: $i,SV116: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV116 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1567,plain,
! [SV117: $i] :
( ( ( empty @ SV117 )
= $true )
| ( ( ! [SY785: $i] :
~ ( empty @ ( set_union2 @ SY785 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1568,plain,
! [SV270: $i,SV118: $i] :
( ( ( empty @ SV118 )
| ( empty @ SV270 )
| ~ ( empty @ ( cartesian_product2 @ SV118 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1569,plain,
! [SV121: $i,SV271: $i] :
( ( ~ ( element @ SV271 @ ( powerset @ SV121 ) )
| ( ( subset_complement @ SV121 @ ( subset_complement @ SV121 @ SV271 ) )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1570,plain,
! [SV122: $i,SV272: $i] :
( ( ~ ( element @ SV272 @ ( powerset @ ( powerset @ SV122 ) ) )
| ( ( complements_of_subsets @ SV122 @ ( complements_of_subsets @ SV122 @ SV272 ) )
= SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1571,plain,
! [SV123: $i] :
( ( proper_subset @ SV123 @ SV123 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1572,plain,
! [SV124: $i,SV273: $i] :
( ( ~ ( element @ SV273 @ ( powerset @ ( powerset @ SV124 ) ) )
| ( ( union_of_subsets @ SV124 @ SV273 )
= ( union @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1573,plain,
! [SV125: $i,SV274: $i] :
( ( ! [SY1115: $i] :
( ~ ( element @ SV274 @ ( powerset @ SV125 ) )
| ~ ( element @ SY1115 @ ( powerset @ SV125 ) )
| ( ( subset_difference @ SV125 @ SV274 @ SY1115 )
= ( set_difference @ SV274 @ SY1115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1574,plain,
! [SV126: $i] :
( ( ( ~ ( ordinal @ SV126 )
| ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV126 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1575,plain,
! [SV275: $i,SV127: $i] :
( ( ~ ( disjoint @ SV127 @ SV275 )
| ( disjoint @ SV275 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1576,plain,
! [SV276: $i,SV129: $i] :
( ( ~ ( in @ SV129 @ SV276 )
| ( element @ SV129 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1577,plain,
! [SV277: $i,SV131: $i] :
( ( ~ ( element @ SV131 @ SV277 )
| ( empty @ SV277 )
| ( in @ SV131 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1578,plain,
! [SV134: $i,SV278: $i] :
( ( ! [SY1116: $i] :
( ~ ( element @ SV278 @ ( powerset @ SY1116 ) )
| ~ ( in @ SV134 @ SV278 )
| ( element @ SV134 @ SY1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1579,plain,
! [SV135: $i,SV279: $i] :
( ( ! [SY1117: $i] :
( ~ ( element @ SV279 @ ( powerset @ SY1117 ) )
| ~ ( in @ SV135 @ SV279 )
| ~ ( empty @ SY1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1580,plain,
! [SV136: $i] :
( ( ( ~ ( empty @ SV136 ) )
= $true )
| ( ( SV136 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1581,plain,
! [SV137: $i,SV280: $i] :
( ( ~ ( empty @ SV280 )
| ~ ( in @ SV137 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1582,plain,
! [SV281: $i,SV138: $i] :
( ( ( SV138 = SV281 )
| ~ ( empty @ SV138 )
| ~ ( empty @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1583,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK74_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1584,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1585,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1586,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1339]) ).
thf(1587,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)],[1340]) ).
thf(1588,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)],[1340]) ).
thf(1589,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1590,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1341]) ).
thf(1591,plain,
! [SV139: $i] :
( ( ( ~ ( relation @ SV139 ) )
= $true )
| ( ( ~ ( ~ ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) )
| ~ ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1592,plain,
! [SV140: $i] :
( ( ( ~ ( relation @ SV140 ) )
= $true )
| ( ( ~ ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) )
| ~ ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1593,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1594,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1595,plain,
! [SV141: $i] :
( ( ( ~ ( relation @ SV141 ) )
= $true )
| ( ( ~ ( ~ ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) )
| ~ ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1596,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK108_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK108_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1597,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK106_C @ SX1 @ SX0 ) @ ( sK107_SY668 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1598,plain,
! [SV142: $i,SV282: $i] :
( ( ~ ( relation @ SV282 )
| ~ ( ~ ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
| ~ ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1599,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1600,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1601,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( in @ SV143 @ SY1126 )
| ~ ( in @ SV283 @ SY1127 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1126 @ SY1127 ) ) )
| ~ ~ ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1602,plain,
! [SV144: $i] :
( ( ~ ! [SY834: $i] :
( ~ ( subset @ SY834 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SY834 @ ( sK87_B @ SV144 ) )
| ( in @ SY834 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1603,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1604,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1605,plain,
! [SV145: $i] :
( ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV145 @ SY839 ) ) )
| ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV145 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV145 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV145 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1606,plain,
! [SV146: $i] :
( ( ( ~ ( relation @ SV146 ) )
= $true )
| ( ( ~ ( ~ ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) )
| ~ ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1607,plain,
! [SV147: $i] :
( ( ( ~ ( relation @ SV147 ) )
= $true )
| ( ( ~ ( ~ ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) )
| ~ ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1608,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK76_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK76_C @ SX1 @ SX0 ) )
!= ( sK76_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1609,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)],[1355]) ).
thf(1610,plain,
! [SV148: $i] :
( ( ( empty @ SV148 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK10_B @ SV148 ) @ ( powerset @ SV148 ) )
| ~ ~ ( empty @ ( sK10_B @ SV148 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1611,plain,
! [SV149: $i] :
( ( ( ~ ( relation @ SV149 ) )
= $true )
| ( ( ~ ( ~ ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) )
| ~ ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1612,plain,
! [SV150: $i] :
( ( ~ ! [SY860: $i] :
( ~ ( subset @ SV150 @ SY860 )
| ! [SY861: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY861 ) @ ( cartesian_product2 @ SY860 @ SY861 ) ) )
| ~ ! [SY862: $i] :
( ~ ( subset @ SV150 @ SY862 )
| ! [SY863: $i] : ( subset @ ( cartesian_product2 @ SY863 @ SV150 ) @ ( cartesian_product2 @ SY863 @ SY862 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1613,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1614,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1615,plain,
! [SV151: $i] :
( ( ( ~ ( relation @ SV151 ) )
= $true )
| ( ( ~ ( ~ ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) )
| ~ ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1616,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1617,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1361]) ).
thf(1618,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1619,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1620,plain,
! [SV152: $i,SV284: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
| ~ ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) ) )
| ( SV152 = SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1621,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1622,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1364]) ).
thf(1623,plain,
( ( ~ ~ ( ~ ( function @ sK91_A )
| ~ ( relation @ sK91_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1624,plain,
( ( ~ ( one_to_one @ sK91_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1625,plain,
! [SV153: $i] :
( ( ~ ! [SY871: $i,SY872: $i] :
( ~ ( ~ ( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV153 )
| ~ ( in @ SY874 @ SY871 )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ~ ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) @ SY871 ) )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) ) )
| ( SY872
= ( cartesian_product2 @ SV153 @ SY871 ) ) )
| ~ ! [SY875: $i,SY876: $i] :
( ( SY876
!= ( cartesian_product2 @ SV153 @ SY875 ) )
| ~ ( ~ ! [SY877: $i] :
( ! [SY878: $i,SY879: $i] :
( ~ ( in @ SY878 @ SV153 )
| ~ ( in @ SY879 @ SY875 )
| ( SY877
!= ( ordered_pair @ SY878 @ SY879 ) ) )
| ( in @ SY877 @ SY876 ) )
| ~ ! [SY880: $i] :
( ~ ( in @ SY880 @ SY876 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) @ SY875 ) )
| ( SY880
!= ( ordered_pair @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1626,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1627,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1367]) ).
thf(1628,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK48_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1629,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1368]) ).
thf(1630,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1631,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1369]) ).
thf(1632,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1633,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1634,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)],[1371]) ).
thf(1635,plain,
( ( ~ ( ordinal @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1371]) ).
thf(1636,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1637,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1372]) ).
thf(1638,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)],[1373]) ).
thf(1639,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)],[1373]) ).
thf(1640,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 )
| ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1641,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1642,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1375]) ).
thf(1643,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK21_SY619 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK20_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK21_SY619 @ SX0 ) ) ) )
| ~ ( ( ( sK20_B @ SX0 )
!= ( sK21_SY619 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1644,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)],[1376]) ).
thf(1645,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1646,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1647,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK83_SY653 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK82_B @ SX0 )
!= ( sK83_SY653 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1378]) ).
thf(1648,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)],[1378]) ).
thf(1649,plain,
! [SV155: $i] :
( ( ~ ! [SY889: $i,SY890: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) ) ) )
| ( SY890
= ( set_difference @ SV155 @ SY889 ) ) )
| ~ ! [SY891: $i,SY892: $i] :
( ( SY892
!= ( set_difference @ SV155 @ SY891 ) )
| ~ ( ~ ! [SY893: $i] :
( ~ ( in @ SY893 @ SV155 )
| ( in @ SY893 @ SY891 )
| ( in @ SY893 @ SY892 ) )
| ~ ~ ( ~ ! [SY894: $i] :
( ~ ( in @ SY894 @ SY892 )
| ( in @ SY894 @ SV155 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY892 )
| ~ ( in @ SX3 @ SY891 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1650,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY627 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK35_SY627 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1651,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK33_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1652,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( relation @ SY1133 )
| ~ ( in @ SV156 @ SY1132 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1133 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1132 ) @ SY1133 ) ) )
| ~ ~ ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) )
| ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1653,plain,
( ( ~ ( empty @ sK94_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1654,plain,
( ( ~ ( relation @ sK94_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1655,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK49_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK49_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1656,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1657,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1658,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1659,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1660,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1661,plain,
! [SV157: $i] :
( ( ( ~ ( function @ SV157 )
| ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( one_to_one @ SV157 )
| ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1662,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)],[1387]) ).
thf(1663,plain,
( ( ~ ( ordinal @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1664,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1665,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1388]) ).
thf(1666,plain,
( ( ~ ( relation @ sK90_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1667,plain,
( ( ~ ( relation_empty_yielding @ sK90_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1668,plain,
! [SV158: $i] :
( ( ( ~ ( ordinal @ SV158 ) )
= $true )
| ( ( ~ ( ~ ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) )
| ~ ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1669,plain,
! [SV159: $i] :
( ( ~ ! [SY916: $i,SY917: $i] :
( ~ ( relation @ SY917 )
| ! [SY918: $i] :
( ~ ( in @ SY918 @ ( relation_rng @ SY917 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY918 ) @ SY917 )
| ~ ( in @ SY918 @ SY916 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SY917 @ SY916 ) ) )
| ~ ! [SY919: $i,SY920: $i] :
( ~ ( relation @ SY920 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SY920 @ SY919 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ ( relation_rng @ SY920 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SY920 @ SY919 @ SV159 ) ) @ SY920 ) )
| ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ SY919 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1670,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1671,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1392]) ).
thf(1672,plain,
! [SV160: $i] :
( ( ( ~ ( relation @ SV160 ) )
= $true )
| ( ( ~ ( ~ ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) )
| ~ ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1673,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1394]) ).
thf(1674,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1394]) ).
thf(1675,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1676,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1677,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1678,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1396]) ).
thf(1679,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1680,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1681,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1682,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1683,plain,
! [SV161: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( relation @ SY924 )
| ~ ( in @ SV161 @ SY924 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SY923 @ SY923 ) )
| ( in @ SV161 @ ( relation_restriction @ SY924 @ SY923 ) ) )
| ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1684,plain,
! [SV162: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( relation @ SY930 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY929 ) @ SY930 )
| ( in @ SV162 @ ( relation_field @ SY930 ) ) )
| ~ ! [SY931: $i,SY932: $i] :
( ~ ( relation @ SY932 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY931 ) @ SY932 )
| ( in @ SY931 @ ( relation_field @ SY932 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1685,plain,
! [SV286: $i,SV163: $i] :
( ( ~ ( ~ ! [SY1138: $i] :
( ! [SY1139: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1138 @ SY1139 ) )
| ( SV163 = SY1138 ) )
| ~ ! [SY1140: $i,SY1141: $i] :
( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1140 @ SY1141 ) )
| ( SV286 = SY1141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1686,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1687,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1402]) ).
thf(1688,plain,
! [SV164: $i] :
( ( ~ ! [SY938: $i,SY939: $i] :
( ~ ( function @ SY939 )
| ~ ( relation @ SY939 )
| ~ ( in @ SY938 @ ( relation_dom @ SY939 ) )
| ~ ( in @ SY938 @ SV164 )
| ( in @ SY938 @ ( relation_dom @ ( relation_dom_restriction @ SY939 @ SV164 ) ) ) )
| ~ ~ ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) )
| ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1689,plain,
! [SV165: $i,SV287: $i] :
( ( ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV287 )
| ~ ( in @ SY1142 @ ( sK3_C @ SV287 @ SV165 ) ) )
| ~ ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 ) )
| ~ ( in @ SV165 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1690,plain,
! [SV166: $i] :
( ( ~ ! [SY946: $i,SY947: $i] :
( ~ ( relation @ SY947 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY946 ) @ SY947 )
| ( in @ SV166 @ ( relation_dom @ SY947 ) ) )
| ~ ! [SY948: $i,SY949: $i] :
( ~ ( relation @ SY949 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY948 ) @ SY949 )
| ( in @ SY948 @ ( relation_rng @ SY949 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1691,plain,
! [SV167: $i] :
( ( ~ ! [SY950: $i] :
( ~ ( subset @ SY950 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SY950 @ ( sK80_B @ SV167 ) )
| ( in @ SY950 @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1692,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK104_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK104_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1693,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1694,plain,
! [SV168: $i] :
( ( ~ ! [SY954: $i,SY955: $i] :
( ~ ( function @ SY955 )
| ~ ( relation @ SY955 )
| ( SY954
!= ( apply @ SY955 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SY955 ) )
| ( in @ ( ordered_pair @ SV168 @ SY954 ) @ SY955 ) )
| ~ ~ ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) )
| ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1695,plain,
( ( ~ ~ ( ~ ( empty @ sK93_A )
| ~ ( relation @ sK93_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1696,plain,
( ( ~ ( function @ sK93_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1697,plain,
! [SV169: $i] :
( ( ( ~ ( function @ SV169 )
| ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1698,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1699,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1700,plain,
! [SV170: $i] :
( ( ( ~ ( function @ SV170 )
| ~ ( relation @ SV170 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1701,plain,
( ( ~ ~ ( ~ ( epsilon_connected @ sK11_A )
| ~ ( epsilon_transitive @ sK11_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1702,plain,
( ( ~ ( ordinal @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1703,plain,
( ( ~ ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1704,plain,
( ( ~ ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1705,plain,
! [SV171: $i] :
( ( ~ ! [SY975: $i,SY976: $i] :
( ~ ( relation @ SY976 )
| ~ ( in @ SV171 @ SY975 )
| ~ ( in @ SV171 @ ( relation_dom @ SY976 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY976 @ SY975 ) ) ) )
| ~ ~ ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) )
| ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1706,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1707,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1708,plain,
( ( ~ ~ ( empty @ sK92_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1709,plain,
( ( ~ ( relation @ sK92_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1710,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1711,plain,
( ( ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1712,plain,
! [SV172: $i] :
( ( ( ~ ( relation @ SV172 ) )
= $true )
| ( ( ! [SY981: $i] :
( ~ ( relation @ SY981 )
| ~ ( ~ ! [SY982: $i] :
( ~ ( relation @ SY982 )
| ~ ( ~ ( ! [SY983: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ SY983 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY983 @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) ) )
| ( SY982
= ( relation_composition @ SV172 @ SY981 ) ) )
| ~ ! [SY984: $i] :
( ~ ( relation @ SY984 )
| ( SY984
!= ( relation_composition @ SV172 @ SY981 ) )
| ~ ( ~ ! [SY985: $i,SY986: $i] :
( ! [SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY985 @ SY987 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY987 @ SY986 ) @ SY981 ) )
| ( in @ ( ordered_pair @ SY985 @ SY986 ) @ SY984 ) )
| ~ ! [SY988: $i,SY989: $i] :
( ~ ( in @ ( ordered_pair @ SY988 @ SY989 ) @ SY984 )
| ~ ( ~ ( in @ ( ordered_pair @ SY988 @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) @ SY989 ) @ SY981 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1713,plain,
! [SV173: $i] :
( ( ( ~ ( relation @ SV173 ) )
= $true )
| ( ( ~ ( ~ ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) )
| ~ ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1714,plain,
! [SV174: $i,SV288: $i] :
( ( ~ ( ~ ! [SY1143: $i,SY1144: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SY1143 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SY1143 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SY1144
= ( unordered_triple @ SV174 @ SV288 @ SY1143 ) ) )
| ~ ! [SY1145: $i,SY1146: $i] :
( ( SY1146
!= ( unordered_triple @ SV174 @ SV288 @ SY1145 ) )
| ~ ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ SY1146 )
| ( SY1147 = SY1145 )
| ( SY1147 = SV174 )
| ( SY1147 = SV288 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1145 )
| ( in @ SX4 @ SY1146 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1146 ) )
| ~ ! [SY1150: $i] :
( ( SY1150 != SV288 )
| ( in @ SY1150 @ SY1146 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1715,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1716,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)],[1422]) ).
thf(1717,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1718,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1719,plain,
! [SV175: $i] :
( ( ~ ! [SY1005: $i,SY1006: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SY1005 ) ) )
| ~ ( ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SV175 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SY1005 ) ) )
| ( SY1006
= ( unordered_pair @ SV175 @ SY1005 ) ) )
| ~ ! [SY1007: $i,SY1008: $i] :
( ( SY1008
!= ( unordered_pair @ SV175 @ SY1007 ) )
| ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SY1008 )
| ( SY1009 = SV175 )
| ( SY1009 = SY1007 ) )
| ~ ~ ( ~ ! [SY1010: $i] :
( ( SY1010 != SV175 )
| ( in @ SY1010 @ SY1008 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1007 )
| ( in @ SX3 @ SY1008 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1720,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK85_SY654 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1721,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)],[1425]) ).
thf(1722,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1723,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1724,plain,
! [SV176: $i,SV289: $i] :
( ( ~ ( function @ SV289 )
| ~ ( relation @ SV289 )
| ~ ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1725,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1726,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1727,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1728,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1729,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1730,plain,
( ( ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1731,plain,
! [SV177: $i] :
( ( ~ ! [SY1016: $i,SY1017: $i] :
( ~ ( in @ SV177 @ SY1017 )
| ~ ( in @ SY1016 @ SY1017 )
| ( subset @ ( unordered_pair @ SV177 @ SY1016 ) @ SY1017 ) )
| ~ ~ ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) )
| ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1732,plain,
! [SV178: $i,SV290: $i] :
( ( ~ ( ordinal @ SV290 )
| ~ ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
| ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
| ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1733,plain,
! [SV179: $i,SV291: $i] :
( ( ~ ( element @ SV291 @ ( powerset @ SV179 ) )
| ~ ( ~ ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) )
| ~ ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1734,plain,
! [SV180: $i] :
( ( ~ ( element @ ( sK7_B @ SV180 ) @ ( powerset @ SV180 ) )
| ~ ( empty @ ( sK7_B @ SV180 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1735,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1736,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1737,plain,
! [SV181: $i] :
( ( ( ~ ( relation @ SV181 ) )
= $true )
| ( ( ~ ( ~ ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) )
| ~ ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1738,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)],[1437]) ).
thf(1739,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)],[1437]) ).
thf(1740,plain,
! [SV182: $i] :
( ( ( ~ ( function @ SV182 )
| ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1741,plain,
! [SV183: $i] :
( ( ( ~ ( ~ ( in @ ( sK111_B @ SV183 ) @ SV183 )
| ~ ( ~ ( ordinal @ ( sK111_B @ SV183 ) )
| ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) ) ) )
= $true )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1742,plain,
! [SV184: $i,SV292: $i] :
( ( ~ ( function @ SV292 )
| ~ ( relation @ SV292 )
| ~ ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1743,plain,
( ( ~ ~ ( ~ ( relation @ sK89_A )
| ~ ( relation_empty_yielding @ sK89_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1744,plain,
( ( ~ ( function @ sK89_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1745,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= ( sK40_SY629 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK40_SY629 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK39_B @ SX0 ) @ ( sK40_SY629 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SX0 ) @ ( sK39_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1746,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1747,plain,
! [SV185: $i] :
( ( ( ~ ( relation @ SV185 ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) )
| ~ ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1748,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1749,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1444]) ).
thf(1750,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)],[1445]) ).
thf(1751,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1445]) ).
thf(1752,plain,
! [SV186: $i] :
( ( ~ ! [SY1054: $i,SY1055: $i] :
( ~ ( relation @ SY1055 )
| ~ ( in @ SV186 @ SY1054 )
| ~ ( in @ SV186 @ ( relation_rng @ SY1055 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1054 @ SY1055 ) ) ) )
| ~ ~ ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) )
| ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1753,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1754,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1755,plain,
! [SV187: $i] :
( ( ~ ! [SY1060: $i,SY1061: $i] :
( ~ ( relation @ SY1061 )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( relation_dom @ SY1061 ) )
| ~ ( in @ ( ordered_pair @ SY1062 @ SV187 ) @ SY1061 )
| ~ ( in @ SY1062 @ SY1060 ) )
| ( in @ SV187 @ ( relation_image @ SY1061 @ SY1060 ) ) )
| ~ ! [SY1063: $i,SY1064: $i] :
( ~ ( relation @ SY1064 )
| ~ ( in @ SV187 @ ( relation_image @ SY1064 @ SY1063 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ ( relation_dom @ SY1064 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SV187 ) @ SY1064 ) )
| ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SY1063 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1756,plain,
! [SV188: $i] :
( ( ( ~ ( relation @ SV188 ) )
= $true )
| ( ( ~ ( ~ ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) )
| ~ ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1757,plain,
( ( ~ ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1758,plain,
( ( ~ ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1759,plain,
! [SV189: $i] :
( ( ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) ) ) )
| ( SY1070
= ( set_intersection2 @ SV189 @ SY1069 ) ) )
| ~ ! [SY1071: $i,SY1072: $i] :
( ( SY1072
!= ( set_intersection2 @ SV189 @ SY1071 ) )
| ~ ( ~ ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV189 )
| ~ ( in @ SY1073 @ SY1071 )
| ( in @ SY1073 @ SY1072 ) )
| ~ ~ ( ~ ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SY1072 )
| ( in @ SY1074 @ SV189 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1072 )
| ( in @ SX3 @ SY1071 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1760,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1761,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1762,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ( ~ ! [SY1161: $i,SY1162: $i] :
( ~ ( in @ SV190 @ SY1161 )
| ~ ( in @ SV293 @ SY1162 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1161 @ SY1162 ) ) )
| ~ ~ ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) )
| ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1763,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
| ~ ( epsilon_connected @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1764,plain,
( ( ~ ( ordinal @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1765,plain,
( ( ~ ( function @ sK95_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1766,plain,
( ( ~ ( relation @ sK95_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1767,plain,
! [SV191: $i,SV294: $i] :
( ( ~ ( ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV191 )
| ~ ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 ) )
| ( element @ SV191 @ ( powerset @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1768,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1769,plain,
( ( ~ ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1770,plain,
! [SV192: $i] :
( ( ( ~ ( relation @ SV192 ) )
= $true )
| ( ( ~ ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) )
| ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1771,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
!= ( sK68_SY645 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
= ( sK68_SY645 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1772,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)],[1459]) ).
thf(1773,plain,
! [SV193: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV193 ) )
= $true )
| ( ( subset @ SV1 @ ( union @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1774,plain,
! [SV2: $i,SV194: $i] :
( ( ( ~ ( relation @ SV194 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV194 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1775,plain,
! [SV3: $i,SV195: $i] :
( ( ( ~ ( relation @ SV195 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV3 @ SV195 ) @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1776,plain,
! [SV4: $i,SV196: $i] :
( ( ( ~ ( relation @ SV196 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV196 ) ) @ ( relation_rng @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1777,plain,
! [SV5: $i,SV197: $i] :
( ( ( ~ ( relation @ SV197 ) )
= $true )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV197 ) )
= ( set_intersection2 @ ( relation_rng @ SV197 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1778,plain,
! [SV295: $i,SV198: $i,SV6: $i] :
( ( ! [SY1167: $i] :
( ~ ( subset @ SV6 @ SV198 )
| ~ ( subset @ SV295 @ SY1167 )
| ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SY1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1779,plain,
! [SV199: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV199 ) )
= $true )
| ( ( ( set_union2 @ SV7 @ SV199 )
= SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1780,plain,
! [SV200: $i,SV8: $i,SV296: $i] :
( ( ~ ( relation @ SV296 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV8 @ SV296 ) @ SV200 )
= ( relation_rng_restriction @ SV8 @ ( relation_dom_restriction @ SV296 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1781,plain,
! [SV9: $i,SV201: $i] :
( ( ( ~ ( relation @ SV201 ) )
= $true )
| ( ( subset @ ( relation_image @ SV201 @ SV9 ) @ ( relation_rng @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1782,plain,
! [SV10: $i,SV202: $i] :
( ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ( relation_image @ SV202 @ SV10 )
= ( relation_image @ SV202 @ ( set_intersection2 @ ( relation_dom @ SV202 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1783,plain,
! [SV11: $i,SV203: $i] :
( ( ( ~ ( relation @ SV203 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV203 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV203 @ ( relation_image @ SV203 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1784,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ( relation_image @ SV12 @ ( relation_dom @ SV12 ) )
= ( relation_rng @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1785,plain,
! [SV13: $i,SV204: $i] :
( ( ( ~ ( relation @ SV204 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV204 @ SV13 ) @ ( relation_dom @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1786,plain,
! [SV205: $i,SV14: $i,SV297: $i] :
( ( ~ ( relation @ SV297 )
| ~ ( subset @ SV14 @ SV205 )
| ( subset @ ( relation_inverse_image @ SV297 @ SV14 ) @ ( relation_inverse_image @ SV297 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1787,plain,
! [SV15: $i,SV206: $i] :
( ( ( ~ ( relation @ SV206 ) )
= $true )
| ( ( ( relation_restriction @ SV206 @ SV15 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV15 @ SV206 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1788,plain,
! [SV17: $i,SV208: $i] :
( ( ( ~ ( relation @ SV208 ) )
= $true )
| ( ( ( relation_restriction @ SV208 @ SV17 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV208 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1789,plain,
! [SV298: $i,SV209: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV209 )
| ~ ( subset @ SV18 @ SV298 )
| ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1790,plain,
! [SV299: $i,SV210: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV210 )
| ~ ( subset @ SV210 @ SV299 )
| ( subset @ SV19 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1791,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( subset @ SV20 @ ( cartesian_product2 @ ( relation_dom @ SV20 ) @ ( relation_rng @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1792,plain,
! [SV211: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV211 ) )
= $true )
| ( ( ! [SY1098: $i] : ( subset @ ( set_intersection2 @ SV21 @ SY1098 ) @ ( set_intersection2 @ SV211 @ SY1098 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1793,plain,
! [SV212: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV212 ) )
= $true )
| ( ( ( set_intersection2 @ SV22 @ SV212 )
= SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1794,plain,
! [SV213: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV213 ) )
= $true )
| ( ( ! [SY1099: $i] : ( subset @ ( set_difference @ SV24 @ SY1099 ) @ ( set_difference @ SV213 @ SY1099 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1795,plain,
! [SV26: $i] :
( ( ( subset @ SV26 @ empty_set )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1796,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ! [SY702: $i] :
( ~ ( relation @ SY702 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SY702 ) ) @ ( relation_dom @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1797,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( ! [SY703: $i] :
( ~ ( relation @ SY703 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SY703 ) ) @ ( relation_rng @ SY703 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1798,plain,
! [SV215: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV215 ) )
= $true )
| ( ( SV215
= ( set_union2 @ SV29 @ ( set_difference @ SV215 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1799,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ! [SY705: $i] :
( ~ ( relation @ SY705 )
| ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SY705 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SY705 ) )
= ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1800,plain,
! [SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ! [SY706: $i] :
( ~ ( relation @ SY706 )
| ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SY706 ) )
| ( ( relation_rng @ ( relation_composition @ SY706 @ SV31 ) )
= ( relation_rng @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1801,plain,
! [SV32: $i,SV216: $i] :
( ( ( ~ ( proper_subset @ SV216 @ SV32 ) )
= $true )
| ( ( ~ ( subset @ SV32 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1802,plain,
! [SV33: $i,SV300: $i,SV217: $i] :
( ( ~ ( disjoint @ SV217 @ SV300 )
| ~ ( subset @ SV33 @ SV217 )
| ( disjoint @ SV33 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1803,plain,
! [SV218: $i,SV34: $i] :
( ( ( ~ ( subset @ ( singleton @ SV34 ) @ ( singleton @ SV218 ) ) )
= $true )
| ( ( SV34 = SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1804,plain,
! [SV36: $i,SV220: $i] :
( ( ( ~ ( relation @ SV220 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV220 @ SV36 ) @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1805,plain,
! [SV301: $i,SV221: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV221 )
| ~ ( subset @ SV301 @ SV221 )
| ( subset @ ( set_union2 @ SV37 @ SV301 ) @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1806,plain,
! [SV38: $i,SV222: $i] :
( ( ( ~ ( relation @ SV222 ) )
= $true )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV222 @ SV38 ) )
= ( set_intersection2 @ ( relation_dom @ SV222 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1807,plain,
! [SV223: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV223 ) )
= $true )
| ( ( subset @ SV39 @ ( union @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1808,plain,
! [SV40: $i,SV224: $i] :
( ( ( ~ ( relation @ SV224 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV224 @ SV40 ) ) @ ( relation_rng @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1498]) ).
thf(1809,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
= $false )
| ( ( relation @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1810,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ! [SY718: $i] : ( relation @ ( relation_restriction @ SV42 @ SY718 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1811,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( relation @ ( relation_inverse @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1812,plain,
! [SV225: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 )
| ~ ( relation @ SV225 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1813,plain,
! [SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ! [SY720: $i] : ( relation @ ( relation_dom_restriction @ SV46 @ SY720 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1814,plain,
! [SV47: $i,SV226: $i] :
( ( ( ~ ( relation @ SV226 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV47 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1815,plain,
! [SV227: $i,SV48: $i] :
( ( ( ~ ( relation @ SV48 )
| ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV48 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1816,plain,
! [SV228: $i,SV49: $i] :
( ( ( ~ ( relation @ SV49 )
| ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV49 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1817,plain,
! [SV229: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 )
| ~ ( relation @ SV229 ) )
= $true )
| ( ( relation @ ( set_difference @ SV50 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1818,plain,
! [SV51: $i] :
( ( ( empty @ SV51 )
= $true )
| ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1819,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1820,plain,
! [SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV53 ) )
= SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1821,plain,
! [SV230: $i,SV56: $i] :
( ( ( ~ ( in @ SV56 @ SV230 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV56 ) @ SV230 )
= SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1822,plain,
! [SV231: $i,SV57: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV57 ) @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV57 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1823,plain,
! [SV232: $i,SV58: $i] :
( ( ( in @ SV58 @ SV232 )
= $true )
| ( ( disjoint @ ( singleton @ SV58 ) @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1824,plain,
! [SV59: $i,SV233: $i] :
( ( ( ~ ( element @ SV233 @ ( powerset @ SV59 ) ) )
= $true )
| ( ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV233 )
| ( in @ SY1102 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1825,plain,
! [SV234: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV234 ) )
= $true )
| ( ( ! [SY1103: $i] :
( ( in @ SY1103 @ SV60 )
| ( subset @ SV60 @ ( set_difference @ SV234 @ ( singleton @ SY1103 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1826,plain,
! [SV235: $i,SV302: $i,SV62: $i] :
( ( ! [SY1168: $i] :
( ( SV62 = SY1168 )
| ( SV62 = SV302 )
| ( ( unordered_pair @ SV62 @ SV235 )
!= ( unordered_pair @ SV302 @ SY1168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1827,plain,
! [SV63: $i,SV236: $i] :
( ( ( ~ ( function @ SV236 )
| ~ ( relation @ SV236 ) )
= $true )
| ( ( subset @ ( relation_image @ SV236 @ ( relation_inverse_image @ SV236 @ SV63 ) ) @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1828,plain,
! [SV64: $i,SV237: $i] :
( ( ( ~ ( function @ SV237 )
| ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) )
| ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1829,plain,
! [SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( ! [SY737: $i] :
( ~ ( relation @ SY737 )
| ( ( relation_rng @ ( relation_composition @ SV65 @ SY737 ) )
= ( relation_image @ SY737 @ ( relation_rng @ SV65 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1830,plain,
! [SV66: $i,SV238: $i] :
( ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ( SV66 = empty_set )
| ~ ( subset @ SV66 @ ( relation_rng @ SV238 ) )
| ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1831,plain,
! [SV67: $i] :
( ( ( epsilon_transitive @ SV67 )
= $false )
| ( ( ! [SY739: $i] :
( ~ ( ordinal @ SY739 )
| ~ ( proper_subset @ SV67 @ SY739 )
| ( in @ SV67 @ SY739 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1832,plain,
! [SV68: $i,SV239: $i] :
( ( ( ~ ( function @ SV239 )
| ~ ( relation @ SV239 ) )
= $true )
| ( ( ! [SY1106: $i] :
( ~ ( function @ SY1106 )
| ~ ( relation @ SY1106 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY1106 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SY1106 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SY1106 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1833,plain,
! [SV69: $i,SV240: $i] :
( ( ( ~ ( function @ SV240 )
| ~ ( relation @ SV240 ) )
= $true )
| ( ( ! [SY1107: $i] :
( ~ ( function @ SY1107 )
| ~ ( relation @ SY1107 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SY1107 ) @ SV69 )
= ( apply @ SY1107 @ ( apply @ SV240 @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1834,plain,
! [SV70: $i,SV241: $i] :
( ( ( ~ ( ordinal @ SV241 ) )
= $true )
| ( ( ~ ( in @ SV70 @ SV241 )
| ( ordinal @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1835,plain,
! [SV71: $i] :
( ( ( ordinal @ SV71 )
= $false )
| ( ( ! [SY745: $i] :
( ~ ( ordinal @ SY745 )
| ( in @ SV71 @ SY745 )
| ( SV71 = SY745 )
| ( in @ SY745 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1836,plain,
! [SV72: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV72 ) )
= $true )
| ( ( ( apply @ ( identity_relation @ SV72 ) @ SV242 )
= SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1837,plain,
! [SV303: $i,SV244: $i,SV74: $i] :
( ( ~ ( in @ SV74 @ SV244 )
| ~ ( in @ SV244 @ SV303 )
| ~ ( in @ SV303 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1838,plain,
! [SV76: $i,SV246: $i] :
( ( ( ~ ( element @ SV246 @ ( powerset @ ( powerset @ SV76 ) ) ) )
= $true )
| ( ( ( SV246 = empty_set )
| ( ( complements_of_subsets @ SV76 @ SV246 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1839,plain,
! [SV247: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV247 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV77 ) @ SV247 )
= SV247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1840,plain,
! [SV79: $i,SV304: $i] :
( ( ( ~ ( element @ SV304 @ ( powerset @ SV79 ) )
| ! [SY1169: $i] :
( ~ ( element @ SY1169 @ SV79 )
| ( in @ SY1169 @ SV304 )
| ( in @ SY1169 @ ( subset_complement @ SV79 @ SV304 ) ) ) )
= $true )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1841,plain,
! [SV249: $i,SV80: $i,SV305: $i] :
( ( ~ ( element @ SV305 @ ( powerset @ SV80 ) )
| ~ ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) )
| ~ ( in @ SV249 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1842,plain,
! [SV81: $i] :
( ( ( relation @ SV81 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK70_B @ SV81 ) @ ( sK71_SY646 @ SV81 ) ) @ SV81 )
| ( SV81 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1843,plain,
! [SV82: $i] :
( ( ( ~ ( function @ SV82 ) )
= $true )
| ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( one_to_one @ SV82 )
| ( one_to_one @ ( function_inverse @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1844,plain,
! [SV84: $i,SV250: $i,SV306: $i] :
( ( ~ ( function @ SV306 )
| ~ ( relation @ SV306 )
| ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1845,plain,
! [SV85: $i,SV251: $i,SV307: $i] :
( ( ~ ( function @ SV307 )
| ~ ( relation @ SV307 )
| ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1846,plain,
! [SV252: $i,SV86: $i] :
( ( ( ! [SY1112: $i] :
( ( singleton @ SV86 )
!= ( unordered_pair @ SV252 @ SY1112 ) ) )
= $true )
| ( ( SV86 = SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1847,plain,
! [SV87: $i,SV253: $i] :
( ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( ( relation_dom_restriction @ SV253 @ SV87 )
= ( relation_composition @ ( identity_relation @ SV87 ) @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1848,plain,
! [SV308: $i,SV254: $i,SV89: $i] :
( ( ( ( singleton @ SV89 )
!= ( unordered_pair @ SV254 @ SV308 ) )
| ( SV254 = SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1849,plain,
! [SV255: $i,SV90: $i] :
( ( ( ~ ( in @ SV90 @ SV255 ) )
= $true )
| ( ( ~ ( in @ SV255 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1850,plain,
! [SV256: $i,SV91: $i] :
( ( ( ~ ( proper_subset @ SV91 @ SV256 ) )
= $true )
| ( ( ~ ( proper_subset @ SV256 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1851,plain,
! [SV92: $i] :
( ( ( empty @ SV92 )
= $false )
| ( ( function @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1852,plain,
! [SV93: $i] :
( ( ( ~ ( epsilon_connected @ SV93 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV93 ) )
= $true )
| ( ( ordinal @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1853,plain,
! [SV260: $i,SV97: $i] :
( ( ( ~ ( ordinal @ SV97 )
| ~ ( ordinal @ SV260 ) )
= $true )
| ( ( ( ordinal_subset @ SV97 @ SV260 )
| ( ordinal_subset @ SV260 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1854,plain,
! [SV99: $i,SV261: $i] :
( ( ( ~ ( element @ SV261 @ ( powerset @ SV99 ) ) )
= $true )
| ( ( ( subset_complement @ SV99 @ SV261 )
= ( set_difference @ SV99 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1855,plain,
! [SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( ( relation_field @ SV101 )
= ( set_union2 @ ( relation_dom @ SV101 ) @ ( relation_rng @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1856,plain,
! [SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ! [SY775: $i] :
( ( relation_restriction @ SV102 @ SY775 )
= ( set_intersection2 @ SV102 @ ( cartesian_product2 @ SY775 @ SY775 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1857,plain,
! [SV103: $i] :
( ( ( ~ ( function @ SV103 ) )
= $true )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( one_to_one @ SV103 )
| ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1858,plain,
! [SV105: $i,SV263: $i] :
( ( ( ~ ( element @ SV263 @ ( powerset @ SV105 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV105 @ SV263 ) @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1859,plain,
! [SV106: $i,SV264: $i] :
( ( ( ~ ( element @ SV264 @ ( powerset @ ( powerset @ SV106 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV106 @ SV264 ) @ ( powerset @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1860,plain,
! [SV107: $i,SV265: $i] :
( ( ( ~ ( element @ SV265 @ ( powerset @ ( powerset @ SV107 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV107 @ SV265 ) @ ( powerset @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1861,plain,
! [SV309: $i,SV108: $i,SV266: $i] :
( ( ~ ( element @ SV266 @ ( powerset @ SV108 ) )
| ~ ( element @ SV309 @ ( powerset @ SV108 ) )
| ( element @ ( subset_difference @ SV108 @ SV266 @ SV309 ) @ ( powerset @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1862,plain,
! [SV109: $i,SV267: $i] :
( ( ( ~ ( element @ SV267 @ ( powerset @ ( powerset @ SV109 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV109 @ SV267 ) @ ( powerset @ ( powerset @ SV109 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1863,plain,
! [SV268: $i,SV113: $i] :
( ( empty @ ( ordered_pair @ SV113 @ SV268 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1864,plain,
! [SV310: $i,SV115: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV115 @ SV310 ) ) )
= $true )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1865,plain,
! [SV269: $i,SV116: $i] :
( ( empty @ ( unordered_pair @ SV116 @ SV269 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1866,plain,
! [SV117: $i,SV311: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV311 @ SV117 ) ) )
= $true )
| ( ( empty @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1867,plain,
! [SV270: $i,SV118: $i] :
( ( ( ( empty @ SV118 )
| ( empty @ SV270 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV118 @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1868,plain,
! [SV121: $i,SV271: $i] :
( ( ( ~ ( element @ SV271 @ ( powerset @ SV121 ) ) )
= $true )
| ( ( ( subset_complement @ SV121 @ ( subset_complement @ SV121 @ SV271 ) )
= SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1869,plain,
! [SV122: $i,SV272: $i] :
( ( ( ~ ( element @ SV272 @ ( powerset @ ( powerset @ SV122 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV122 @ ( complements_of_subsets @ SV122 @ SV272 ) )
= SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1870,plain,
! [SV124: $i,SV273: $i] :
( ( ( ~ ( element @ SV273 @ ( powerset @ ( powerset @ SV124 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV124 @ SV273 )
= ( union @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1871,plain,
! [SV312: $i,SV125: $i,SV274: $i] :
( ( ~ ( element @ SV274 @ ( powerset @ SV125 ) )
| ~ ( element @ SV312 @ ( powerset @ SV125 ) )
| ( ( subset_difference @ SV125 @ SV274 @ SV312 )
= ( set_difference @ SV274 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1872,plain,
! [SV126: $i] :
( ( ( ~ ( ordinal @ SV126 ) )
= $true )
| ( ( ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV126 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1873,plain,
! [SV275: $i,SV127: $i] :
( ( ( ~ ( disjoint @ SV127 @ SV275 ) )
= $true )
| ( ( disjoint @ SV275 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1874,plain,
! [SV276: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ SV276 ) )
= $true )
| ( ( element @ SV129 @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1875,plain,
! [SV277: $i,SV131: $i] :
( ( ( ~ ( element @ SV131 @ SV277 ) )
= $true )
| ( ( ( empty @ SV277 )
| ( in @ SV131 @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1876,plain,
! [SV134: $i,SV313: $i,SV278: $i] :
( ( ~ ( element @ SV278 @ ( powerset @ SV313 ) )
| ~ ( in @ SV134 @ SV278 )
| ( element @ SV134 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1877,plain,
! [SV135: $i,SV314: $i,SV279: $i] :
( ( ~ ( element @ SV279 @ ( powerset @ SV314 ) )
| ~ ( in @ SV135 @ SV279 )
| ~ ( empty @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1878,plain,
! [SV136: $i] :
( ( ( empty @ SV136 )
= $false )
| ( ( SV136 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1879,plain,
! [SV137: $i,SV280: $i] :
( ( ( ~ ( empty @ SV280 ) )
= $true )
| ( ( ~ ( in @ SV137 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1880,plain,
! [SV281: $i,SV138: $i] :
( ( ( ( SV138 = SV281 )
| ~ ( empty @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK74_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1882,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1883,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1884,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1885,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)],[1587]) ).
thf(1886,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)],[1588]) ).
thf(1887,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1589]) ).
thf(1888,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1889,plain,
! [SV139: $i] :
( ( ( relation @ SV139 )
= $false )
| ( ( ~ ( ~ ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) )
| ~ ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1890,plain,
! [SV140: $i] :
( ( ( relation @ SV140 )
= $false )
| ( ( ~ ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) )
| ~ ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1891,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( function @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1892,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( one_to_one @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1893,plain,
! [SV141: $i] :
( ( ( relation @ SV141 )
= $false )
| ( ( ~ ( ~ ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) )
| ~ ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1894,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK108_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK108_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1895,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK106_C @ SX1 @ SX0 ) @ ( sK107_SY668 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1896,plain,
! [SV142: $i,SV282: $i] :
( ( ( ~ ( relation @ SV282 ) )
= $true )
| ( ( ~ ( ~ ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
| ~ ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1897,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1898,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1899,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( in @ SV143 @ SY1126 )
| ~ ( in @ SV283 @ SY1127 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1126 @ SY1127 ) ) )
| ~ ~ ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1900,plain,
! [SV144: $i] :
( ( ~ ! [SY834: $i] :
( ~ ( subset @ SY834 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SY834 @ ( sK87_B @ SV144 ) )
| ( in @ SY834 @ ( sK87_B @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1901,plain,
! [SV144: $i] :
( ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1902,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK99_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1903,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1904,plain,
! [SV145: $i] :
( ( ~ ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV145 @ SY839 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1905,plain,
! [SV145: $i] :
( ( ~ ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV145 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV145 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV145 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1906,plain,
! [SV146: $i] :
( ( ( relation @ SV146 )
= $false )
| ( ( ~ ( ~ ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) )
| ~ ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1907,plain,
! [SV147: $i] :
( ( ( relation @ SV147 )
= $false )
| ( ( ~ ( ~ ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) )
| ~ ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1908,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( sK76_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( ( ( apply @ SX1 @ ( sK76_C @ SX1 @ SX0 ) )
!= ( sK76_C @ SX1 @ SX0 ) ) ) )
| ( ( relation_dom @ SX1 )
!= SX0 )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1909,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)],[1609]) ).
thf(1910,plain,
! [SV148: $i] :
( ( ( ~ ( element @ ( sK10_B @ SV148 ) @ ( powerset @ SV148 ) )
| ~ ~ ( empty @ ( sK10_B @ SV148 ) ) )
= $false )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1911,plain,
! [SV149: $i] :
( ( ( relation @ SV149 )
= $false )
| ( ( ~ ( ~ ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) )
| ~ ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1912,plain,
! [SV150: $i] :
( ( ~ ! [SY860: $i] :
( ~ ( subset @ SV150 @ SY860 )
| ! [SY861: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY861 ) @ ( cartesian_product2 @ SY860 @ SY861 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1913,plain,
! [SV150: $i] :
( ( ~ ! [SY862: $i] :
( ~ ( subset @ SV150 @ SY862 )
| ! [SY863: $i] : ( subset @ ( cartesian_product2 @ SY863 @ SV150 ) @ ( cartesian_product2 @ SY863 @ SY862 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1612]) ).
thf(1914,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1915,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1916,plain,
! [SV151: $i] :
( ( ( relation @ SV151 )
= $false )
| ( ( ~ ( ~ ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) )
| ~ ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1917,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1616]) ).
thf(1918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1919,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1920,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1921,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
| ~ ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) ) ) )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1922,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1923,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1924,plain,
( ( ~ ( ~ ( function @ sK91_A )
| ~ ( relation @ sK91_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1623]) ).
thf(1925,plain,
( ( one_to_one @ sK91_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1926,plain,
! [SV153: $i] :
( ( ~ ! [SY871: $i,SY872: $i] :
( ~ ( ~ ( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV153 )
| ~ ( in @ SY874 @ SY871 )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ~ ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) @ SY871 ) )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) ) )
| ( SY872
= ( cartesian_product2 @ SV153 @ SY871 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1927,plain,
! [SV153: $i] :
( ( ~ ! [SY875: $i,SY876: $i] :
( ( SY876
!= ( cartesian_product2 @ SV153 @ SY875 ) )
| ~ ( ~ ! [SY877: $i] :
( ! [SY878: $i,SY879: $i] :
( ~ ( in @ SY878 @ SV153 )
| ~ ( in @ SY879 @ SY875 )
| ( SY877
!= ( ordered_pair @ SY878 @ SY879 ) ) )
| ( in @ SY877 @ SY876 ) )
| ~ ! [SY880: $i] :
( ~ ( in @ SY880 @ SY876 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) @ SY875 ) )
| ( SY880
!= ( ordered_pair @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1928,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1929,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1930,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK48_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1628]) ).
thf(1931,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1933,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1936,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)],[1634]) ).
thf(1937,plain,
( ( ordinal @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( ordinal_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ordinal @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( ordinal_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1940,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)],[1638]) ).
thf(1941,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)],[1639]) ).
thf(1942,plain,
! [SV154: $i] :
( ( ( ~ ( function @ SV154 ) )
= $true )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1943,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1944,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1945,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SX0 ) @ ( relation_dom @ SX0 ) )
| ~ ( in @ ( sK21_SY619 @ SX0 ) @ ( relation_dom @ SX0 ) ) )
| ( ( apply @ SX0 @ ( sK20_B @ SX0 ) )
!= ( apply @ SX0 @ ( sK21_SY619 @ SX0 ) ) ) )
| ~ ( ( ( sK20_B @ SX0 )
!= ( sK21_SY619 @ SX0 ) ) ) )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1946,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)],[1644]) ).
thf(1947,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1949,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SX0 ) @ ( sK83_SY653 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SX0 ) @ ( sK82_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK82_B @ SX0 )
!= ( sK83_SY653 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1950,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)],[1648]) ).
thf(1951,plain,
! [SV155: $i] :
( ( ~ ! [SY889: $i,SY890: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) ) ) )
| ( SY890
= ( set_difference @ SV155 @ SY889 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1952,plain,
! [SV155: $i] :
( ( ~ ! [SY891: $i,SY892: $i] :
( ( SY892
!= ( set_difference @ SV155 @ SY891 ) )
| ~ ( ~ ! [SY893: $i] :
( ~ ( in @ SY893 @ SV155 )
| ( in @ SY893 @ SY891 )
| ( in @ SY893 @ SY892 ) )
| ~ ~ ( ~ ! [SY894: $i] :
( ~ ( in @ SY894 @ SY892 )
| ( in @ SY894 @ SV155 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY892 )
| ~ ( in @ SX3 @ SY891 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1953,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SX1 @ SX0 ) @ ( sK35_SY627 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK35_SY627 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK34_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1954,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK33_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK33_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1955,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( relation @ SY1133 )
| ~ ( in @ SV156 @ SY1132 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1133 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1132 ) @ SY1133 ) ) )
| ~ ~ ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) )
| ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1956,plain,
( ( empty @ sK94_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1957,plain,
( ( relation @ sK94_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1958,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK49_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK49_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK49_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1960,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1961,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( ordinal @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1963,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1964,plain,
! [SV157: $i] :
( ( ( ~ ( function @ SV157 ) )
= $true )
| ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( one_to_one @ SV157 )
| ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1965,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)],[1662]) ).
thf(1966,plain,
( ( ordinal @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1967,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
= ( relation_dom @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1968,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1969,plain,
( ( relation @ sK90_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1970,plain,
( ( relation_empty_yielding @ sK90_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1971,plain,
! [SV158: $i] :
( ( ( ordinal @ SV158 )
= $false )
| ( ( ~ ( ~ ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) )
| ~ ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1972,plain,
! [SV159: $i] :
( ( ~ ! [SY916: $i,SY917: $i] :
( ~ ( relation @ SY917 )
| ! [SY918: $i] :
( ~ ( in @ SY918 @ ( relation_rng @ SY917 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY918 ) @ SY917 )
| ~ ( in @ SY918 @ SY916 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SY917 @ SY916 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1973,plain,
! [SV159: $i] :
( ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( relation @ SY920 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SY920 @ SY919 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ ( relation_rng @ SY920 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SY920 @ SY919 @ SV159 ) ) @ SY920 ) )
| ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ SY919 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1669]) ).
thf(1974,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1975,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1976,plain,
! [SV160: $i] :
( ( ( relation @ SV160 )
= $false )
| ( ( ~ ( ~ ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) )
| ~ ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1977,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1978,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1979,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1980,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1981,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1982,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1983,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1984,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1985,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1986,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1987,plain,
! [SV161: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( relation @ SY924 )
| ~ ( in @ SV161 @ SY924 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SY923 @ SY923 ) )
| ( in @ SV161 @ ( relation_restriction @ SY924 @ SY923 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1988,plain,
! [SV161: $i] :
( ( ~ ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1683]) ).
thf(1989,plain,
! [SV162: $i] :
( ( ~ ! [SY929: $i,SY930: $i] :
( ~ ( relation @ SY930 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY929 ) @ SY930 )
| ( in @ SV162 @ ( relation_field @ SY930 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1990,plain,
! [SV162: $i] :
( ( ~ ! [SY931: $i,SY932: $i] :
( ~ ( relation @ SY932 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY931 ) @ SY932 )
| ( in @ SY931 @ ( relation_field @ SY932 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1684]) ).
thf(1991,plain,
! [SV286: $i,SV163: $i] :
( ( ~ ! [SY1138: $i] :
( ! [SY1139: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1138 @ SY1139 ) )
| ( SV163 = SY1138 ) )
| ~ ! [SY1140: $i,SY1141: $i] :
( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1140 @ SY1141 ) )
| ( SV286 = SY1141 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1992,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1993,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1994,plain,
! [SV164: $i] :
( ( ~ ! [SY938: $i,SY939: $i] :
( ~ ( function @ SY939 )
| ~ ( relation @ SY939 )
| ~ ( in @ SY938 @ ( relation_dom @ SY939 ) )
| ~ ( in @ SY938 @ SV164 )
| ( in @ SY938 @ ( relation_dom @ ( relation_dom_restriction @ SY939 @ SV164 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1995,plain,
! [SV164: $i] :
( ( ~ ~ ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) )
| ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1996,plain,
! [SV165: $i,SV287: $i] :
( ( ( ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV287 )
| ~ ( in @ SY1142 @ ( sK3_C @ SV287 @ SV165 ) ) )
| ~ ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 ) ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(1997,plain,
! [SV166: $i] :
( ( ~ ! [SY946: $i,SY947: $i] :
( ~ ( relation @ SY947 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY946 ) @ SY947 )
| ( in @ SV166 @ ( relation_dom @ SY947 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1998,plain,
! [SV166: $i] :
( ( ~ ! [SY948: $i,SY949: $i] :
( ~ ( relation @ SY949 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY948 ) @ SY949 )
| ( in @ SY948 @ ( relation_rng @ SY949 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1999,plain,
! [SV167: $i] :
( ( ~ ! [SY950: $i] :
( ~ ( subset @ SY950 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SY950 @ ( sK80_B @ SV167 ) )
| ( in @ SY950 @ ( sK80_B @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(2000,plain,
! [SV167: $i] :
( ( ~ ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(2001,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK104_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK104_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(2002,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(2003,plain,
! [SV168: $i] :
( ( ~ ! [SY954: $i,SY955: $i] :
( ~ ( function @ SY955 )
| ~ ( relation @ SY955 )
| ( SY954
!= ( apply @ SY955 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SY955 ) )
| ( in @ ( ordered_pair @ SV168 @ SY954 ) @ SY955 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1694]) ).
thf(2004,plain,
! [SV168: $i] :
( ( ~ ~ ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) )
| ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1694]) ).
thf(2005,plain,
( ( ~ ( ~ ( empty @ sK93_A )
| ~ ( relation @ sK93_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(2006,plain,
( ( function @ sK93_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(2007,plain,
! [SV169: $i] :
( ( ( ~ ( function @ SV169 ) )
= $true )
| ( ( ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(2008,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(2009,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(2010,plain,
! [SV170: $i] :
( ( ( ~ ( function @ SV170 ) )
= $true )
| ( ( ~ ( relation @ SV170 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(2011,plain,
( ( ~ ( ~ ( epsilon_connected @ sK11_A )
| ~ ( epsilon_transitive @ sK11_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(2012,plain,
( ( ordinal @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(2013,plain,
( ( ! [SX0: $i] : ( function @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(2014,plain,
( ( ! [SX0: $i] : ( relation @ ( identity_relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(2015,plain,
! [SV171: $i] :
( ( ~ ! [SY975: $i,SY976: $i] :
( ~ ( relation @ SY976 )
| ~ ( in @ SV171 @ SY975 )
| ~ ( in @ SV171 @ ( relation_dom @ SY976 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY976 @ SY975 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(2016,plain,
! [SV171: $i] :
( ( ~ ~ ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) )
| ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(2017,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(2018,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(2019,plain,
( ( ~ ( empty @ sK92_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(2020,plain,
( ( relation @ sK92_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(2021,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(2022,plain,
( ( ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(2023,plain,
! [SV172: $i] :
( ( ( relation @ SV172 )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( relation @ SY981 )
| ~ ( ~ ! [SY982: $i] :
( ~ ( relation @ SY982 )
| ~ ( ~ ( ! [SY983: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ SY983 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY983 @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY981 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY982 @ SY981 @ SV172 ) @ ( sK18_SY614 @ SY982 @ SY981 @ SV172 ) ) @ SY982 ) ) )
| ( SY982
= ( relation_composition @ SV172 @ SY981 ) ) )
| ~ ! [SY984: $i] :
( ~ ( relation @ SY984 )
| ( SY984
!= ( relation_composition @ SV172 @ SY981 ) )
| ~ ( ~ ! [SY985: $i,SY986: $i] :
( ! [SY987: $i] :
( ~ ( in @ ( ordered_pair @ SY985 @ SY987 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY987 @ SY986 ) @ SY981 ) )
| ( in @ ( ordered_pair @ SY985 @ SY986 ) @ SY984 ) )
| ~ ! [SY988: $i,SY989: $i] :
( ~ ( in @ ( ordered_pair @ SY988 @ SY989 ) @ SY984 )
| ~ ( ~ ( in @ ( ordered_pair @ SY988 @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY989 @ SY988 @ SY984 @ SY981 @ SV172 ) @ SY989 ) @ SY981 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(2024,plain,
! [SV173: $i] :
( ( ( relation @ SV173 )
= $false )
| ( ( ~ ( ~ ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) )
| ~ ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(2025,plain,
! [SV174: $i,SV288: $i] :
( ( ~ ! [SY1143: $i,SY1144: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SY1143 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SY1143 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SY1144
= ( unordered_triple @ SV174 @ SV288 @ SY1143 ) ) )
| ~ ! [SY1145: $i,SY1146: $i] :
( ( SY1146
!= ( unordered_triple @ SV174 @ SV288 @ SY1145 ) )
| ~ ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ SY1146 )
| ( SY1147 = SY1145 )
| ( SY1147 = SV174 )
| ( SY1147 = SV288 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1145 )
| ( in @ SX4 @ SY1146 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1146 ) )
| ~ ! [SY1150: $i] :
( ( SY1150 != SV288 )
| ( in @ SY1150 @ SY1146 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(2026,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(2027,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)],[1716]) ).
thf(2028,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(2029,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(2030,plain,
! [SV175: $i] :
( ( ~ ! [SY1005: $i,SY1006: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SY1005 ) ) )
| ~ ( ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SV175 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SY1005 ) ) )
| ( SY1006
= ( unordered_pair @ SV175 @ SY1005 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(2031,plain,
! [SV175: $i] :
( ( ~ ! [SY1007: $i,SY1008: $i] :
( ( SY1008
!= ( unordered_pair @ SV175 @ SY1007 ) )
| ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SY1008 )
| ( SY1009 = SV175 )
| ( SY1009 = SY1007 ) )
| ~ ~ ( ~ ! [SY1010: $i] :
( ( SY1010 != SV175 )
| ( in @ SY1010 @ SY1008 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1007 )
| ( in @ SX3 @ SY1008 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(2032,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK85_SY654 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SX0 ) @ ( sK86_SY656 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(2033,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)],[1721]) ).
thf(2034,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(2035,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(2036,plain,
! [SV176: $i,SV289: $i] :
( ( ( ~ ( function @ SV289 )
| ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(2037,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(2038,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(2039,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( function @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(2040,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ( relation @ ( function_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(2041,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(2042,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(2043,plain,
! [SV177: $i] :
( ( ~ ! [SY1016: $i,SY1017: $i] :
( ~ ( in @ SV177 @ SY1017 )
| ~ ( in @ SY1016 @ SY1017 )
| ( subset @ ( unordered_pair @ SV177 @ SY1016 ) @ SY1017 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(2044,plain,
! [SV177: $i] :
( ( ~ ~ ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) )
| ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(2045,plain,
! [SV178: $i,SV290: $i] :
( ( ( ~ ( ordinal @ SV290 ) )
= $true )
| ( ( ~ ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
| ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
| ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(2046,plain,
! [SV179: $i,SV291: $i] :
( ( ( ~ ( element @ SV291 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) )
| ~ ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(2047,plain,
! [SV180: $i] :
( ( ~ ( element @ ( sK7_B @ SV180 ) @ ( powerset @ SV180 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(2048,plain,
! [SV180: $i] :
( ( ~ ( empty @ ( sK7_B @ SV180 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(2049,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(2050,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(2051,plain,
! [SV181: $i] :
( ( ( relation @ SV181 )
= $false )
| ( ( ~ ( ~ ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) )
| ~ ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(2052,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)],[1738]) ).
thf(2053,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)],[1739]) ).
thf(2054,plain,
! [SV182: $i] :
( ( ( ~ ( function @ SV182 ) )
= $true )
| ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(2055,plain,
! [SV183: $i] :
( ( ( ~ ( in @ ( sK111_B @ SV183 ) @ SV183 )
| ~ ( ~ ( ordinal @ ( sK111_B @ SV183 ) )
| ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) ) )
= $false )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(2056,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ( function @ SV292 )
| ~ ( relation @ SV292 ) )
= $true )
| ( ( ~ ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(2057,plain,
( ( ~ ( ~ ( relation @ sK89_A )
| ~ ( relation_empty_yielding @ sK89_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(2058,plain,
( ( function @ sK89_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1744]) ).
thf(2059,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SX0 )
!= ( sK40_SY629 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK40_SY629 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK39_B @ SX0 ) @ ( sK40_SY629 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SX0 ) @ ( sK39_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(2060,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(2061,plain,
! [SV185: $i] :
( ( ( relation @ SV185 )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) )
| ~ ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(2062,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(2063,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(2064,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)],[1750]) ).
thf(2065,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( one_to_one @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(2066,plain,
! [SV186: $i] :
( ( ~ ! [SY1054: $i,SY1055: $i] :
( ~ ( relation @ SY1055 )
| ~ ( in @ SV186 @ SY1054 )
| ~ ( in @ SV186 @ ( relation_rng @ SY1055 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1054 @ SY1055 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(2067,plain,
! [SV186: $i] :
( ( ~ ~ ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) )
| ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(2068,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(2069,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(2070,plain,
! [SV187: $i] :
( ( ~ ! [SY1060: $i,SY1061: $i] :
( ~ ( relation @ SY1061 )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( relation_dom @ SY1061 ) )
| ~ ( in @ ( ordered_pair @ SY1062 @ SV187 ) @ SY1061 )
| ~ ( in @ SY1062 @ SY1060 ) )
| ( in @ SV187 @ ( relation_image @ SY1061 @ SY1060 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(2071,plain,
! [SV187: $i] :
( ( ~ ! [SY1063: $i,SY1064: $i] :
( ~ ( relation @ SY1064 )
| ~ ( in @ SV187 @ ( relation_image @ SY1064 @ SY1063 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ ( relation_dom @ SY1064 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SV187 ) @ SY1064 ) )
| ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SY1063 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(2072,plain,
! [SV188: $i] :
( ( ( relation @ SV188 )
= $false )
| ( ( ~ ( ~ ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) )
| ~ ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(2073,plain,
( ( ! [SX0: $i] :
( ( relation_dom @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(2074,plain,
( ( ! [SX0: $i] :
( ( relation_rng @ ( identity_relation @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(2075,plain,
! [SV189: $i] :
( ( ~ ! [SY1069: $i,SY1070: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) ) ) )
| ( SY1070
= ( set_intersection2 @ SV189 @ SY1069 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(2076,plain,
! [SV189: $i] :
( ( ~ ! [SY1071: $i,SY1072: $i] :
( ( SY1072
!= ( set_intersection2 @ SV189 @ SY1071 ) )
| ~ ( ~ ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV189 )
| ~ ( in @ SY1073 @ SY1071 )
| ( in @ SY1073 @ SY1072 ) )
| ~ ~ ( ~ ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SY1072 )
| ( in @ SY1074 @ SV189 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1072 )
| ( in @ SX3 @ SY1071 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(2077,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ~ ( epsilon_transitive @ SX0 )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(2078,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(2079,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ! [SY1161: $i,SY1162: $i] :
( ~ ( in @ SV190 @ SY1161 )
| ~ ( in @ SV293 @ SY1162 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1161 @ SY1162 ) ) )
| ~ ~ ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) )
| ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(2080,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
| ~ ( epsilon_connected @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(2081,plain,
( ( ordinal @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(2082,plain,
( ( function @ sK95_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(2083,plain,
( ( relation @ sK95_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(2084,plain,
! [SV191: $i,SV294: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV191 )
| ~ ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 ) ) )
= $true )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2085,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(2086,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ! [SX1: $i] : ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(2087,plain,
! [SV192: $i] :
( ( ( relation @ SV192 )
= $false )
| ( ( ~ ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) )
| ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(2088,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
!= ( sK68_SY645 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SX1 @ SX0 )
= ( sK68_SY645 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK67_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK67_C @ SX1 @ SX0 ) @ ( sK68_SY645 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(2089,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)],[1772]) ).
thf(2090,plain,
! [SV193: $i,SV1: $i] :
( ( ( in @ SV1 @ SV193 )
= $false )
| ( ( subset @ SV1 @ ( union @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(2091,plain,
! [SV2: $i,SV194: $i] :
( ( ( relation @ SV194 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV2 @ SV194 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(2092,plain,
! [SV3: $i,SV195: $i] :
( ( ( relation @ SV195 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV3 @ SV195 ) @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(2093,plain,
! [SV4: $i,SV196: $i] :
( ( ( relation @ SV196 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV4 @ SV196 ) ) @ ( relation_rng @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(2094,plain,
! [SV5: $i,SV197: $i] :
( ( ( relation @ SV197 )
= $false )
| ( ( ( relation_rng @ ( relation_rng_restriction @ SV5 @ SV197 ) )
= ( set_intersection2 @ ( relation_rng @ SV197 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(2095,plain,
! [SV315: $i,SV295: $i,SV198: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV198 )
| ~ ( subset @ SV295 @ SV315 )
| ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2096,plain,
! [SV199: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV199 )
= $false )
| ( ( ( set_union2 @ SV7 @ SV199 )
= SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(2097,plain,
! [SV200: $i,SV8: $i,SV296: $i] :
( ( ( ~ ( relation @ SV296 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV8 @ SV296 ) @ SV200 )
= ( relation_rng_restriction @ SV8 @ ( relation_dom_restriction @ SV296 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2098,plain,
! [SV9: $i,SV201: $i] :
( ( ( relation @ SV201 )
= $false )
| ( ( subset @ ( relation_image @ SV201 @ SV9 ) @ ( relation_rng @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(2099,plain,
! [SV10: $i,SV202: $i] :
( ( ( relation @ SV202 )
= $false )
| ( ( ( relation_image @ SV202 @ SV10 )
= ( relation_image @ SV202 @ ( set_intersection2 @ ( relation_dom @ SV202 ) @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2100,plain,
! [SV11: $i,SV203: $i] :
( ( ( relation @ SV203 )
= $false )
| ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV203 ) )
| ( subset @ SV11 @ ( relation_inverse_image @ SV203 @ ( relation_image @ SV203 @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(2101,plain,
! [SV13: $i,SV204: $i] :
( ( ( relation @ SV204 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV204 @ SV13 ) @ ( relation_dom @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(2102,plain,
! [SV205: $i,SV14: $i,SV297: $i] :
( ( ( ~ ( relation @ SV297 ) )
= $true )
| ( ( ~ ( subset @ SV14 @ SV205 )
| ( subset @ ( relation_inverse_image @ SV297 @ SV14 ) @ ( relation_inverse_image @ SV297 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(2103,plain,
! [SV15: $i,SV206: $i] :
( ( ( relation @ SV206 )
= $false )
| ( ( ( relation_restriction @ SV206 @ SV15 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV15 @ SV206 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(2104,plain,
! [SV17: $i,SV208: $i] :
( ( ( relation @ SV208 )
= $false )
| ( ( ( relation_restriction @ SV208 @ SV17 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV208 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2105,plain,
! [SV298: $i,SV209: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV209 )
| ~ ( subset @ SV18 @ SV298 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2106,plain,
! [SV299: $i,SV210: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV210 )
| ~ ( subset @ SV210 @ SV299 ) )
= $true )
| ( ( subset @ SV19 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2107,plain,
! [SV211: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV211 )
= $false )
| ( ( ! [SY1098: $i] : ( subset @ ( set_intersection2 @ SV21 @ SY1098 ) @ ( set_intersection2 @ SV211 @ SY1098 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(2108,plain,
! [SV212: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV212 )
= $false )
| ( ( ( set_intersection2 @ SV22 @ SV212 )
= SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2109,plain,
! [SV213: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV213 )
= $false )
| ( ( ! [SY1099: $i] : ( subset @ ( set_difference @ SV24 @ SY1099 ) @ ( set_difference @ SV213 @ SY1099 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(2110,plain,
! [SV27: $i,SV316: $i] :
( ( ( ~ ( relation @ SV316 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SV316 ) ) @ ( relation_dom @ SV27 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2111,plain,
! [SV28: $i,SV317: $i] :
( ( ( ~ ( relation @ SV317 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SV317 ) ) @ ( relation_rng @ SV317 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2112,plain,
! [SV215: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV215 )
= $false )
| ( ( SV215
= ( set_union2 @ SV29 @ ( set_difference @ SV215 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(2113,plain,
! [SV30: $i,SV318: $i] :
( ( ( ~ ( relation @ SV318 )
| ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SV318 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SV318 ) )
= ( relation_dom @ SV30 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2114,plain,
! [SV31: $i,SV319: $i] :
( ( ( ~ ( relation @ SV319 )
| ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SV319 ) )
| ( ( relation_rng @ ( relation_composition @ SV319 @ SV31 ) )
= ( relation_rng @ SV31 ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2115,plain,
! [SV32: $i,SV216: $i] :
( ( ( proper_subset @ SV216 @ SV32 )
= $false )
| ( ( ~ ( subset @ SV32 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(2116,plain,
! [SV33: $i,SV300: $i,SV217: $i] :
( ( ( ~ ( disjoint @ SV217 @ SV300 )
| ~ ( subset @ SV33 @ SV217 ) )
= $true )
| ( ( disjoint @ SV33 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(2117,plain,
! [SV218: $i,SV34: $i] :
( ( ( subset @ ( singleton @ SV34 ) @ ( singleton @ SV218 ) )
= $false )
| ( ( SV34 = SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2118,plain,
! [SV36: $i,SV220: $i] :
( ( ( relation @ SV220 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV220 @ SV36 ) @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(2119,plain,
! [SV301: $i,SV221: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV221 )
| ~ ( subset @ SV301 @ SV221 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV37 @ SV301 ) @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1805]) ).
thf(2120,plain,
! [SV38: $i,SV222: $i] :
( ( ( relation @ SV222 )
= $false )
| ( ( ( relation_dom @ ( relation_dom_restriction @ SV222 @ SV38 ) )
= ( set_intersection2 @ ( relation_dom @ SV222 ) @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2121,plain,
! [SV223: $i,SV39: $i] :
( ( ( in @ SV39 @ SV223 )
= $false )
| ( ( subset @ SV39 @ ( union @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(2122,plain,
! [SV40: $i,SV224: $i] :
( ( ( relation @ SV224 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV224 @ SV40 ) ) @ ( relation_rng @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(2123,plain,
! [SV320: $i,SV42: $i] :
( ( ( relation @ ( relation_restriction @ SV42 @ SV320 ) )
= $true )
| ( ( relation @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2124,plain,
! [SV225: $i,SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2125,plain,
! [SV321: $i,SV46: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV46 @ SV321 ) )
= $true )
| ( ( relation @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2126,plain,
! [SV47: $i,SV226: $i] :
( ( ( relation @ SV226 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV47 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2127,plain,
! [SV227: $i,SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV48 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(2128,plain,
! [SV228: $i,SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV49 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2129,plain,
! [SV229: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( relation @ SV229 ) )
= $true )
| ( ( relation @ ( set_difference @ SV50 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2130,plain,
! [SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( empty @ SV51 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV51 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2131,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(2132,plain,
! [SV230: $i,SV56: $i] :
( ( ( in @ SV56 @ SV230 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV56 ) @ SV230 )
= SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(2133,plain,
! [SV231: $i,SV57: $i] :
( ( ( disjoint @ ( singleton @ SV57 ) @ SV231 )
= $false )
| ( ( ~ ( in @ SV57 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2134,plain,
! [SV59: $i,SV233: $i] :
( ( ( element @ SV233 @ ( powerset @ SV59 ) )
= $false )
| ( ( ! [SY1102: $i] :
( ~ ( in @ SY1102 @ SV233 )
| ( in @ SY1102 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2135,plain,
! [SV234: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV234 )
= $false )
| ( ( ! [SY1103: $i] :
( ( in @ SY1103 @ SV60 )
| ( subset @ SV60 @ ( set_difference @ SV234 @ ( singleton @ SY1103 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(2136,plain,
! [SV235: $i,SV302: $i,SV322: $i,SV62: $i] :
( ( ( SV62 = SV322 )
| ( SV62 = SV302 )
| ( ( unordered_pair @ SV62 @ SV235 )
!= ( unordered_pair @ SV302 @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2137,plain,
! [SV63: $i,SV236: $i] :
( ( ( ~ ( function @ SV236 ) )
= $true )
| ( ( ~ ( relation @ SV236 ) )
= $true )
| ( ( subset @ ( relation_image @ SV236 @ ( relation_inverse_image @ SV236 @ SV63 ) ) @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2138,plain,
! [SV64: $i,SV237: $i] :
( ( ( ~ ( function @ SV237 ) )
= $true )
| ( ( ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) )
| ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2139,plain,
! [SV65: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 )
| ( ( relation_rng @ ( relation_composition @ SV65 @ SV323 ) )
= ( relation_image @ SV323 @ ( relation_rng @ SV65 ) ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2140,plain,
! [SV66: $i,SV238: $i] :
( ( ( relation @ SV238 )
= $false )
| ( ( ( SV66 = empty_set )
| ~ ( subset @ SV66 @ ( relation_rng @ SV238 ) )
| ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(2141,plain,
! [SV67: $i,SV324: $i] :
( ( ( ~ ( ordinal @ SV324 )
| ~ ( proper_subset @ SV67 @ SV324 )
| ( in @ SV67 @ SV324 ) )
= $true )
| ( ( epsilon_transitive @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2142,plain,
! [SV68: $i,SV239: $i] :
( ( ( ~ ( function @ SV239 ) )
= $true )
| ( ( ~ ( relation @ SV239 ) )
= $true )
| ( ( ! [SY1106: $i] :
( ~ ( function @ SY1106 )
| ~ ( relation @ SY1106 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY1106 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SY1106 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SY1106 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2143,plain,
! [SV69: $i,SV240: $i] :
( ( ( ~ ( function @ SV240 ) )
= $true )
| ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ! [SY1107: $i] :
( ~ ( function @ SY1107 )
| ~ ( relation @ SY1107 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SY1107 ) @ SV69 )
= ( apply @ SY1107 @ ( apply @ SV240 @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(2144,plain,
! [SV70: $i,SV241: $i] :
( ( ( ordinal @ SV241 )
= $false )
| ( ( ~ ( in @ SV70 @ SV241 )
| ( ordinal @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2145,plain,
! [SV71: $i,SV325: $i] :
( ( ( ~ ( ordinal @ SV325 )
| ( in @ SV71 @ SV325 )
| ( SV71 = SV325 )
| ( in @ SV325 @ SV71 ) )
= $true )
| ( ( ordinal @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2146,plain,
! [SV72: $i,SV242: $i] :
( ( ( in @ SV242 @ SV72 )
= $false )
| ( ( ( apply @ ( identity_relation @ SV72 ) @ SV242 )
= SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2147,plain,
! [SV303: $i,SV244: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ SV244 )
| ~ ( in @ SV244 @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV303 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2148,plain,
! [SV76: $i,SV246: $i] :
( ( ( element @ SV246 @ ( powerset @ ( powerset @ SV76 ) ) )
= $false )
| ( ( ( SV246 = empty_set )
| ( ( complements_of_subsets @ SV76 @ SV246 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2149,plain,
! [SV247: $i,SV77: $i] :
( ( ( in @ SV77 @ SV247 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV77 ) @ SV247 )
= SV247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2150,plain,
! [SV79: $i,SV304: $i] :
( ( ( ~ ( element @ SV304 @ ( powerset @ SV79 ) ) )
= $true )
| ( ( ! [SY1169: $i] :
( ~ ( element @ SY1169 @ SV79 )
| ( in @ SY1169 @ SV304 )
| ( in @ SY1169 @ ( subset_complement @ SV79 @ SV304 ) ) ) )
= $true )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2151,plain,
! [SV249: $i,SV80: $i,SV305: $i] :
( ( ( ~ ( element @ SV305 @ ( powerset @ SV80 ) ) )
= $true )
| ( ( ~ ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) )
| ~ ( in @ SV249 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2152,plain,
! [SV81: $i] :
( ( ( in @ ( ordered_pair @ ( sK70_B @ SV81 ) @ ( sK71_SY646 @ SV81 ) ) @ SV81 )
= $true )
| ( ( SV81 = empty_set )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2153,plain,
! [SV82: $i] :
( ( ( function @ SV82 )
= $false )
| ( ( ~ ( relation @ SV82 ) )
= $true )
| ( ( ~ ( one_to_one @ SV82 )
| ( one_to_one @ ( function_inverse @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2154,plain,
! [SV84: $i,SV250: $i,SV306: $i] :
( ( ( ~ ( function @ SV306 )
| ~ ( relation @ SV306 ) )
= $true )
| ( ( ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2155,plain,
! [SV85: $i,SV251: $i,SV307: $i] :
( ( ( ~ ( function @ SV307 )
| ~ ( relation @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2156,plain,
! [SV326: $i,SV252: $i,SV86: $i] :
( ( ( ( ( singleton @ SV86 )
!= ( unordered_pair @ SV252 @ SV326 ) ) )
= $true )
| ( ( SV86 = SV252 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2157,plain,
! [SV87: $i,SV253: $i] :
( ( ( relation @ SV253 )
= $false )
| ( ( ( relation_dom_restriction @ SV253 @ SV87 )
= ( relation_composition @ ( identity_relation @ SV87 ) @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2158,plain,
! [SV308: $i,SV254: $i,SV89: $i] :
( ( ( ( ( singleton @ SV89 )
!= ( unordered_pair @ SV254 @ SV308 ) ) )
= $true )
| ( ( SV254 = SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2159,plain,
! [SV255: $i,SV90: $i] :
( ( ( in @ SV90 @ SV255 )
= $false )
| ( ( ~ ( in @ SV255 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1849]) ).
thf(2160,plain,
! [SV256: $i,SV91: $i] :
( ( ( proper_subset @ SV91 @ SV256 )
= $false )
| ( ( ~ ( proper_subset @ SV256 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2161,plain,
! [SV93: $i] :
( ( ( epsilon_connected @ SV93 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV93 ) )
= $true )
| ( ( ordinal @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2162,plain,
! [SV260: $i,SV97: $i] :
( ( ( ~ ( ordinal @ SV97 ) )
= $true )
| ( ( ~ ( ordinal @ SV260 ) )
= $true )
| ( ( ( ordinal_subset @ SV97 @ SV260 )
| ( ordinal_subset @ SV260 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2163,plain,
! [SV99: $i,SV261: $i] :
( ( ( element @ SV261 @ ( powerset @ SV99 ) )
= $false )
| ( ( ( subset_complement @ SV99 @ SV261 )
= ( set_difference @ SV99 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2164,plain,
! [SV327: $i,SV102: $i] :
( ( ( ( relation_restriction @ SV102 @ SV327 )
= ( set_intersection2 @ SV102 @ ( cartesian_product2 @ SV327 @ SV327 ) ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2165,plain,
! [SV103: $i] :
( ( ( function @ SV103 )
= $false )
| ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ~ ( one_to_one @ SV103 )
| ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2166,plain,
! [SV105: $i,SV263: $i] :
( ( ( element @ SV263 @ ( powerset @ SV105 ) )
= $false )
| ( ( element @ ( subset_complement @ SV105 @ SV263 ) @ ( powerset @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2167,plain,
! [SV106: $i,SV264: $i] :
( ( ( element @ SV264 @ ( powerset @ ( powerset @ SV106 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV106 @ SV264 ) @ ( powerset @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2168,plain,
! [SV107: $i,SV265: $i] :
( ( ( element @ SV265 @ ( powerset @ ( powerset @ SV107 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV107 @ SV265 ) @ ( powerset @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2169,plain,
! [SV309: $i,SV108: $i,SV266: $i] :
( ( ( ~ ( element @ SV266 @ ( powerset @ SV108 ) )
| ~ ( element @ SV309 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV108 @ SV266 @ SV309 ) @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2170,plain,
! [SV109: $i,SV267: $i] :
( ( ( element @ SV267 @ ( powerset @ ( powerset @ SV109 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV109 @ SV267 ) @ ( powerset @ ( powerset @ SV109 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(2171,plain,
! [SV310: $i,SV115: $i] :
( ( ( empty @ ( set_union2 @ SV115 @ SV310 ) )
= $false )
| ( ( empty @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2172,plain,
! [SV117: $i,SV311: $i] :
( ( ( empty @ ( set_union2 @ SV311 @ SV117 ) )
= $false )
| ( ( empty @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2173,plain,
! [SV270: $i,SV118: $i] :
( ( ( empty @ SV118 )
= $true )
| ( ( empty @ SV270 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV118 @ SV270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2174,plain,
! [SV121: $i,SV271: $i] :
( ( ( element @ SV271 @ ( powerset @ SV121 ) )
= $false )
| ( ( ( subset_complement @ SV121 @ ( subset_complement @ SV121 @ SV271 ) )
= SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2175,plain,
! [SV122: $i,SV272: $i] :
( ( ( element @ SV272 @ ( powerset @ ( powerset @ SV122 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV122 @ ( complements_of_subsets @ SV122 @ SV272 ) )
= SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2176,plain,
! [SV124: $i,SV273: $i] :
( ( ( element @ SV273 @ ( powerset @ ( powerset @ SV124 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV124 @ SV273 )
= ( union @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2177,plain,
! [SV312: $i,SV125: $i,SV274: $i] :
( ( ( ~ ( element @ SV274 @ ( powerset @ SV125 ) )
| ~ ( element @ SV312 @ ( powerset @ SV125 ) ) )
= $true )
| ( ( ( subset_difference @ SV125 @ SV274 @ SV312 )
= ( set_difference @ SV274 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2178,plain,
! [SV126: $i] :
( ( ( ordinal @ SV126 )
= $false )
| ( ( ! [B: $i] :
~ ( ordinal @ B ) )
= $true )
| ( ( ordinal_subset @ SV126 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2179,plain,
! [SV275: $i,SV127: $i] :
( ( ( disjoint @ SV127 @ SV275 )
= $false )
| ( ( disjoint @ SV275 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(2180,plain,
! [SV276: $i,SV129: $i] :
( ( ( in @ SV129 @ SV276 )
= $false )
| ( ( element @ SV129 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2181,plain,
! [SV277: $i,SV131: $i] :
( ( ( element @ SV131 @ SV277 )
= $false )
| ( ( ( empty @ SV277 )
| ( in @ SV131 @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2182,plain,
! [SV134: $i,SV313: $i,SV278: $i] :
( ( ( ~ ( element @ SV278 @ ( powerset @ SV313 ) )
| ~ ( in @ SV134 @ SV278 ) )
= $true )
| ( ( element @ SV134 @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2183,plain,
! [SV135: $i,SV314: $i,SV279: $i] :
( ( ( ~ ( element @ SV279 @ ( powerset @ SV314 ) )
| ~ ( in @ SV135 @ SV279 ) )
= $true )
| ( ( ~ ( empty @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2184,plain,
! [SV137: $i,SV280: $i] :
( ( ( empty @ SV280 )
= $false )
| ( ( ~ ( in @ SV137 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2185,plain,
! [SV281: $i,SV138: $i] :
( ( ( SV138 = SV281 )
= $true )
| ( ( ~ ( empty @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2186,plain,
! [SV328: $i] :
( ( ! [SY1170: $i] :
( ( disjoint @ SV328 @ SY1170 )
| ( in @ ( sK74_C @ SY1170 @ SV328 ) @ ( set_intersection2 @ SV328 @ SY1170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2187,plain,
! [SV329: $i] :
( ( ! [SY1171: $i] :
( ! [SY1172: $i] :
~ ( in @ SY1172 @ ( set_intersection2 @ SV329 @ SY1171 ) )
| ~ ( disjoint @ SV329 @ SY1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2188,plain,
! [SV330: $i] :
( ( ! [SY1173: $i] :
( ~ ( function @ SY1173 )
| ~ ( relation @ SY1173 )
| ( function @ ( relation_rng_restriction @ SV330 @ SY1173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2189,plain,
! [SV331: $i] :
( ( ! [SY1174: $i] :
( ~ ( function @ SY1174 )
| ~ ( relation @ SY1174 )
| ( relation @ ( relation_rng_restriction @ SV331 @ SY1174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2190,plain,
! [SV332: $i] :
( ( ~ ( function @ SV332 )
| ~ ( relation @ SV332 )
| ~ ( one_to_one @ SV332 )
| ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2191,plain,
! [SV333: $i] :
( ( ~ ( function @ SV333 )
| ~ ( relation @ SV333 )
| ~ ( one_to_one @ SV333 )
| ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2192,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2193,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2194,plain,
! [SV139: $i] :
( ( ( ~ ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) )
| ~ ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2195,plain,
! [SV140: $i] :
( ( ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) )
| ~ ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(2196,plain,
! [SV334: $i] :
( ( ~ ( function @ SV334 )
| ~ ( relation @ SV334 )
| ~ ( one_to_one @ SV334 )
| ( function @ ( relation_inverse @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2197,plain,
! [SV335: $i] :
( ( ~ ( function @ SV335 )
| ~ ( relation @ SV335 )
| ~ ( one_to_one @ SV335 )
| ( relation @ ( relation_inverse @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2198,plain,
! [SV141: $i] :
( ( ( ~ ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) )
| ~ ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2199,plain,
! [SV336: $i] :
( ( ~ ( ~ ! [SY1175: $i,SY1176: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SY1175 @ SY1176 ) )
| ~ ( in @ ( sK108_B @ SV336 ) @ SV336 ) )
| ( relation @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2200,plain,
! [SV337: $i] :
( ( ~ ( relation @ SV337 )
| ! [SY1177: $i] :
( ( SY1177
= ( ordered_pair @ ( sK106_C @ SY1177 @ SV337 ) @ ( sK107_SY668 @ SY1177 @ SV337 ) ) )
| ~ ( in @ SY1177 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2201,plain,
! [SV142: $i,SV282: $i] :
( ( ( relation @ SV282 )
= $false )
| ( ( ~ ( ~ ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
| ~ ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2202,plain,
! [SV338: $i] :
( ( ~ ( empty @ SV338 )
| ( empty @ ( relation_inverse @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2203,plain,
! [SV339: $i] :
( ( ~ ( empty @ SV339 )
| ( relation @ ( relation_inverse @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2204,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ! [SY1126: $i,SY1127: $i] :
( ~ ( in @ SV143 @ SY1126 )
| ~ ( in @ SV283 @ SY1127 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1126 @ SY1127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2205,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ~ ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1899]) ).
thf(2206,plain,
! [SV144: $i] :
( ( ! [SY834: $i] :
( ~ ( subset @ SY834 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SY834 @ ( sK87_B @ SV144 ) )
| ( in @ SY834 @ ( sK87_B @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2207,plain,
! [SV144: $i] :
( ( ~ ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(2208,plain,
! [SV340: $i] :
( ( ! [SY1178: $i] :
( ~ ( ~ ( in @ ( sK99_C @ SY1178 @ SV340 ) @ SV340 )
| ~ ~ ( in @ ( sK99_C @ SY1178 @ SV340 ) @ SY1178 ) )
| ( subset @ SV340 @ SY1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2209,plain,
! [SV341: $i] :
( ( ! [SY1179: $i] :
( ~ ( subset @ SV341 @ SY1179 )
| ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV341 )
| ( in @ SY1180 @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2210,plain,
! [SV145: $i] :
( ( ! [SY839: $i,SY840: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ~ ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ~ ( ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY840 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SY840 @ SY839 @ SV145 ) @ SY839 ) ) )
| ( SY840
= ( set_union2 @ SV145 @ SY839 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2211,plain,
! [SV145: $i] :
( ( ! [SY841: $i,SY842: $i] :
( ( SY842
!= ( set_union2 @ SV145 @ SY841 ) )
| ~ ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SY842 )
| ( in @ SY843 @ SV145 )
| ( in @ SY843 @ SY841 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV145 )
| ( in @ SY844 @ SY842 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY841 )
| ( in @ SX3 @ SY842 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(2212,plain,
! [SV146: $i] :
( ( ( ~ ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) )
| ~ ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(2213,plain,
! [SV147: $i] :
( ( ( ~ ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) )
| ~ ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2214,plain,
! [SV342: $i] :
( ( ! [SY1181: $i] :
( ~ ( function @ SY1181 )
| ~ ( relation @ SY1181 )
| ~ ( ~ ( in @ ( sK76_C @ SY1181 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SY1181 @ ( sK76_C @ SY1181 @ SV342 ) )
!= ( sK76_C @ SY1181 @ SV342 ) ) ) )
| ( ( relation_dom @ SY1181 )
!= SV342 )
| ( SY1181
= ( identity_relation @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2215,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)],[1909]) ).
thf(2216,plain,
! [SV148: $i] :
( ( ( ~ ( element @ ( sK10_B @ SV148 ) @ ( powerset @ SV148 ) ) )
= $false )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(2217,plain,
! [SV148: $i] :
( ( ( ~ ~ ( empty @ ( sK10_B @ SV148 ) ) )
= $false )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(2218,plain,
! [SV149: $i] :
( ( ( ~ ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) )
| ~ ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2219,plain,
! [SV150: $i] :
( ( ! [SY860: $i] :
( ~ ( subset @ SV150 @ SY860 )
| ! [SY861: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY861 ) @ ( cartesian_product2 @ SY860 @ SY861 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(2220,plain,
! [SV150: $i] :
( ( ! [SY862: $i] :
( ~ ( subset @ SV150 @ SY862 )
| ! [SY863: $i] : ( subset @ ( cartesian_product2 @ SY863 @ SV150 ) @ ( cartesian_product2 @ SY863 @ SY862 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2221,plain,
! [SV343: $i] :
( ( ! [SY1182: $i] :
( ( ( set_difference @ SV343 @ SY1182 )
!= empty_set )
| ( subset @ SV343 @ SY1182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2222,plain,
! [SV344: $i] :
( ( ! [SY1183: $i] :
( ~ ( subset @ SV344 @ SY1183 )
| ( ( set_difference @ SV344 @ SY1183 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2223,plain,
! [SV151: $i] :
( ( ( ~ ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) )
| ~ ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2224,plain,
! [SV345: $i] :
( ( ! [SY1184: $i] :
( ( ( set_difference @ SV345 @ ( singleton @ SY1184 ) )
!= SV345 )
| ~ ( in @ SY1184 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2225,plain,
! [SV346: $i] :
( ( ! [SY1185: $i] :
( ( in @ SY1185 @ SV346 )
| ( ( set_difference @ SV346 @ ( singleton @ SY1185 ) )
= SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2226,plain,
! [SV347: $i] :
( ( ! [SY1186: $i] :
( ( ( set_difference @ SV347 @ SY1186 )
!= SV347 )
| ( disjoint @ SV347 @ SY1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2227,plain,
! [SV348: $i] :
( ( ! [SY1187: $i] :
( ~ ( disjoint @ SV348 @ SY1187 )
| ( ( set_difference @ SV348 @ SY1187 )
= SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2228,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
| ~ ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) ) )
= $false )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2229,plain,
! [SV349: $i] :
( ( ! [SY1188: $i] :
( ~ ( empty @ SV349 )
| ~ ( relation @ SY1188 )
| ( empty @ ( relation_composition @ SY1188 @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2230,plain,
! [SV350: $i] :
( ( ! [SY1189: $i] :
( ~ ( empty @ SV350 )
| ~ ( relation @ SY1189 )
| ( relation @ ( relation_composition @ SY1189 @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2231,plain,
( ( ~ ( function @ sK91_A )
| ~ ( relation @ sK91_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(2232,plain,
! [SV153: $i] :
( ( ! [SY871: $i,SY872: $i] :
( ~ ( ~ ( ! [SY873: $i,SY874: $i] :
( ~ ( in @ SY873 @ SV153 )
| ~ ( in @ SY874 @ SY871 )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ SY873 @ SY874 ) ) )
| ~ ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) @ SY871 ) )
| ( ( sK43_D @ SY872 @ SY871 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SY872 @ SY871 @ SV153 ) @ ( sK45_SY635 @ SY872 @ SY871 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SY872 @ SY871 @ SV153 ) @ SY872 ) ) )
| ( SY872
= ( cartesian_product2 @ SV153 @ SY871 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2233,plain,
! [SV153: $i] :
( ( ! [SY875: $i,SY876: $i] :
( ( SY876
!= ( cartesian_product2 @ SV153 @ SY875 ) )
| ~ ( ~ ! [SY877: $i] :
( ! [SY878: $i,SY879: $i] :
( ~ ( in @ SY878 @ SV153 )
| ~ ( in @ SY879 @ SY875 )
| ( SY877
!= ( ordered_pair @ SY878 @ SY879 ) ) )
| ( in @ SY877 @ SY876 ) )
| ~ ! [SY880: $i] :
( ~ ( in @ SY880 @ SY876 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) @ SY875 ) )
| ( SY880
!= ( ordered_pair @ ( sK41_E @ SY880 @ SY876 @ SY875 @ SV153 ) @ ( sK42_SY630 @ SY880 @ SY876 @ SY875 @ SV153 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2234,plain,
! [SV351: $i] :
( ( ! [SY1190: $i] :
( ( ( set_intersection2 @ SV351 @ SY1190 )
!= empty_set )
| ( disjoint @ SV351 @ SY1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2235,plain,
! [SV352: $i] :
( ( ! [SY1191: $i] :
( ~ ( disjoint @ SV352 @ SY1191 )
| ( ( set_intersection2 @ SV352 @ SY1191 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2236,plain,
! [SV353: $i] :
( ( ( in @ ( sK48_B @ SV353 ) @ SV353 )
| ( SV353 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2237,plain,
! [SV354: $i] :
( ( ( SV354 != empty_set )
| ! [SY1192: $i] :
~ ( in @ SY1192 @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2238,plain,
! [SV355: $i] :
( ( ! [SY1193: $i] :
( ~ ( subset @ SV355 @ ( singleton @ SY1193 ) )
| ( SV355 = empty_set )
| ( SV355
= ( singleton @ SY1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2239,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2240,plain,
! [SV356: $i] :
( ( ! [SY1194: $i] :
( ~ ( ~ ( ~ ( in @ ( sK105_C @ SY1194 @ SV356 ) @ SY1194 )
| ~ ( subset @ ( sK105_C @ SY1194 @ SV356 ) @ SV356 ) )
| ~ ( ( in @ ( sK105_C @ SY1194 @ SV356 ) @ SY1194 )
| ( subset @ ( sK105_C @ SY1194 @ SV356 ) @ SV356 ) ) )
| ( SY1194
= ( powerset @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2241,plain,
! [SV357: $i] :
( ( ! [SY1195: $i] :
( ( SY1195
!= ( powerset @ SV357 ) )
| ~ ( ~ ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SY1195 )
| ( subset @ SY1196 @ SV357 ) )
| ~ ! [SY1197: $i] :
( ~ ( subset @ SY1197 @ SV357 )
| ( in @ SY1197 @ SY1195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2242,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)],[1936]) ).
thf(2243,plain,
! [SV358: $i] :
( ( ! [SY1198: $i] :
( ~ ( ordinal @ SV358 )
| ~ ( ordinal @ SY1198 )
| ~ ( ordinal_subset @ SV358 @ SY1198 )
| ( subset @ SV358 @ SY1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2244,plain,
! [SV359: $i] :
( ( ! [SY1199: $i] :
( ~ ( ordinal @ SV359 )
| ~ ( ordinal @ SY1199 )
| ~ ( subset @ SV359 @ SY1199 )
| ( ordinal_subset @ SV359 @ SY1199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2245,plain,
! [SV360: $i] :
( ( ! [SY1200: $i] :
( ~ ( function @ SY1200 )
| ~ ( relation @ SY1200 )
| ~ ( in @ SV360 @ ( relation_rng @ SY1200 ) )
| ~ ( one_to_one @ SY1200 )
| ( SV360
= ( apply @ SY1200 @ ( apply @ ( function_inverse @ SY1200 ) @ SV360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2246,plain,
! [SV361: $i] :
( ( ! [SY1201: $i] :
( ~ ( function @ SY1201 )
| ~ ( relation @ SY1201 )
| ~ ( in @ SV361 @ ( relation_rng @ SY1201 ) )
| ~ ( one_to_one @ SY1201 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SY1201 ) @ SY1201 ) @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2247,plain,
! [SV154: $i] :
( ( ( function @ SV154 )
= $false )
| ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2248,plain,
! [SV362: $i] :
( ( ~ ( relation @ SV362 )
| ( ( relation_dom @ SV362 )
!= empty_set )
| ( SV362 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2249,plain,
! [SV363: $i] :
( ( ~ ( relation @ SV363 )
| ( ( relation_rng @ SV363 )
!= empty_set )
| ( SV363 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2250,plain,
! [SV364: $i] :
( ( ~ ( function @ SV364 )
| ~ ( relation @ SV364 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
| ( one_to_one @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2251,plain,
! [SV365: $i] :
( ( ~ ( function @ SV365 )
| ~ ( relation @ SV365 )
| ~ ( one_to_one @ SV365 )
| ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2252,plain,
! [SV366: $i] :
( ( ! [SY1204: $i] :
( ~ ( in @ SV366 @ SY1204 )
| ( subset @ ( singleton @ SV366 ) @ SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2253,plain,
! [SV367: $i] :
( ( ! [SY1205: $i] :
( ~ ( subset @ ( singleton @ SV367 ) @ SY1205 )
| ( in @ SV367 @ SY1205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2254,plain,
! [SV368: $i] :
( ( ~ ( relation @ SV368 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
| ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) )
| ( antisymmetric @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2255,plain,
! [SV369: $i] :
( ( ~ ( relation @ SV369 )
| ~ ( antisymmetric @ SV369 )
| ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ ( ordered_pair @ SY1206 @ SY1207 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV369 )
| ( SY1206 = SY1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2256,plain,
! [SV155: $i] :
( ( ! [SY889: $i,SY890: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) )
| ~ ( ~ ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY889 )
| ( in @ ( sK32_D @ SY890 @ SY889 @ SV155 ) @ SY890 ) ) ) )
| ( SY890
= ( set_difference @ SV155 @ SY889 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2257,plain,
! [SV155: $i] :
( ( ! [SY891: $i,SY892: $i] :
( ( SY892
!= ( set_difference @ SV155 @ SY891 ) )
| ~ ( ~ ! [SY893: $i] :
( ~ ( in @ SY893 @ SV155 )
| ( in @ SY893 @ SY891 )
| ( in @ SY893 @ SY892 ) )
| ~ ~ ( ~ ! [SY894: $i] :
( ~ ( in @ SY894 @ SY892 )
| ( in @ SY894 @ SV155 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY892 )
| ~ ( in @ SX3 @ SY891 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2258,plain,
! [SV370: $i] :
( ( ! [SY1208: $i] :
( ~ ( ~ ( ! [SY1209: $i] :
( ~ ( in @ ( sK34_C @ SY1208 @ SV370 ) @ SY1209 )
| ~ ( in @ SY1209 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SY1208 @ SV370 ) @ SY1208 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SY1208 @ SV370 ) @ ( sK35_SY627 @ SY1208 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SY1208 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SY1208 @ SV370 ) @ SY1208 ) ) )
| ( SY1208
= ( union @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2259,plain,
! [SV371: $i] :
( ( ! [SY1210: $i] :
( ( SY1210
!= ( union @ SV371 ) )
| ~ ( ~ ! [SY1211: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1211 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1211 @ SY1210 ) )
| ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SY1210 )
| ~ ( ~ ( in @ SY1213 @ ( sK33_D @ SY1213 @ SY1210 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1213 @ SY1210 @ SV371 ) @ SV371 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2260,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ! [SY1132: $i,SY1133: $i] :
( ~ ( relation @ SY1133 )
| ~ ( in @ SV156 @ SY1132 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1133 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1132 ) @ SY1133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2261,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ~ ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) )
| ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2262,plain,
! [SV372: $i] :
( ( ! [SY1214: $i] :
( ~ ( ~ ( ( ( sK49_C @ SY1214 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SY1214 @ SV372 ) @ SY1214 ) )
| ~ ( ( ( sK49_C @ SY1214 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SY1214 @ SV372 ) @ SY1214 ) ) )
| ( SY1214
= ( singleton @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2263,plain,
! [SV373: $i] :
( ( ! [SY1215: $i] :
( ( SY1215
!= ( singleton @ SV373 ) )
| ~ ( ~ ! [SY1216: $i] :
( ( SY1216 != SV373 )
| ( in @ SY1216 @ SY1215 ) )
| ~ ! [SY1217: $i] :
( ~ ( in @ SY1217 @ SY1215 )
| ( SY1217 = SV373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2264,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2265,plain,
! [SV374: $i] :
( ( ~ ( ordinal @ SV374 )
| ( ordinal @ ( union @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2266,plain,
! [SV375: $i] :
( ( ! [SY1218: $i] :
( ( ( set_difference @ SV375 @ SY1218 )
!= empty_set )
| ( subset @ SV375 @ SY1218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2267,plain,
! [SV376: $i] :
( ( ! [SY1219: $i] :
( ~ ( subset @ SV376 @ SY1219 )
| ( ( set_difference @ SV376 @ SY1219 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2268,plain,
! [SV157: $i] :
( ( ( function @ SV157 )
= $false )
| ( ( ~ ( relation @ SV157 ) )
= $true )
| ( ( ~ ( one_to_one @ SV157 )
| ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2269,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)],[1965]) ).
thf(2270,plain,
! [SV377: $i] :
( ( ~ ( relation @ SV377 )
| ( ( relation_rng @ SV377 )
= ( relation_dom @ ( relation_inverse @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2271,plain,
! [SV378: $i] :
( ( ~ ( relation @ SV378 )
| ( ( relation_dom @ SV378 )
= ( relation_rng @ ( relation_inverse @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2272,plain,
! [SV158: $i] :
( ( ( ~ ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) )
| ~ ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2273,plain,
! [SV159: $i] :
( ( ! [SY916: $i,SY917: $i] :
( ~ ( relation @ SY917 )
| ! [SY918: $i] :
( ~ ( in @ SY918 @ ( relation_rng @ SY917 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY918 ) @ SY917 )
| ~ ( in @ SY918 @ SY916 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SY917 @ SY916 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2274,plain,
! [SV159: $i] :
( ( ! [SY919: $i,SY920: $i] :
( ~ ( relation @ SY920 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SY920 @ SY919 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ ( relation_rng @ SY920 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SY920 @ SY919 @ SV159 ) ) @ SY920 ) )
| ~ ( in @ ( sK78_D @ SY920 @ SY919 @ SV159 ) @ SY919 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2275,plain,
! [SV379: $i] :
( ( ~ ( empty @ SV379 )
| ( empty @ ( relation_rng @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2276,plain,
! [SV380: $i] :
( ( ~ ( empty @ SV380 )
| ( relation @ ( relation_rng @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2277,plain,
! [SV160: $i] :
( ( ( ~ ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) )
| ~ ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2278,plain,
! [SV381: $i] :
( ( ! [SY1220: $i] :
( ~ ( in @ SV381 @ SY1220 )
| ( subset @ ( singleton @ SV381 ) @ SY1220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2279,plain,
! [SV382: $i] :
( ( ! [SY1221: $i] :
( ~ ( subset @ ( singleton @ SV382 ) @ SY1221 )
| ( in @ SV382 @ SY1221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2280,plain,
! [SV383: $i] :
( ( ~ ( relation @ SV383 )
| ( ( relation_dom @ SV383 )
!= empty_set )
| ( ( relation_rng @ SV383 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2281,plain,
! [SV384: $i] :
( ( ~ ( relation @ SV384 )
| ( ( relation_rng @ SV384 )
!= empty_set )
| ( ( relation_dom @ SV384 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2282,plain,
! [SV385: $i] :
( ( ! [SY1222: $i] :
( ( SV385 = SY1222 )
| ~ ( subset @ SV385 @ SY1222 )
| ( proper_subset @ SV385 @ SY1222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2283,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2284,plain,
! [SV386: $i] :
( ( ! [SY1223: $i] :
( ~ ( subset @ SV386 @ ( singleton @ SY1223 ) )
| ( SV386 = empty_set )
| ( SV386
= ( singleton @ SY1223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2285,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2286,plain,
! [SV161: $i] :
( ( ! [SY923: $i,SY924: $i] :
( ~ ( relation @ SY924 )
| ~ ( in @ SV161 @ SY924 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SY923 @ SY923 ) )
| ( in @ SV161 @ ( relation_restriction @ SY924 @ SY923 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2287,plain,
! [SV161: $i] :
( ( ~ ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2288,plain,
! [SV162: $i] :
( ( ! [SY929: $i,SY930: $i] :
( ~ ( relation @ SY930 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY929 ) @ SY930 )
| ( in @ SV162 @ ( relation_field @ SY930 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2289,plain,
! [SV162: $i] :
( ( ! [SY931: $i,SY932: $i] :
( ~ ( relation @ SY932 )
| ~ ( in @ ( ordered_pair @ SV162 @ SY931 ) @ SY932 )
| ( in @ SY931 @ ( relation_field @ SY932 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2290,plain,
! [SV286: $i,SV163: $i] :
( ( ~ ! [SY1138: $i] :
( ! [SY1139: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1138 @ SY1139 ) )
| ( SV163 = SY1138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2291,plain,
! [SV286: $i,SV163: $i] :
( ( ~ ! [SY1140: $i,SY1141: $i] :
( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1140 @ SY1141 ) )
| ( SV286 = SY1141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2292,plain,
! [SV387: $i] :
( ( ! [SY1224: $i] :
( ~ ( element @ SV387 @ ( powerset @ SY1224 ) )
| ( subset @ SV387 @ SY1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2293,plain,
! [SV388: $i] :
( ( ! [SY1225: $i] :
( ~ ( subset @ SV388 @ SY1225 )
| ( element @ SV388 @ ( powerset @ SY1225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2294,plain,
! [SV164: $i] :
( ( ! [SY938: $i,SY939: $i] :
( ~ ( function @ SY939 )
| ~ ( relation @ SY939 )
| ~ ( in @ SY938 @ ( relation_dom @ SY939 ) )
| ~ ( in @ SY938 @ SV164 )
| ( in @ SY938 @ ( relation_dom @ ( relation_dom_restriction @ SY939 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1994]) ).
thf(2295,plain,
! [SV164: $i] :
( ( ~ ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) )
| ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2296,plain,
! [SV165: $i,SV287: $i] :
( ( ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV287 )
| ~ ( in @ SY1142 @ ( sK3_C @ SV287 @ SV165 ) ) )
| ~ ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 ) )
= $false )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2297,plain,
! [SV166: $i] :
( ( ! [SY946: $i,SY947: $i] :
( ~ ( relation @ SY947 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY946 ) @ SY947 )
| ( in @ SV166 @ ( relation_dom @ SY947 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2298,plain,
! [SV166: $i] :
( ( ! [SY948: $i,SY949: $i] :
( ~ ( relation @ SY949 )
| ~ ( in @ ( ordered_pair @ SV166 @ SY948 ) @ SY949 )
| ( in @ SY948 @ ( relation_rng @ SY949 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2299,plain,
! [SV167: $i] :
( ( ! [SY950: $i] :
( ~ ( subset @ SY950 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SY950 @ ( sK80_B @ SV167 ) )
| ( in @ SY950 @ ( sK80_B @ SV167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2300,plain,
! [SV167: $i] :
( ( ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2301,plain,
! [SV389: $i] :
( ( ~ ( ~ ( in @ ( sK104_B @ SV389 ) @ SV389 )
| ~ ~ ( subset @ ( sK104_B @ SV389 ) @ SV389 ) )
| ( epsilon_transitive @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2302,plain,
! [SV390: $i] :
( ( ~ ( epsilon_transitive @ SV390 )
| ! [SY1226: $i] :
( ~ ( in @ SY1226 @ SV390 )
| ( subset @ SY1226 @ SV390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2303,plain,
! [SV168: $i] :
( ( ! [SY954: $i,SY955: $i] :
( ~ ( function @ SY955 )
| ~ ( relation @ SY955 )
| ( SY954
!= ( apply @ SY955 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SY955 ) )
| ( in @ ( ordered_pair @ SV168 @ SY954 ) @ SY955 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2304,plain,
! [SV168: $i] :
( ( ~ ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) )
| ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2305,plain,
( ( ~ ( empty @ sK93_A )
| ~ ( relation @ sK93_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2306,plain,
! [SV169: $i] :
( ( ( function @ SV169 )
= $false )
| ( ( ~ ( relation @ SV169 ) )
= $true )
| ( ( ~ ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2307,plain,
! [SV391: $i] :
( ( ! [SY1227: $i] :
( ( disjoint @ SV391 @ SY1227 )
| ~ ( ~ ( in @ ( sK75_C @ SY1227 @ SV391 ) @ SV391 )
| ~ ( in @ ( sK75_C @ SY1227 @ SV391 ) @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2308,plain,
! [SV392: $i] :
( ( ! [SY1228: $i] :
( ! [SY1229: $i] :
( ~ ( in @ SY1229 @ SV392 )
| ~ ( in @ SY1229 @ SY1228 ) )
| ~ ( disjoint @ SV392 @ SY1228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2309,plain,
! [SV170: $i] :
( ( ( function @ SV170 )
= $false )
| ( ( ~ ( relation @ SV170 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2310,plain,
( ( ~ ( epsilon_connected @ sK11_A )
| ~ ( epsilon_transitive @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2311,plain,
! [SV393: $i] :
( ( function @ ( identity_relation @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2312,plain,
! [SV394: $i] :
( ( relation @ ( identity_relation @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2313,plain,
! [SV171: $i] :
( ( ! [SY975: $i,SY976: $i] :
( ~ ( relation @ SY976 )
| ~ ( in @ SV171 @ SY975 )
| ~ ( in @ SV171 @ ( relation_dom @ SY976 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY976 @ SY975 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2314,plain,
! [SV171: $i] :
( ( ~ ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) )
| ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2016]) ).
thf(2315,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2316,plain,
( ( empty @ sK92_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2317,plain,
! [SV395: $i] :
( ( ( SV395
!= ( union @ SV395 ) )
| ( being_limit_ordinal @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2318,plain,
! [SV396: $i] :
( ( ~ ( being_limit_ordinal @ SV396 )
| ( SV396
= ( union @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2319,plain,
! [SV172: $i,SV397: $i] :
( ( ( ~ ( relation @ SV397 )
| ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) )
| ~ ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2320,plain,
! [SV173: $i] :
( ( ( ~ ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) )
| ~ ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2321,plain,
! [SV174: $i,SV288: $i] :
( ( ~ ! [SY1143: $i,SY1144: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SY1143 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SY1143 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SY1144
= ( unordered_triple @ SV174 @ SV288 @ SY1143 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2025]) ).
thf(2322,plain,
! [SV288: $i,SV174: $i] :
( ( ~ ! [SY1145: $i,SY1146: $i] :
( ( SY1146
!= ( unordered_triple @ SV174 @ SV288 @ SY1145 ) )
| ~ ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ SY1146 )
| ( SY1147 = SY1145 )
| ( SY1147 = SV174 )
| ( SY1147 = SV288 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1145 )
| ( in @ SX4 @ SY1146 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1146 ) )
| ~ ! [SY1150: $i] :
( ( SY1150 != SV288 )
| ( in @ SY1150 @ SY1146 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2025]) ).
thf(2323,plain,
! [SV398: $i] :
( ( ~ ( relation @ SV398 )
| ~ ( relation_empty_yielding @ SV398 )
| ! [SY1238: $i] : ( relation @ ( relation_dom_restriction @ SV398 @ SY1238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2324,plain,
! [SV399: $i] :
( ( ~ ( relation @ SV399 )
| ~ ( relation_empty_yielding @ SV399 )
| ! [SY1239: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SY1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2325,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2326,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2327,plain,
! [SV175: $i] :
( ( ! [SY1005: $i,SY1006: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
!= SY1005 ) ) )
| ~ ( ( in @ ( sK47_D @ SY1006 @ SY1005 @ SV175 ) @ SY1006 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SV175 )
| ( ( sK47_D @ SY1006 @ SY1005 @ SV175 )
= SY1005 ) ) )
| ( SY1006
= ( unordered_pair @ SV175 @ SY1005 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2328,plain,
! [SV175: $i] :
( ( ! [SY1007: $i,SY1008: $i] :
( ( SY1008
!= ( unordered_pair @ SV175 @ SY1007 ) )
| ~ ( ~ ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SY1008 )
| ( SY1009 = SV175 )
| ( SY1009 = SY1007 ) )
| ~ ~ ( ~ ! [SY1010: $i] :
( ( SY1010 != SV175 )
| ( in @ SY1010 @ SY1008 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1007 )
| ( in @ SX3 @ SY1008 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2329,plain,
! [SV400: $i] :
( ( ~ ( relation @ SV400 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ( transitive @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2330,plain,
! [SV401: $i] :
( ( ~ ( relation @ SV401 )
| ~ ( transitive @ SV401 )
| ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( in @ ( ordered_pair @ SY1240 @ SY1241 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1241 @ SY1242 ) @ SV401 )
| ( in @ ( ordered_pair @ SY1240 @ SY1242 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2331,plain,
! [SV402: $i] :
( ( ~ ( empty @ SV402 )
| ( empty @ ( relation_dom @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2332,plain,
! [SV403: $i] :
( ( ~ ( empty @ SV403 )
| ( relation @ ( relation_dom @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2333,plain,
! [SV176: $i,SV289: $i] :
( ( ( ~ ( function @ SV289 ) )
= $true )
| ( ( ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2334,plain,
! [SV404: $i] :
( ( ! [SY1243: $i] :
( ~ ( subset @ SV404 @ SY1243 )
| ~ ( subset @ SY1243 @ SV404 )
| ( SV404 = SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2335,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2336,plain,
! [SV405: $i] :
( ( ~ ( function @ SV405 )
| ~ ( relation @ SV405 )
| ( function @ ( function_inverse @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2337,plain,
! [SV406: $i] :
( ( ~ ( function @ SV406 )
| ~ ( relation @ SV406 )
| ( relation @ ( function_inverse @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2338,plain,
! [SV177: $i] :
( ( ! [SY1016: $i,SY1017: $i] :
( ~ ( in @ SV177 @ SY1017 )
| ~ ( in @ SY1016 @ SY1017 )
| ( subset @ ( unordered_pair @ SV177 @ SY1016 ) @ SY1017 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2339,plain,
! [SV177: $i] :
( ( ~ ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) )
| ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2340,plain,
! [SV178: $i,SV290: $i] :
( ( ( ordinal @ SV290 )
= $false )
| ( ( ~ ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
| ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
| ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2341,plain,
! [SV179: $i,SV291: $i] :
( ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false )
| ( ( ~ ( ~ ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) )
| ~ ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2342,plain,
! [SV180: $i] :
( ( element @ ( sK7_B @ SV180 ) @ ( powerset @ SV180 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2343,plain,
! [SV180: $i] :
( ( empty @ ( sK7_B @ SV180 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2344,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2345,plain,
! [SV407: $i] :
( ( ~ ( empty @ SV407 )
| ( ordinal @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2346,plain,
! [SV181: $i] :
( ( ( ~ ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) )
| ~ ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2347,plain,
! [SV408: $i] :
( ( ! [SY1244: $i] :
( ~ ( function @ SV408 )
| ~ ( relation @ SV408 )
| ~ ( relation @ SY1244 )
| ~ ( function @ SY1244 )
| ( function @ ( relation_composition @ SV408 @ SY1244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2348,plain,
! [SV409: $i] :
( ( ! [SY1245: $i] :
( ~ ( function @ SV409 )
| ~ ( relation @ SV409 )
| ~ ( relation @ SY1245 )
| ~ ( function @ SY1245 )
| ( relation @ ( relation_composition @ SV409 @ SY1245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2349,plain,
! [SV182: $i] :
( ( ( function @ SV182 )
= $false )
| ( ( ~ ( relation @ SV182 ) )
= $true )
| ( ( ~ ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2350,plain,
! [SV183: $i] :
( ( ( ~ ( in @ ( sK111_B @ SV183 ) @ SV183 ) )
= $false )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2055]) ).
thf(2351,plain,
! [SV183: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK111_B @ SV183 ) )
| ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) ) )
= $false )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2055]) ).
thf(2352,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ( function @ SV292 ) )
= $true )
| ( ( ~ ( relation @ SV292 ) )
= $true )
| ( ( ~ ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2353,plain,
( ( ~ ( relation @ sK89_A )
| ~ ( relation_empty_yielding @ sK89_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2354,plain,
! [SV410: $i] :
( ( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) ) )
| ( epsilon_connected @ SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2355,plain,
! [SV411: $i] :
( ( ~ ( epsilon_connected @ SV411 )
| ! [SY1246: $i,SY1247: $i] :
( ( SY1246 = SY1247 )
| ~ ( in @ SY1246 @ SV411 )
| ~ ( in @ SY1247 @ SV411 )
| ( in @ SY1246 @ SY1247 )
| ( in @ SY1247 @ SY1246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2356,plain,
! [SV185: $i] :
( ( ( ~ ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) )
| ~ ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2357,plain,
! [SV412: $i] :
( ( ~ ( ordinal @ SV412 )
| ( epsilon_connected @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2358,plain,
! [SV413: $i] :
( ( ~ ( ordinal @ SV413 )
| ( epsilon_transitive @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2359,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)],[2064]) ).
thf(2360,plain,
! [SV414: $i] :
( ( ~ ( empty @ SV414 )
| ~ ( relation @ SV414 )
| ~ ( function @ SV414 )
| ( one_to_one @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2361,plain,
! [SV186: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
( ~ ( relation @ SY1055 )
| ~ ( in @ SV186 @ SY1054 )
| ~ ( in @ SV186 @ ( relation_rng @ SY1055 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1054 @ SY1055 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2362,plain,
! [SV186: $i] :
( ( ~ ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) )
| ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2067]) ).
thf(2363,plain,
! [SV415: $i] :
( ( ! [SY1248: $i] :
( ~ ( empty @ SV415 )
| ~ ( relation @ SY1248 )
| ( empty @ ( relation_composition @ SV415 @ SY1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2364,plain,
! [SV416: $i] :
( ( ! [SY1249: $i] :
( ~ ( empty @ SV416 )
| ~ ( relation @ SY1249 )
| ( relation @ ( relation_composition @ SV416 @ SY1249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2365,plain,
! [SV187: $i] :
( ( ! [SY1060: $i,SY1061: $i] :
( ~ ( relation @ SY1061 )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( relation_dom @ SY1061 ) )
| ~ ( in @ ( ordered_pair @ SY1062 @ SV187 ) @ SY1061 )
| ~ ( in @ SY1062 @ SY1060 ) )
| ( in @ SV187 @ ( relation_image @ SY1061 @ SY1060 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2366,plain,
! [SV187: $i] :
( ( ! [SY1063: $i,SY1064: $i] :
( ~ ( relation @ SY1064 )
| ~ ( in @ SV187 @ ( relation_image @ SY1064 @ SY1063 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ ( relation_dom @ SY1064 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SV187 ) @ SY1064 ) )
| ~ ( in @ ( sK79_D @ SY1064 @ SY1063 @ SV187 ) @ SY1063 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2367,plain,
! [SV188: $i] :
( ( ( ~ ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) )
| ~ ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2368,plain,
! [SV417: $i] :
( ( ( relation_dom @ ( identity_relation @ SV417 ) )
= SV417 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2369,plain,
! [SV418: $i] :
( ( ( relation_rng @ ( identity_relation @ SV418 ) )
= SV418 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2370,plain,
! [SV189: $i] :
( ( ! [SY1069: $i,SY1070: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ~ ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) )
| ~ ( ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1069 )
| ( in @ ( sK38_D @ SY1070 @ SY1069 @ SV189 ) @ SY1070 ) ) ) )
| ( SY1070
= ( set_intersection2 @ SV189 @ SY1069 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2371,plain,
! [SV189: $i] :
( ( ! [SY1071: $i,SY1072: $i] :
( ( SY1072
!= ( set_intersection2 @ SV189 @ SY1071 ) )
| ~ ( ~ ! [SY1073: $i] :
( ~ ( in @ SY1073 @ SV189 )
| ~ ( in @ SY1073 @ SY1071 )
| ( in @ SY1073 @ SY1072 ) )
| ~ ~ ( ~ ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SY1072 )
| ( in @ SY1074 @ SV189 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1072 )
| ( in @ SX3 @ SY1071 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2076]) ).
thf(2372,plain,
! [SV419: $i] :
( ( ~ ( epsilon_connected @ SV419 )
| ~ ( epsilon_transitive @ SV419 )
| ( ordinal @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2373,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2374,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ! [SY1161: $i,SY1162: $i] :
( ~ ( in @ SV190 @ SY1161 )
| ~ ( in @ SV293 @ SY1162 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1161 @ SY1162 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2375,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ~ ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) )
| ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2079]) ).
thf(2376,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
| ~ ( epsilon_connected @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2377,plain,
! [SV191: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV191 )
| ~ ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 ) )
= $false )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2378,plain,
! [SV420: $i] :
( ( ~ ( function @ SV420 )
| ~ ( relation @ SV420 )
| ! [SY1250: $i] : ( function @ ( relation_dom_restriction @ SV420 @ SY1250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2379,plain,
! [SV421: $i] :
( ( ~ ( function @ SV421 )
| ~ ( relation @ SV421 )
| ! [SY1251: $i] : ( relation @ ( relation_dom_restriction @ SV421 @ SY1251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2380,plain,
! [SV192: $i] :
( ( ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) )
| ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2381,plain,
! [SV422: $i] :
( ( ! [SY1252: $i] :
( ~ ( relation @ SY1252 )
| ~ ( ~ ( ( ( sK67_C @ SY1252 @ SV422 )
!= ( sK68_SY645 @ SY1252 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SY1252 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SY1252 @ SV422 ) @ ( sK68_SY645 @ SY1252 @ SV422 ) ) @ SY1252 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SY1252 @ SV422 )
= ( sK68_SY645 @ SY1252 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SY1252 @ SV422 ) @ ( sK68_SY645 @ SY1252 @ SV422 ) ) @ SY1252 ) )
| ~ ( ( in @ ( sK67_C @ SY1252 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SY1252 @ SV422 ) @ ( sK68_SY645 @ SY1252 @ SV422 ) ) @ SY1252 ) ) ) )
| ( SY1252
= ( identity_relation @ SV422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2382,plain,
! [SV423: $i] :
( ( ! [SY1253: $i] :
( ~ ( relation @ SY1253 )
| ( SY1253
!= ( identity_relation @ SV423 ) )
| ~ ( ~ ! [SY1254: $i,SY1255: $i] :
( ( SY1254 != SY1255 )
| ~ ( in @ SY1254 @ SV423 )
| ( in @ ( ordered_pair @ SY1254 @ SY1255 ) @ SY1253 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY1253 )
| ( SX2 = SX3 ) )
| ~ ! [SY1258: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY1258 @ SX3 ) @ SY1253 )
| ( in @ SY1258 @ SV423 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2383,plain,
! [SV315: $i,SV295: $i,SV198: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV198 )
| ~ ( subset @ SV295 @ SV315 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2384,plain,
! [SV200: $i,SV8: $i,SV296: $i] :
( ( ( relation @ SV296 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV8 @ SV296 ) @ SV200 )
= ( relation_rng_restriction @ SV8 @ ( relation_dom_restriction @ SV296 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2385,plain,
! [SV203: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ ( relation_dom @ SV203 ) ) )
= $true )
| ( ( subset @ SV11 @ ( relation_inverse_image @ SV203 @ ( relation_image @ SV203 @ SV11 ) ) )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2386,plain,
! [SV205: $i,SV14: $i,SV297: $i] :
( ( ( relation @ SV297 )
= $false )
| ( ( ~ ( subset @ SV14 @ SV205 )
| ( subset @ ( relation_inverse_image @ SV297 @ SV14 ) @ ( relation_inverse_image @ SV297 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2387,plain,
! [SV298: $i,SV209: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV209 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV298 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2388,plain,
! [SV299: $i,SV210: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV210 ) )
= $true )
| ( ( ~ ( subset @ SV210 @ SV299 ) )
= $true )
| ( ( subset @ SV19 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2389,plain,
! [SV211: $i,SV424: $i,SV21: $i] :
( ( ( subset @ ( set_intersection2 @ SV21 @ SV424 ) @ ( set_intersection2 @ SV211 @ SV424 ) )
= $true )
| ( ( subset @ SV21 @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2390,plain,
! [SV213: $i,SV425: $i,SV24: $i] :
( ( ( subset @ ( set_difference @ SV24 @ SV425 ) @ ( set_difference @ SV213 @ SV425 ) )
= $true )
| ( ( subset @ SV24 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2391,plain,
! [SV27: $i,SV316: $i] :
( ( ( ~ ( relation @ SV316 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SV316 ) ) @ ( relation_dom @ SV27 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2392,plain,
! [SV28: $i,SV317: $i] :
( ( ( ~ ( relation @ SV317 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SV317 ) ) @ ( relation_rng @ SV317 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2393,plain,
! [SV30: $i,SV318: $i] :
( ( ( ~ ( relation @ SV318 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SV318 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SV318 ) )
= ( relation_dom @ SV30 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2394,plain,
! [SV31: $i,SV319: $i] :
( ( ( ~ ( relation @ SV319 ) )
= $true )
| ( ( ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SV319 ) )
| ( ( relation_rng @ ( relation_composition @ SV319 @ SV31 ) )
= ( relation_rng @ SV31 ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2395,plain,
! [SV216: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV216 )
= $false )
| ( ( proper_subset @ SV216 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2396,plain,
! [SV33: $i,SV300: $i,SV217: $i] :
( ( ( ~ ( disjoint @ SV217 @ SV300 ) )
= $true )
| ( ( ~ ( subset @ SV33 @ SV217 ) )
= $true )
| ( ( disjoint @ SV33 @ SV300 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2397,plain,
! [SV301: $i,SV221: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV221 ) )
= $true )
| ( ( ~ ( subset @ SV301 @ SV221 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV37 @ SV301 ) @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2398,plain,
! [SV225: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ~ ( relation @ SV225 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV44 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2399,plain,
! [SV227: $i,SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( ~ ( relation @ SV227 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV48 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2400,plain,
! [SV228: $i,SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( ~ ( relation @ SV228 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV49 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2401,plain,
! [SV229: $i,SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( relation @ SV229 ) )
= $true )
| ( ( relation @ ( set_difference @ SV50 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2402,plain,
! [SV51: $i] :
( ( ( empty @ ( relation_dom @ SV51 ) )
= $false )
| ( ( empty @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2403,plain,
! [SV52: $i] :
( ( ( empty @ ( relation_rng @ SV52 ) )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2404,plain,
! [SV231: $i,SV57: $i] :
( ( ( in @ SV57 @ SV231 )
= $false )
| ( ( disjoint @ ( singleton @ SV57 ) @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2405,plain,
! [SV59: $i,SV233: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ SV233 )
| ( in @ SV426 @ SV59 ) )
= $true )
| ( ( element @ SV233 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2406,plain,
! [SV234: $i,SV60: $i,SV427: $i] :
( ( ( ( in @ SV427 @ SV60 )
| ( subset @ SV60 @ ( set_difference @ SV234 @ ( singleton @ SV427 ) ) ) )
= $true )
| ( ( subset @ SV60 @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2407,plain,
! [SV235: $i,SV302: $i,SV322: $i,SV62: $i] :
( ( ( SV62 = SV322 )
= $true )
| ( ( ( SV62 = SV302 )
| ( ( unordered_pair @ SV62 @ SV235 )
!= ( unordered_pair @ SV302 @ SV322 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2408,plain,
! [SV63: $i,SV236: $i] :
( ( ( function @ SV236 )
= $false )
| ( ( ~ ( relation @ SV236 ) )
= $true )
| ( ( subset @ ( relation_image @ SV236 @ ( relation_inverse_image @ SV236 @ SV63 ) ) @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2409,plain,
! [SV64: $i,SV237: $i] :
( ( ( function @ SV237 )
= $false )
| ( ( ~ ( relation @ SV237 ) )
= $true )
| ( ( ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) )
| ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2410,plain,
! [SV65: $i,SV323: $i] :
( ( ( ~ ( relation @ SV323 ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV65 @ SV323 ) )
= ( relation_image @ SV323 @ ( relation_rng @ SV65 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2411,plain,
! [SV238: $i,SV66: $i] :
( ( ( ( SV66 = empty_set )
| ~ ( subset @ SV66 @ ( relation_rng @ SV238 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true )
| ( ( relation @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2412,plain,
! [SV67: $i,SV324: $i] :
( ( ( ~ ( ordinal @ SV324 ) )
= $true )
| ( ( ~ ( proper_subset @ SV67 @ SV324 )
| ( in @ SV67 @ SV324 ) )
= $true )
| ( ( epsilon_transitive @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2413,plain,
! [SV68: $i,SV239: $i] :
( ( ( function @ SV239 )
= $false )
| ( ( ~ ( relation @ SV239 ) )
= $true )
| ( ( ! [SY1106: $i] :
( ~ ( function @ SY1106 )
| ~ ( relation @ SY1106 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY1106 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SY1106 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SY1106 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2414,plain,
! [SV69: $i,SV240: $i] :
( ( ( function @ SV240 )
= $false )
| ( ( ~ ( relation @ SV240 ) )
= $true )
| ( ( ! [SY1107: $i] :
( ~ ( function @ SY1107 )
| ~ ( relation @ SY1107 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SY1107 ) @ SV69 )
= ( apply @ SY1107 @ ( apply @ SV240 @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2415,plain,
! [SV241: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV241 ) )
= $true )
| ( ( ordinal @ SV70 )
= $true )
| ( ( ordinal @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2416,plain,
! [SV71: $i,SV325: $i] :
( ( ( ~ ( ordinal @ SV325 ) )
= $true )
| ( ( ( in @ SV71 @ SV325 )
| ( SV71 = SV325 )
| ( in @ SV325 @ SV71 ) )
= $true )
| ( ( ordinal @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2417,plain,
! [SV303: $i,SV244: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ SV244 ) )
= $true )
| ( ( ~ ( in @ SV244 @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV303 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2418,plain,
! [SV76: $i,SV246: $i] :
( ( ( SV246 = empty_set )
= $true )
| ( ( ( ( complements_of_subsets @ SV76 @ SV246 )
!= empty_set ) )
= $true )
| ( ( element @ SV246 @ ( powerset @ ( powerset @ SV76 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2419,plain,
! [SV79: $i,SV304: $i] :
( ( ( element @ SV304 @ ( powerset @ SV79 ) )
= $false )
| ( ( ! [SY1169: $i] :
( ~ ( element @ SY1169 @ SV79 )
| ( in @ SY1169 @ SV304 )
| ( in @ SY1169 @ ( subset_complement @ SV79 @ SV304 ) ) ) )
= $true )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2420,plain,
! [SV249: $i,SV80: $i,SV305: $i] :
( ( ( element @ SV305 @ ( powerset @ SV80 ) )
= $false )
| ( ( ~ ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) )
| ~ ( in @ SV249 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2421,plain,
! [SV82: $i] :
( ( ( relation @ SV82 )
= $false )
| ( ( function @ SV82 )
= $false )
| ( ( ~ ( one_to_one @ SV82 )
| ( one_to_one @ ( function_inverse @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2422,plain,
! [SV84: $i,SV250: $i,SV306: $i] :
( ( ( ~ ( function @ SV306 ) )
= $true )
| ( ( ~ ( relation @ SV306 ) )
= $true )
| ( ( ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2423,plain,
! [SV85: $i,SV251: $i,SV307: $i] :
( ( ( ~ ( function @ SV307 ) )
= $true )
| ( ( ~ ( relation @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2424,plain,
! [SV326: $i,SV252: $i,SV86: $i] :
( ( ( ( singleton @ SV86 )
= ( unordered_pair @ SV252 @ SV326 ) )
= $false )
| ( ( SV86 = SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2425,plain,
! [SV308: $i,SV254: $i,SV89: $i] :
( ( ( ( singleton @ SV89 )
= ( unordered_pair @ SV254 @ SV308 ) )
= $false )
| ( ( SV254 = SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2426,plain,
! [SV90: $i,SV255: $i] :
( ( ( in @ SV255 @ SV90 )
= $false )
| ( ( in @ SV90 @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2427,plain,
! [SV91: $i,SV256: $i] :
( ( ( proper_subset @ SV256 @ SV91 )
= $false )
| ( ( proper_subset @ SV91 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2428,plain,
! [SV93: $i] :
( ( ( epsilon_transitive @ SV93 )
= $false )
| ( ( epsilon_connected @ SV93 )
= $false )
| ( ( ordinal @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2429,plain,
! [SV260: $i,SV97: $i] :
( ( ( ordinal @ SV97 )
= $false )
| ( ( ~ ( ordinal @ SV260 ) )
= $true )
| ( ( ( ordinal_subset @ SV97 @ SV260 )
| ( ordinal_subset @ SV260 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2430,plain,
! [SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( function @ SV103 )
= $false )
| ( ( ~ ( one_to_one @ SV103 )
| ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2431,plain,
! [SV309: $i,SV108: $i,SV266: $i] :
( ( ( ~ ( element @ SV266 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( ~ ( element @ SV309 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV108 @ SV266 @ SV309 ) @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2432,plain,
! [SV270: $i,SV118: $i] :
( ( ( empty @ ( cartesian_product2 @ SV118 @ SV270 ) )
= $false )
| ( ( empty @ SV270 )
= $true )
| ( ( empty @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2433,plain,
! [SV312: $i,SV125: $i,SV274: $i] :
( ( ( ~ ( element @ SV274 @ ( powerset @ SV125 ) ) )
= $true )
| ( ( ~ ( element @ SV312 @ ( powerset @ SV125 ) ) )
= $true )
| ( ( ( subset_difference @ SV125 @ SV274 @ SV312 )
= ( set_difference @ SV274 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2434,plain,
! [SV126: $i,SV428: $i] :
( ( ( ~ ( ordinal @ SV428 ) )
= $true )
| ( ( ordinal @ SV126 )
= $false )
| ( ( ordinal_subset @ SV126 @ SV126 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2435,plain,
! [SV131: $i,SV277: $i] :
( ( ( empty @ SV277 )
= $true )
| ( ( in @ SV131 @ SV277 )
= $true )
| ( ( element @ SV131 @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2436,plain,
! [SV134: $i,SV313: $i,SV278: $i] :
( ( ( ~ ( element @ SV278 @ ( powerset @ SV313 ) ) )
= $true )
| ( ( ~ ( in @ SV134 @ SV278 ) )
= $true )
| ( ( element @ SV134 @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2437,plain,
! [SV135: $i,SV314: $i,SV279: $i] :
( ( ( ~ ( element @ SV279 @ ( powerset @ SV314 ) ) )
= $true )
| ( ( ~ ( in @ SV135 @ SV279 ) )
= $true )
| ( ( ~ ( empty @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2438,plain,
! [SV280: $i,SV137: $i] :
( ( ( in @ SV137 @ SV280 )
= $false )
| ( ( empty @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2439,plain,
! [SV281: $i,SV138: $i] :
( ( ( empty @ SV138 )
= $false )
| ( ( SV138 = SV281 )
= $true )
| ( ( ~ ( empty @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2440,plain,
! [SV429: $i,SV328: $i] :
( ( ( disjoint @ SV328 @ SV429 )
| ( in @ ( sK74_C @ SV429 @ SV328 ) @ ( set_intersection2 @ SV328 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2441,plain,
! [SV430: $i,SV329: $i] :
( ( ! [SY1260: $i] :
~ ( in @ SY1260 @ ( set_intersection2 @ SV329 @ SV430 ) )
| ~ ( disjoint @ SV329 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2442,plain,
! [SV330: $i,SV431: $i] :
( ( ~ ( function @ SV431 )
| ~ ( relation @ SV431 )
| ( function @ ( relation_rng_restriction @ SV330 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2443,plain,
! [SV331: $i,SV432: $i] :
( ( ~ ( function @ SV432 )
| ~ ( relation @ SV432 )
| ( relation @ ( relation_rng_restriction @ SV331 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2444,plain,
! [SV332: $i] :
( ( ( ~ ( function @ SV332 )
| ~ ( relation @ SV332 ) )
= $true )
| ( ( ~ ( one_to_one @ SV332 )
| ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2445,plain,
! [SV333: $i] :
( ( ( ~ ( function @ SV333 )
| ~ ( relation @ SV333 ) )
= $true )
| ( ( ~ ( one_to_one @ SV333 )
| ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2446,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2192]) ).
thf(2447,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2192]) ).
thf(2448,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2449,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2450,plain,
! [SV139: $i] :
( ( ( ~ ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2451,plain,
! [SV139: $i] :
( ( ( ~ ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2452,plain,
! [SV140: $i] :
( ( ( ~ ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2453,plain,
! [SV140: $i] :
( ( ( ~ ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2454,plain,
! [SV334: $i] :
( ( ( ~ ( function @ SV334 )
| ~ ( relation @ SV334 )
| ~ ( one_to_one @ SV334 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2455,plain,
! [SV335: $i] :
( ( ( ~ ( function @ SV335 )
| ~ ( relation @ SV335 )
| ~ ( one_to_one @ SV335 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2456,plain,
! [SV141: $i] :
( ( ( ~ ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) ) )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2457,plain,
! [SV141: $i] :
( ( ( ~ ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2458,plain,
! [SV336: $i] :
( ( ( ~ ( ~ ! [SY1175: $i,SY1176: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SY1175 @ SY1176 ) )
| ~ ( in @ ( sK108_B @ SV336 ) @ SV336 ) ) )
= $true )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2459,plain,
! [SV337: $i] :
( ( ( ~ ( relation @ SV337 ) )
= $true )
| ( ( ! [SY1177: $i] :
( ( SY1177
= ( ordered_pair @ ( sK106_C @ SY1177 @ SV337 ) @ ( sK107_SY668 @ SY1177 @ SV337 ) ) )
| ~ ( in @ SY1177 @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2460,plain,
! [SV142: $i,SV282: $i] :
( ( ( ~ ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
| ~ ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2461,plain,
! [SV338: $i] :
( ( ( ~ ( empty @ SV338 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2462,plain,
! [SV339: $i] :
( ( ( ~ ( empty @ SV339 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2463,plain,
! [SV283: $i,SV143: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ~ ( in @ SV143 @ SY1126 )
| ~ ( in @ SV283 @ SY1127 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1126 @ SY1127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2204]) ).
thf(2464,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2465,plain,
! [SV144: $i,SV433: $i] :
( ( ~ ( subset @ SV433 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SV433 @ ( sK87_B @ SV144 ) )
| ( in @ SV433 @ ( sK87_B @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2466,plain,
! [SV144: $i] :
( ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) )
| ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2467,plain,
! [SV340: $i,SV434: $i] :
( ( ~ ( ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV340 )
| ~ ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 ) )
| ( subset @ SV340 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2468,plain,
! [SV435: $i,SV341: $i] :
( ( ~ ( subset @ SV341 @ SV435 )
| ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SV341 )
| ( in @ SY1261 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2469,plain,
! [SV145: $i,SV436: $i] :
( ( ! [SY1262: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SY1262 )
| ~ ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SY1262 )
| ~ ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SV436 ) ) )
| ~ ( ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SY1262 )
| ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SY1262 @ SV436 @ SV145 ) @ SV436 ) ) )
| ( SY1262
= ( set_union2 @ SV145 @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2470,plain,
! [SV437: $i,SV145: $i] :
( ( ! [SY1263: $i] :
( ( SY1263
!= ( set_union2 @ SV145 @ SV437 ) )
| ~ ( ~ ! [SY1264: $i] :
( ~ ( in @ SY1264 @ SY1263 )
| ( in @ SY1264 @ SV145 )
| ( in @ SY1264 @ SV437 ) )
| ~ ~ ( ~ ! [SY844: $i] :
( ~ ( in @ SY844 @ SV145 )
| ( in @ SY844 @ SY1263 ) )
| ~ ! [SY1266: $i] :
( ~ ( in @ SY1266 @ SV437 )
| ( in @ SY1266 @ SY1263 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2471,plain,
! [SV146: $i] :
( ( ( ~ ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2212]) ).
thf(2472,plain,
! [SV146: $i] :
( ( ( ~ ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2212]) ).
thf(2473,plain,
! [SV147: $i] :
( ( ( ~ ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) ) )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2213]) ).
thf(2474,plain,
! [SV147: $i] :
( ( ( ~ ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2213]) ).
thf(2475,plain,
! [SV342: $i,SV438: $i] :
( ( ~ ( function @ SV438 )
| ~ ( relation @ SV438 )
| ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 )
| ( SV438
= ( identity_relation @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2476,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)],[2215]) ).
thf(2477,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2478,plain,
! [SV148: $i] :
( ( ( element @ ( sK10_B @ SV148 ) @ ( powerset @ SV148 ) )
= $true )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2479,plain,
! [SV148: $i] :
( ( ( ~ ( empty @ ( sK10_B @ SV148 ) ) )
= $true )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2480,plain,
! [SV149: $i] :
( ( ( ~ ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) ) )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2481,plain,
! [SV149: $i] :
( ( ( ~ ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2482,plain,
! [SV439: $i,SV150: $i] :
( ( ~ ( subset @ SV150 @ SV439 )
| ! [SY1267: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY1267 ) @ ( cartesian_product2 @ SV439 @ SY1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2483,plain,
! [SV440: $i,SV150: $i] :
( ( ~ ( subset @ SV150 @ SV440 )
| ! [SY1268: $i] : ( subset @ ( cartesian_product2 @ SY1268 @ SV150 ) @ ( cartesian_product2 @ SY1268 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2484,plain,
! [SV441: $i,SV343: $i] :
( ( ( ( set_difference @ SV343 @ SV441 )
!= empty_set )
| ( subset @ SV343 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2485,plain,
! [SV442: $i,SV344: $i] :
( ( ~ ( subset @ SV344 @ SV442 )
| ( ( set_difference @ SV344 @ SV442 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2486,plain,
! [SV151: $i] :
( ( ( ~ ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) ) )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2487,plain,
! [SV151: $i] :
( ( ( ~ ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2223]) ).
thf(2488,plain,
! [SV443: $i,SV345: $i] :
( ( ( ( set_difference @ SV345 @ ( singleton @ SV443 ) )
!= SV345 )
| ~ ( in @ SV443 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2489,plain,
! [SV346: $i,SV444: $i] :
( ( ( in @ SV444 @ SV346 )
| ( ( set_difference @ SV346 @ ( singleton @ SV444 ) )
= SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2490,plain,
! [SV445: $i,SV347: $i] :
( ( ( ( set_difference @ SV347 @ SV445 )
!= SV347 )
| ( disjoint @ SV347 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2491,plain,
! [SV446: $i,SV348: $i] :
( ( ~ ( disjoint @ SV348 @ SV446 )
| ( ( set_difference @ SV348 @ SV446 )
= SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2492,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) ) )
= $false )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2493,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) ) )
= $false )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2494,plain,
! [SV447: $i,SV349: $i] :
( ( ~ ( empty @ SV349 )
| ~ ( relation @ SV447 )
| ( empty @ ( relation_composition @ SV447 @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2495,plain,
! [SV448: $i,SV350: $i] :
( ( ~ ( empty @ SV350 )
| ~ ( relation @ SV448 )
| ( relation @ ( relation_composition @ SV448 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2496,plain,
( ( ~ ( function @ sK91_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2497,plain,
( ( ~ ( relation @ sK91_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2231]) ).
thf(2498,plain,
! [SV449: $i,SV153: $i] :
( ( ! [SY1269: $i] :
( ~ ( ~ ( ! [SY1270: $i,SY1271: $i] :
( ~ ( in @ SY1270 @ SV153 )
| ~ ( in @ SY1271 @ SV449 )
| ( ( sK43_D @ SY1269 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1270 @ SY1271 ) ) )
| ~ ( in @ ( sK43_D @ SY1269 @ SV449 @ SV153 ) @ SY1269 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SY1269 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SY1269 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SY1269 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SY1269 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SY1269 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SY1269 @ SV449 @ SV153 ) @ SY1269 ) ) )
| ( SY1269
= ( cartesian_product2 @ SV153 @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2499,plain,
! [SV450: $i,SV153: $i] :
( ( ! [SY1272: $i] :
( ( SY1272
!= ( cartesian_product2 @ SV153 @ SV450 ) )
| ~ ( ~ ! [SY1273: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1273
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1273 @ SY1272 ) )
| ~ ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SY1272 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1276 @ SY1272 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1276 @ SY1272 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1276
!= ( ordered_pair @ ( sK41_E @ SY1276 @ SY1272 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1276 @ SY1272 @ SV450 @ SV153 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2500,plain,
! [SV451: $i,SV351: $i] :
( ( ( ( set_intersection2 @ SV351 @ SV451 )
!= empty_set )
| ( disjoint @ SV351 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2501,plain,
! [SV452: $i,SV352: $i] :
( ( ~ ( disjoint @ SV352 @ SV452 )
| ( ( set_intersection2 @ SV352 @ SV452 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2502,plain,
! [SV353: $i] :
( ( ( in @ ( sK48_B @ SV353 ) @ SV353 )
= $true )
| ( ( SV353 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2503,plain,
! [SV354: $i] :
( ( ( ( SV354 != empty_set ) )
= $true )
| ( ( ! [SY1192: $i] :
~ ( in @ SY1192 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2504,plain,
! [SV453: $i,SV355: $i] :
( ( ~ ( subset @ SV355 @ ( singleton @ SV453 ) )
| ( SV355 = empty_set )
| ( SV355
= ( singleton @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2505,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2506,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2507,plain,
! [SV356: $i,SV454: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
| ~ ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) ) )
| ( SV454
= ( powerset @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2508,plain,
! [SV357: $i,SV455: $i] :
( ( ( SV455
!= ( powerset @ SV357 ) )
| ~ ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) )
| ~ ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2509,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)],[2242]) ).
thf(2510,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2242]) ).
thf(2511,plain,
! [SV456: $i,SV358: $i] :
( ( ~ ( ordinal @ SV358 )
| ~ ( ordinal @ SV456 )
| ~ ( ordinal_subset @ SV358 @ SV456 )
| ( subset @ SV358 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2512,plain,
! [SV457: $i,SV359: $i] :
( ( ~ ( ordinal @ SV359 )
| ~ ( ordinal @ SV457 )
| ~ ( subset @ SV359 @ SV457 )
| ( ordinal_subset @ SV359 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2513,plain,
! [SV360: $i,SV458: $i] :
( ( ~ ( function @ SV458 )
| ~ ( relation @ SV458 )
| ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 )
| ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2514,plain,
! [SV361: $i,SV459: $i] :
( ( ~ ( function @ SV459 )
| ~ ( relation @ SV459 )
| ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2515,plain,
! [SV154: $i] :
( ( ( relation @ SV154 )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( ~ ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2516,plain,
! [SV362: $i] :
( ( ( ~ ( relation @ SV362 ) )
= $true )
| ( ( ( ( relation_dom @ SV362 )
!= empty_set )
| ( SV362 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2517,plain,
! [SV363: $i] :
( ( ( ~ ( relation @ SV363 ) )
= $true )
| ( ( ( ( relation_rng @ SV363 )
!= empty_set )
| ( SV363 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2518,plain,
! [SV364: $i] :
( ( ( ~ ( function @ SV364 )
| ~ ( relation @ SV364 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
| ( one_to_one @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2519,plain,
! [SV365: $i] :
( ( ( ~ ( function @ SV365 )
| ~ ( relation @ SV365 ) )
= $true )
| ( ( ~ ( one_to_one @ SV365 )
| ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2520,plain,
! [SV460: $i,SV366: $i] :
( ( ~ ( in @ SV366 @ SV460 )
| ( subset @ ( singleton @ SV366 ) @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2521,plain,
! [SV461: $i,SV367: $i] :
( ( ~ ( subset @ ( singleton @ SV367 ) @ SV461 )
| ( in @ SV367 @ SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2522,plain,
! [SV368: $i] :
( ( ( ~ ( relation @ SV368 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
| ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) )
| ( antisymmetric @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2523,plain,
! [SV369: $i] :
( ( ( ~ ( relation @ SV369 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV369 )
| ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ ( ordered_pair @ SY1206 @ SY1207 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV369 )
| ( SY1206 = SY1207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2524,plain,
! [SV155: $i,SV462: $i] :
( ( ! [SY1279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SY1279 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SY1279 ) )
| ~ ( ~ ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SY1279 @ SV462 @ SV155 ) @ SY1279 ) ) ) )
| ( SY1279
= ( set_difference @ SV155 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2525,plain,
! [SV463: $i,SV155: $i] :
( ( ! [SY1280: $i] :
( ( SY1280
!= ( set_difference @ SV155 @ SV463 ) )
| ~ ( ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV155 )
| ( in @ SY1281 @ SV463 )
| ( in @ SY1281 @ SY1280 ) )
| ~ ~ ( ~ ! [SY894: $i] :
( ~ ( in @ SY894 @ SY1280 )
| ( in @ SY894 @ SV155 ) )
| ~ ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SY1280 )
| ~ ( in @ SY1283 @ SV463 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2526,plain,
! [SV370: $i,SV464: $i] :
( ( ~ ( ~ ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) ) )
| ( SV464
= ( union @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2527,plain,
! [SV371: $i,SV465: $i] :
( ( ( SV465
!= ( union @ SV371 ) )
| ~ ( ~ ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) )
| ~ ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2528,plain,
! [SV285: $i,SV156: $i] :
( ( ! [SY1132: $i,SY1133: $i] :
( ~ ( relation @ SY1133 )
| ~ ( in @ SV156 @ SY1132 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1133 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1132 ) @ SY1133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2260]) ).
thf(2529,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) )
| ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2530,plain,
! [SV372: $i,SV466: $i] :
( ( ~ ( ~ ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
| ~ ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) ) )
| ( SV466
= ( singleton @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2531,plain,
! [SV373: $i,SV467: $i] :
( ( ( SV467
!= ( singleton @ SV373 ) )
| ~ ( ~ ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) )
| ~ ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2532,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2533,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2264]) ).
thf(2534,plain,
! [SV374: $i] :
( ( ( ~ ( ordinal @ SV374 ) )
= $true )
| ( ( ordinal @ ( union @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2535,plain,
! [SV468: $i,SV375: $i] :
( ( ( ( set_difference @ SV375 @ SV468 )
!= empty_set )
| ( subset @ SV375 @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2536,plain,
! [SV469: $i,SV376: $i] :
( ( ~ ( subset @ SV376 @ SV469 )
| ( ( set_difference @ SV376 @ SV469 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2537,plain,
! [SV157: $i] :
( ( ( relation @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( ~ ( one_to_one @ SV157 )
| ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2538,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)],[2269]) ).
thf(2539,plain,
( ( ~ ( epsilon_connected @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2269]) ).
thf(2540,plain,
! [SV377: $i] :
( ( ( ~ ( relation @ SV377 ) )
= $true )
| ( ( ( relation_rng @ SV377 )
= ( relation_dom @ ( relation_inverse @ SV377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2541,plain,
! [SV378: $i] :
( ( ( ~ ( relation @ SV378 ) )
= $true )
| ( ( ( relation_dom @ SV378 )
= ( relation_rng @ ( relation_inverse @ SV378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2542,plain,
! [SV158: $i] :
( ( ( ~ ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) ) )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2543,plain,
! [SV158: $i] :
( ( ( ~ ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2544,plain,
! [SV470: $i,SV159: $i] :
( ( ! [SY1290: $i] :
( ~ ( relation @ SY1290 )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ ( relation_rng @ SY1290 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY1291 ) @ SY1290 )
| ~ ( in @ SY1291 @ SV470 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SY1290 @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2545,plain,
! [SV471: $i,SV159: $i] :
( ( ! [SY1292: $i] :
( ~ ( relation @ SY1292 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SY1292 @ SV471 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SY1292 @ SV471 @ SV159 ) @ ( relation_rng @ SY1292 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SY1292 @ SV471 @ SV159 ) ) @ SY1292 ) )
| ~ ( in @ ( sK78_D @ SY1292 @ SV471 @ SV159 ) @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2546,plain,
! [SV379: $i] :
( ( ( ~ ( empty @ SV379 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2547,plain,
! [SV380: $i] :
( ( ( ~ ( empty @ SV380 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2548,plain,
! [SV160: $i] :
( ( ( ~ ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) ) )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2549,plain,
! [SV160: $i] :
( ( ( ~ ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2277]) ).
thf(2550,plain,
! [SV472: $i,SV381: $i] :
( ( ~ ( in @ SV381 @ SV472 )
| ( subset @ ( singleton @ SV381 ) @ SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2551,plain,
! [SV473: $i,SV382: $i] :
( ( ~ ( subset @ ( singleton @ SV382 ) @ SV473 )
| ( in @ SV382 @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2552,plain,
! [SV383: $i] :
( ( ( ~ ( relation @ SV383 ) )
= $true )
| ( ( ( ( relation_dom @ SV383 )
!= empty_set )
| ( ( relation_rng @ SV383 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2553,plain,
! [SV384: $i] :
( ( ( ~ ( relation @ SV384 ) )
= $true )
| ( ( ( ( relation_rng @ SV384 )
!= empty_set )
| ( ( relation_dom @ SV384 )
= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2554,plain,
! [SV474: $i,SV385: $i] :
( ( ( SV385 = SV474 )
| ~ ( subset @ SV385 @ SV474 )
| ( proper_subset @ SV385 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2555,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2556,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2283]) ).
thf(2557,plain,
! [SV475: $i,SV386: $i] :
( ( ~ ( subset @ SV386 @ ( singleton @ SV475 ) )
| ( SV386 = empty_set )
| ( SV386
= ( singleton @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2558,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2559,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2560,plain,
! [SV476: $i,SV161: $i] :
( ( ! [SY1293: $i] :
( ~ ( relation @ SY1293 )
| ~ ( in @ SV161 @ SY1293 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) )
| ( in @ SV161 @ ( relation_restriction @ SY1293 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2561,plain,
! [SV161: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) )
| ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2562,plain,
! [SV477: $i,SV162: $i] :
( ( ! [SY1294: $i] :
( ~ ( relation @ SY1294 )
| ~ ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SY1294 )
| ( in @ SV162 @ ( relation_field @ SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2563,plain,
! [SV478: $i,SV162: $i] :
( ( ! [SY1295: $i] :
( ~ ( relation @ SY1295 )
| ~ ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SY1295 )
| ( in @ SV478 @ ( relation_field @ SY1295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2564,plain,
! [SV286: $i,SV163: $i] :
( ( ! [SY1138: $i] :
( ! [SY1139: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1138 @ SY1139 ) )
| ( SV163 = SY1138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2290]) ).
thf(2565,plain,
! [SV286: $i,SV163: $i] :
( ( ! [SY1140: $i,SY1141: $i] :
( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SY1140 @ SY1141 ) )
| ( SV286 = SY1141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2566,plain,
! [SV479: $i,SV387: $i] :
( ( ~ ( element @ SV387 @ ( powerset @ SV479 ) )
| ( subset @ SV387 @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2567,plain,
! [SV480: $i,SV388: $i] :
( ( ~ ( subset @ SV388 @ SV480 )
| ( element @ SV388 @ ( powerset @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2568,plain,
! [SV164: $i,SV481: $i] :
( ( ! [SY1296: $i] :
( ~ ( function @ SY1296 )
| ~ ( relation @ SY1296 )
| ~ ( in @ SV481 @ ( relation_dom @ SY1296 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SY1296 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2569,plain,
! [SV164: $i] :
( ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) )
| ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2570,plain,
! [SV165: $i,SV287: $i] :
( ( ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV287 )
| ~ ( in @ SY1142 @ ( sK3_C @ SV287 @ SV165 ) ) ) )
= $false )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2571,plain,
! [SV165: $i,SV287: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 ) )
= $false )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2572,plain,
! [SV482: $i,SV166: $i] :
( ( ! [SY1297: $i] :
( ~ ( relation @ SY1297 )
| ~ ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SY1297 )
| ( in @ SV166 @ ( relation_dom @ SY1297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2573,plain,
! [SV483: $i,SV166: $i] :
( ( ! [SY1298: $i] :
( ~ ( relation @ SY1298 )
| ~ ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SY1298 )
| ( in @ SV483 @ ( relation_rng @ SY1298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2574,plain,
! [SV167: $i,SV484: $i] :
( ( ~ ( subset @ SV484 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SV484 @ ( sK80_B @ SV167 ) )
| ( in @ SV484 @ ( sK80_B @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2575,plain,
! [SV167: $i] :
( ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) )
| ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2576,plain,
! [SV389: $i] :
( ( ( ~ ( ~ ( in @ ( sK104_B @ SV389 ) @ SV389 )
| ~ ~ ( subset @ ( sK104_B @ SV389 ) @ SV389 ) ) )
= $true )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2577,plain,
! [SV390: $i] :
( ( ( ~ ( epsilon_transitive @ SV390 ) )
= $true )
| ( ( ! [SY1226: $i] :
( ~ ( in @ SY1226 @ SV390 )
| ( subset @ SY1226 @ SV390 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2578,plain,
! [SV168: $i,SV485: $i] :
( ( ! [SY1299: $i] :
( ~ ( function @ SY1299 )
| ~ ( relation @ SY1299 )
| ( SV485
!= ( apply @ SY1299 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SY1299 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SY1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2579,plain,
! [SV168: $i] :
( ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) )
| ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2580,plain,
( ( ~ ( empty @ sK93_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2581,plain,
( ( ~ ( relation @ sK93_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2305]) ).
thf(2582,plain,
! [SV169: $i] :
( ( ( relation @ SV169 )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( ~ ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2583,plain,
! [SV486: $i,SV391: $i] :
( ( ( disjoint @ SV391 @ SV486 )
| ~ ( ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV391 )
| ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2584,plain,
! [SV487: $i,SV392: $i] :
( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV392 )
| ~ ( in @ SY1300 @ SV487 ) )
| ~ ( disjoint @ SV392 @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2585,plain,
! [SV170: $i] :
( ( ( relation @ SV170 )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2586,plain,
( ( ~ ( epsilon_connected @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2587,plain,
( ( ~ ( epsilon_transitive @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2310]) ).
thf(2588,plain,
! [SV488: $i,SV171: $i] :
( ( ! [SY1301: $i] :
( ~ ( relation @ SY1301 )
| ~ ( in @ SV171 @ SV488 )
| ~ ( in @ SV171 @ ( relation_dom @ SY1301 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY1301 @ SV488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2589,plain,
! [SV171: $i] :
( ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) )
| ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2590,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2591,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2592,plain,
! [SV395: $i] :
( ( ( ( SV395
!= ( union @ SV395 ) ) )
= $true )
| ( ( being_limit_ordinal @ SV395 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2593,plain,
! [SV396: $i] :
( ( ( ~ ( being_limit_ordinal @ SV396 ) )
= $true )
| ( ( SV396
= ( union @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2594,plain,
! [SV172: $i,SV397: $i] :
( ( ( ~ ( relation @ SV397 ) )
= $true )
| ( ( ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) )
| ~ ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2595,plain,
! [SV173: $i] :
( ( ( ~ ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2596,plain,
! [SV173: $i] :
( ( ( ~ ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2597,plain,
! [SV174: $i,SV288: $i] :
( ( ! [SY1143: $i,SY1144: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SY1143 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 ) @ SY1144 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SY1143 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY1144 @ SY1143 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SY1144
= ( unordered_triple @ SV174 @ SV288 @ SY1143 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2598,plain,
! [SV288: $i,SV174: $i] :
( ( ! [SY1145: $i,SY1146: $i] :
( ( SY1146
!= ( unordered_triple @ SV174 @ SV288 @ SY1145 ) )
| ~ ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ SY1146 )
| ( SY1147 = SY1145 )
| ( SY1147 = SV174 )
| ( SY1147 = SV288 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1145 )
| ( in @ SX4 @ SY1146 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1146 ) )
| ~ ! [SY1150: $i] :
( ( SY1150 != SV288 )
| ( in @ SY1150 @ SY1146 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2599,plain,
! [SV398: $i] :
( ( ( ~ ( relation @ SV398 )
| ~ ( relation_empty_yielding @ SV398 ) )
= $true )
| ( ( ! [SY1238: $i] : ( relation @ ( relation_dom_restriction @ SV398 @ SY1238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2600,plain,
! [SV399: $i] :
( ( ( ~ ( relation @ SV399 )
| ~ ( relation_empty_yielding @ SV399 ) )
= $true )
| ( ( ! [SY1239: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2601,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2602,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2603,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2604,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2326]) ).
thf(2605,plain,
! [SV175: $i,SV489: $i] :
( ( ! [SY1302: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SY1302 @ SV489 @ SV175 ) @ SY1302 )
| ( ( sK47_D @ SY1302 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SY1302 @ SV489 @ SV175 ) @ SY1302 )
| ( ( sK47_D @ SY1302 @ SV489 @ SV175 )
!= SV489 ) ) )
| ~ ( ( in @ ( sK47_D @ SY1302 @ SV489 @ SV175 ) @ SY1302 )
| ( ( sK47_D @ SY1302 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SY1302 @ SV489 @ SV175 )
= SV489 ) ) )
| ( SY1302
= ( unordered_pair @ SV175 @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2606,plain,
! [SV490: $i,SV175: $i] :
( ( ! [SY1303: $i] :
( ( SY1303
!= ( unordered_pair @ SV175 @ SV490 ) )
| ~ ( ~ ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SY1303 )
| ( SY1304 = SV175 )
| ( SY1304 = SV490 ) )
| ~ ~ ( ~ ! [SY1010: $i] :
( ( SY1010 != SV175 )
| ( in @ SY1010 @ SY1303 ) )
| ~ ! [SY1306: $i] :
( ( SY1306 != SV490 )
| ( in @ SY1306 @ SY1303 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2607,plain,
! [SV400: $i] :
( ( ( ~ ( relation @ SV400 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ( transitive @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2608,plain,
! [SV401: $i] :
( ( ( ~ ( relation @ SV401 ) )
= $true )
| ( ( ~ ( transitive @ SV401 )
| ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( in @ ( ordered_pair @ SY1240 @ SY1241 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1241 @ SY1242 ) @ SV401 )
| ( in @ ( ordered_pair @ SY1240 @ SY1242 ) @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2609,plain,
! [SV402: $i] :
( ( ( ~ ( empty @ SV402 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2610,plain,
! [SV403: $i] :
( ( ( ~ ( empty @ SV403 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2611,plain,
! [SV176: $i,SV289: $i] :
( ( ( function @ SV289 )
= $false )
| ( ( ~ ( relation @ SV289 ) )
= $true )
| ( ( ~ ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2612,plain,
! [SV491: $i,SV404: $i] :
( ( ~ ( subset @ SV404 @ SV491 )
| ~ ( subset @ SV491 @ SV404 )
| ( SV404 = SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2613,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2614,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2615,plain,
! [SV405: $i] :
( ( ( ~ ( function @ SV405 )
| ~ ( relation @ SV405 ) )
= $true )
| ( ( function @ ( function_inverse @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2616,plain,
! [SV406: $i] :
( ( ( ~ ( function @ SV406 )
| ~ ( relation @ SV406 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2617,plain,
! [SV492: $i,SV177: $i] :
( ( ! [SY1307: $i] :
( ~ ( in @ SV177 @ SY1307 )
| ~ ( in @ SV492 @ SY1307 )
| ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SY1307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2618,plain,
! [SV177: $i] :
( ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) )
| ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2619,plain,
! [SV178: $i,SV290: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
| ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2620,plain,
! [SV291: $i,SV179: $i] :
( ( ( ~ ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) )
| ~ ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2621,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2622,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2623,plain,
! [SV407: $i] :
( ( ( ~ ( empty @ SV407 ) )
= $true )
| ( ( ordinal @ SV407 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2624,plain,
! [SV181: $i] :
( ( ( ~ ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) ) )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2625,plain,
! [SV181: $i] :
( ( ( ~ ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2626,plain,
! [SV493: $i,SV408: $i] :
( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 )
| ~ ( relation @ SV493 )
| ~ ( function @ SV493 )
| ( function @ ( relation_composition @ SV408 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2627,plain,
! [SV494: $i,SV409: $i] :
( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 )
| ~ ( relation @ SV494 )
| ~ ( function @ SV494 )
| ( relation @ ( relation_composition @ SV409 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2628,plain,
! [SV182: $i] :
( ( ( relation @ SV182 )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( ~ ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2629,plain,
! [SV183: $i] :
( ( ( in @ ( sK111_B @ SV183 ) @ SV183 )
= $true )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2350]) ).
thf(2630,plain,
! [SV183: $i] :
( ( ( ~ ( ordinal @ ( sK111_B @ SV183 ) )
| ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) )
= $true )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2631,plain,
! [SV184: $i,SV292: $i] :
( ( ( function @ SV292 )
= $false )
| ( ( ~ ( relation @ SV292 ) )
= $true )
| ( ( ~ ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2632,plain,
( ( ~ ( relation @ sK89_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2633,plain,
( ( ~ ( relation_empty_yielding @ sK89_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2353]) ).
thf(2634,plain,
! [SV410: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2635,plain,
! [SV411: $i] :
( ( ( ~ ( epsilon_connected @ SV411 ) )
= $true )
| ( ( ! [SY1246: $i,SY1247: $i] :
( ( SY1246 = SY1247 )
| ~ ( in @ SY1246 @ SV411 )
| ~ ( in @ SY1247 @ SV411 )
| ( in @ SY1246 @ SY1247 )
| ( in @ SY1247 @ SY1246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2636,plain,
! [SV185: $i] :
( ( ( ~ ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) ) )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2637,plain,
! [SV185: $i] :
( ( ( ~ ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2638,plain,
! [SV412: $i] :
( ( ( ~ ( ordinal @ SV412 ) )
= $true )
| ( ( epsilon_connected @ SV412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2639,plain,
! [SV413: $i] :
( ( ( ~ ( ordinal @ SV413 ) )
= $true )
| ( ( epsilon_transitive @ SV413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2640,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2641,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2359]) ).
thf(2642,plain,
! [SV414: $i] :
( ( ( ~ ( empty @ SV414 )
| ~ ( relation @ SV414 )
| ~ ( function @ SV414 ) )
= $true )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2643,plain,
! [SV495: $i,SV186: $i] :
( ( ! [SY1308: $i] :
( ~ ( relation @ SY1308 )
| ~ ( in @ SV186 @ SV495 )
| ~ ( in @ SV186 @ ( relation_rng @ SY1308 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SY1308 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2644,plain,
! [SV186: $i] :
( ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) )
| ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2645,plain,
! [SV496: $i,SV415: $i] :
( ( ~ ( empty @ SV415 )
| ~ ( relation @ SV496 )
| ( empty @ ( relation_composition @ SV415 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2646,plain,
! [SV497: $i,SV416: $i] :
( ( ~ ( empty @ SV416 )
| ~ ( relation @ SV497 )
| ( relation @ ( relation_composition @ SV416 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2647,plain,
! [SV498: $i,SV187: $i] :
( ( ! [SY1309: $i] :
( ~ ( relation @ SY1309 )
| ! [SY1310: $i] :
( ~ ( in @ SY1310 @ ( relation_dom @ SY1309 ) )
| ~ ( in @ ( ordered_pair @ SY1310 @ SV187 ) @ SY1309 )
| ~ ( in @ SY1310 @ SV498 ) )
| ( in @ SV187 @ ( relation_image @ SY1309 @ SV498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2648,plain,
! [SV499: $i,SV187: $i] :
( ( ! [SY1311: $i] :
( ~ ( relation @ SY1311 )
| ~ ( in @ SV187 @ ( relation_image @ SY1311 @ SV499 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SY1311 @ SV499 @ SV187 ) @ ( relation_dom @ SY1311 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SY1311 @ SV499 @ SV187 ) @ SV187 ) @ SY1311 ) )
| ~ ( in @ ( sK79_D @ SY1311 @ SV499 @ SV187 ) @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2649,plain,
! [SV188: $i] :
( ( ( ~ ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) ) )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2650,plain,
! [SV188: $i] :
( ( ( ~ ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2651,plain,
! [SV189: $i,SV500: $i] :
( ( ! [SY1312: $i] :
( ~ ( ~ ( ~ ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SY1312 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SY1312 ) )
| ~ ( ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SY1312 @ SV500 @ SV189 ) @ SY1312 ) ) ) )
| ( SY1312
= ( set_intersection2 @ SV189 @ SV500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2652,plain,
! [SV501: $i,SV189: $i] :
( ( ! [SY1313: $i] :
( ( SY1313
!= ( set_intersection2 @ SV189 @ SV501 ) )
| ~ ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ SV189 )
| ~ ( in @ SY1314 @ SV501 )
| ( in @ SY1314 @ SY1313 ) )
| ~ ~ ( ~ ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SY1313 )
| ( in @ SY1074 @ SV189 ) )
| ~ ! [SY1316: $i] :
( ~ ( in @ SY1316 @ SY1313 )
| ( in @ SY1316 @ SV501 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2653,plain,
! [SV419: $i] :
( ( ( ~ ( epsilon_connected @ SV419 )
| ~ ( epsilon_transitive @ SV419 ) )
= $true )
| ( ( ordinal @ SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(2654,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2655,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2656,plain,
! [SV293: $i,SV190: $i] :
( ( ! [SY1161: $i,SY1162: $i] :
( ~ ( in @ SV190 @ SY1161 )
| ~ ( in @ SV293 @ SY1162 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1161 @ SY1162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2657,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) )
| ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2658,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2659,plain,
( ( ~ ( epsilon_connected @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2376]) ).
thf(2660,plain,
! [SV191: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV191 ) )
= $false )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2661,plain,
! [SV191: $i,SV294: $i] :
( ( ( ~ ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 ) )
= $false )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2662,plain,
! [SV420: $i] :
( ( ( ~ ( function @ SV420 )
| ~ ( relation @ SV420 ) )
= $true )
| ( ( ! [SY1250: $i] : ( function @ ( relation_dom_restriction @ SV420 @ SY1250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2663,plain,
! [SV421: $i] :
( ( ( ~ ( function @ SV421 )
| ~ ( relation @ SV421 ) )
= $true )
| ( ( ! [SY1251: $i] : ( relation @ ( relation_dom_restriction @ SV421 @ SY1251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2664,plain,
! [SV192: $i] :
( ( ( ~ ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2665,plain,
! [SV192: $i] :
( ( ( ~ ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2666,plain,
! [SV422: $i,SV502: $i] :
( ( ~ ( relation @ SV502 )
| ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
| ( SV502
= ( identity_relation @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2667,plain,
! [SV423: $i,SV503: $i] :
( ( ~ ( relation @ SV503 )
| ( SV503
!= ( identity_relation @ SV423 ) )
| ~ ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2668,plain,
! [SV315: $i,SV295: $i,SV198: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV198 ) )
= $true )
| ( ( ~ ( subset @ SV295 @ SV315 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2669,plain,
! [SV203: $i,SV11: $i] :
( ( ( subset @ SV11 @ ( relation_dom @ SV203 ) )
= $false )
| ( ( subset @ SV11 @ ( relation_inverse_image @ SV203 @ ( relation_image @ SV203 @ SV11 ) ) )
= $true )
| ( ( relation @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2670,plain,
! [SV297: $i,SV205: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV205 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV297 @ SV14 ) @ ( relation_inverse_image @ SV297 @ SV205 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2671,plain,
! [SV298: $i,SV209: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV209 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV298 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2672,plain,
! [SV299: $i,SV210: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV210 )
= $false )
| ( ( ~ ( subset @ SV210 @ SV299 ) )
= $true )
| ( ( subset @ SV19 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2673,plain,
! [SV27: $i,SV316: $i] :
( ( ( relation @ SV316 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV27 @ SV316 ) ) @ ( relation_dom @ SV27 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2674,plain,
! [SV28: $i,SV317: $i] :
( ( ( relation @ SV317 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV28 @ SV317 ) ) @ ( relation_rng @ SV317 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2675,plain,
! [SV30: $i,SV318: $i] :
( ( ( relation @ SV318 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SV318 ) )
| ( ( relation_dom @ ( relation_composition @ SV30 @ SV318 ) )
= ( relation_dom @ SV30 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2676,plain,
! [SV31: $i,SV319: $i] :
( ( ( relation @ SV319 )
= $false )
| ( ( ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SV319 ) )
| ( ( relation_rng @ ( relation_composition @ SV319 @ SV31 ) )
= ( relation_rng @ SV31 ) ) )
= $true )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2394]) ).
thf(2677,plain,
! [SV33: $i,SV300: $i,SV217: $i] :
( ( ( disjoint @ SV217 @ SV300 )
= $false )
| ( ( ~ ( subset @ SV33 @ SV217 ) )
= $true )
| ( ( disjoint @ SV33 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2678,plain,
! [SV301: $i,SV221: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV221 )
= $false )
| ( ( ~ ( subset @ SV301 @ SV221 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV37 @ SV301 ) @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2679,plain,
! [SV44: $i,SV225: $i] :
( ( ( relation @ SV225 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( relation @ ( relation_composition @ SV44 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2680,plain,
! [SV48: $i,SV227: $i] :
( ( ( relation @ SV227 )
= $false )
| ( ( relation @ SV48 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV48 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2681,plain,
! [SV49: $i,SV228: $i] :
( ( ( relation @ SV228 )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ ( set_union2 @ SV49 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2682,plain,
! [SV50: $i,SV229: $i] :
( ( ( relation @ SV229 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( relation @ ( set_difference @ SV50 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2683,plain,
! [SV59: $i,SV233: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ SV233 ) )
= $true )
| ( ( in @ SV426 @ SV59 )
= $true )
| ( ( element @ SV233 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2684,plain,
! [SV234: $i,SV60: $i,SV427: $i] :
( ( ( in @ SV427 @ SV60 )
= $true )
| ( ( subset @ SV60 @ ( set_difference @ SV234 @ ( singleton @ SV427 ) ) )
= $true )
| ( ( subset @ SV60 @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2685,plain,
! [SV322: $i,SV235: $i,SV302: $i,SV62: $i] :
( ( ( SV62 = SV302 )
= $true )
| ( ( ( ( unordered_pair @ SV62 @ SV235 )
!= ( unordered_pair @ SV302 @ SV322 ) ) )
= $true )
| ( ( SV62 = SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2686,plain,
! [SV63: $i,SV236: $i] :
( ( ( relation @ SV236 )
= $false )
| ( ( function @ SV236 )
= $false )
| ( ( subset @ ( relation_image @ SV236 @ ( relation_inverse_image @ SV236 @ SV63 ) ) @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2687,plain,
! [SV64: $i,SV237: $i] :
( ( ( relation @ SV237 )
= $false )
| ( ( function @ SV237 )
= $false )
| ( ( ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) )
| ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2688,plain,
! [SV65: $i,SV323: $i] :
( ( ( relation @ SV323 )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV65 @ SV323 ) )
= ( relation_image @ SV323 @ ( relation_rng @ SV65 ) ) )
= $true )
| ( ( relation @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2689,plain,
! [SV238: $i,SV66: $i] :
( ( ( SV66 = empty_set )
= $true )
| ( ( ~ ( subset @ SV66 @ ( relation_rng @ SV238 ) ) )
= $true )
| ( ( ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true )
| ( ( relation @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2690,plain,
! [SV67: $i,SV324: $i] :
( ( ( ordinal @ SV324 )
= $false )
| ( ( ~ ( proper_subset @ SV67 @ SV324 )
| ( in @ SV67 @ SV324 ) )
= $true )
| ( ( epsilon_transitive @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2691,plain,
! [SV68: $i,SV239: $i] :
( ( ( relation @ SV239 )
= $false )
| ( ( function @ SV239 )
= $false )
| ( ( ! [SY1106: $i] :
( ~ ( function @ SY1106 )
| ~ ( relation @ SY1106 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SY1106 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SY1106 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SY1106 @ SV68 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2692,plain,
! [SV69: $i,SV240: $i] :
( ( ( relation @ SV240 )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( ! [SY1107: $i] :
( ~ ( function @ SY1107 )
| ~ ( relation @ SY1107 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SY1107 ) @ SV69 )
= ( apply @ SY1107 @ ( apply @ SV240 @ SV69 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2693,plain,
! [SV241: $i,SV70: $i] :
( ( ( in @ SV70 @ SV241 )
= $false )
| ( ( ordinal @ SV70 )
= $true )
| ( ( ordinal @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2694,plain,
! [SV71: $i,SV325: $i] :
( ( ( ordinal @ SV325 )
= $false )
| ( ( ( in @ SV71 @ SV325 )
| ( SV71 = SV325 )
| ( in @ SV325 @ SV71 ) )
= $true )
| ( ( ordinal @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2695,plain,
! [SV303: $i,SV244: $i,SV74: $i] :
( ( ( in @ SV74 @ SV244 )
= $false )
| ( ( ~ ( in @ SV244 @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV303 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2696,plain,
! [SV246: $i,SV76: $i] :
( ( ( ( complements_of_subsets @ SV76 @ SV246 )
= empty_set )
= $false )
| ( ( SV246 = empty_set )
= $true )
| ( ( element @ SV246 @ ( powerset @ ( powerset @ SV76 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2697,plain,
! [SV304: $i,SV79: $i,SV504: $i] :
( ( ( ~ ( element @ SV504 @ SV79 )
| ( in @ SV504 @ SV304 )
| ( in @ SV504 @ ( subset_complement @ SV79 @ SV304 ) ) )
= $true )
| ( ( element @ SV304 @ ( powerset @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2698,plain,
! [SV305: $i,SV80: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) ) )
= $true )
| ( ( ~ ( in @ SV249 @ SV305 ) )
= $true )
| ( ( element @ SV305 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2699,plain,
! [SV82: $i] :
( ( ( ~ ( one_to_one @ SV82 ) )
= $true )
| ( ( one_to_one @ ( function_inverse @ SV82 ) )
= $true )
| ( ( function @ SV82 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2700,plain,
! [SV84: $i,SV250: $i,SV306: $i] :
( ( ( function @ SV306 )
= $false )
| ( ( ~ ( relation @ SV306 ) )
= $true )
| ( ( ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2701,plain,
! [SV85: $i,SV251: $i,SV307: $i] :
( ( ( function @ SV307 )
= $false )
| ( ( ~ ( relation @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2702,plain,
! [SV97: $i,SV260: $i] :
( ( ( ordinal @ SV260 )
= $false )
| ( ( ordinal @ SV97 )
= $false )
| ( ( ( ordinal_subset @ SV97 @ SV260 )
| ( ordinal_subset @ SV260 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2703,plain,
! [SV103: $i] :
( ( ( ~ ( one_to_one @ SV103 ) )
= $true )
| ( ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) )
= $true )
| ( ( function @ SV103 )
= $false )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2704,plain,
! [SV309: $i,SV108: $i,SV266: $i] :
( ( ( element @ SV266 @ ( powerset @ SV108 ) )
= $false )
| ( ( ~ ( element @ SV309 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV108 @ SV266 @ SV309 ) @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2705,plain,
! [SV312: $i,SV125: $i,SV274: $i] :
( ( ( element @ SV274 @ ( powerset @ SV125 ) )
= $false )
| ( ( ~ ( element @ SV312 @ ( powerset @ SV125 ) ) )
= $true )
| ( ( ( subset_difference @ SV125 @ SV274 @ SV312 )
= ( set_difference @ SV274 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2706,plain,
! [SV126: $i,SV428: $i] :
( ( ( ordinal @ SV428 )
= $false )
| ( ( ordinal @ SV126 )
= $false )
| ( ( ordinal_subset @ SV126 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2707,plain,
! [SV134: $i,SV313: $i,SV278: $i] :
( ( ( element @ SV278 @ ( powerset @ SV313 ) )
= $false )
| ( ( ~ ( in @ SV134 @ SV278 ) )
= $true )
| ( ( element @ SV134 @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2708,plain,
! [SV135: $i,SV314: $i,SV279: $i] :
( ( ( element @ SV279 @ ( powerset @ SV314 ) )
= $false )
| ( ( ~ ( in @ SV135 @ SV279 ) )
= $true )
| ( ( ~ ( empty @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2709,plain,
! [SV138: $i,SV281: $i] :
( ( ( empty @ SV281 )
= $false )
| ( ( SV138 = SV281 )
= $true )
| ( ( empty @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2710,plain,
! [SV429: $i,SV328: $i] :
( ( ( disjoint @ SV328 @ SV429 )
= $true )
| ( ( in @ ( sK74_C @ SV429 @ SV328 ) @ ( set_intersection2 @ SV328 @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2711,plain,
! [SV430: $i,SV329: $i] :
( ( ( ! [SY1260: $i] :
~ ( in @ SY1260 @ ( set_intersection2 @ SV329 @ SV430 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV329 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2712,plain,
! [SV330: $i,SV431: $i] :
( ( ( ~ ( function @ SV431 )
| ~ ( relation @ SV431 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV330 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2713,plain,
! [SV331: $i,SV432: $i] :
( ( ( ~ ( function @ SV432 )
| ~ ( relation @ SV432 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV331 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2714,plain,
! [SV332: $i] :
( ( ( ~ ( function @ SV332 ) )
= $true )
| ( ( ~ ( relation @ SV332 ) )
= $true )
| ( ( ~ ( one_to_one @ SV332 )
| ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2715,plain,
! [SV333: $i] :
( ( ( ~ ( function @ SV333 ) )
= $true )
| ( ( ~ ( relation @ SV333 ) )
= $true )
| ( ( ~ ( one_to_one @ SV333 )
| ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2716,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2446]) ).
thf(2717,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2447]) ).
thf(2718,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2448]) ).
thf(2719,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2720,plain,
! [SV139: $i] :
( ( ( ! [SY802: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SY802 @ SV139 )
!= ( sK25_SY621 @ SY802 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SY802 @ SV139 ) @ SY802 )
| ~ ( in @ ( sK25_SY621 @ SY802 @ SV139 ) @ SY802 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY802 @ SV139 ) @ ( sK25_SY621 @ SY802 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SY802 @ SV139 ) @ ( sK24_C @ SY802 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SY802 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2721,plain,
! [SV139: $i] :
( ( ( ! [SY803: $i] :
( ~ ( is_connected_in @ SV139 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ( SY804 = SY805 )
| ~ ( in @ SY804 @ SY803 )
| ~ ( in @ SY805 @ SY803 )
| ( in @ ( ordered_pair @ SY804 @ SY805 ) @ SV139 )
| ( in @ ( ordered_pair @ SY805 @ SY804 ) @ SV139 ) ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2451]) ).
thf(2722,plain,
! [SV140: $i] :
( ( ( ! [SY806: $i,SY807: $i] :
( ~ ( ~ ( ! [SY808: $i] :
( ~ ( in @ ( ordered_pair @ SY808 @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY808 @ SY806 ) )
| ~ ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ ( sK59_D @ SY807 @ SY806 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY807 @ SY806 @ SV140 ) @ SY806 ) )
| ( in @ ( sK59_D @ SY807 @ SY806 @ SV140 ) @ SY807 ) ) )
| ( SY807
= ( relation_image @ SV140 @ SY806 ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2452]) ).
thf(2723,plain,
! [SV140: $i] :
( ( ( ! [SY809: $i,SY810: $i] :
( ( SY810
!= ( relation_image @ SV140 @ SY809 ) )
| ~ ( ~ ! [SY811: $i] :
( ! [SY812: $i] :
( ~ ( in @ ( ordered_pair @ SY812 @ SY811 ) @ SV140 )
| ~ ( in @ SY812 @ SY809 ) )
| ( in @ SY811 @ SY810 ) )
| ~ ! [SY813: $i] :
( ~ ( in @ SY813 @ SY810 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY813 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY813 @ SY810 @ SY809 @ SV140 ) @ SY809 ) ) ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2724,plain,
! [SV334: $i] :
( ( ( ~ ( function @ SV334 )
| ~ ( relation @ SV334 ) )
= $true )
| ( ( ~ ( one_to_one @ SV334 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2725,plain,
! [SV335: $i] :
( ( ( ~ ( function @ SV335 )
| ~ ( relation @ SV335 ) )
= $true )
| ( ( ~ ( one_to_one @ SV335 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(2726,plain,
! [SV141: $i] :
( ( ( ! [SY814: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SY814 @ SV141 ) @ SY814 )
| ~ ( in @ ( sK37_SY628 @ SY814 @ SV141 ) @ SY814 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SY814 @ SV141 ) @ ( sK37_SY628 @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SY814 @ SV141 ) @ ( sK36_C @ SY814 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SY814 @ SV141 )
!= ( sK37_SY628 @ SY814 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SY814 ) ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2456]) ).
thf(2727,plain,
! [SV141: $i] :
( ( ( ! [SY815: $i] :
( ~ ( is_antisymmetric_in @ SV141 @ SY815 )
| ! [SY816: $i,SY817: $i] :
( ~ ( in @ SY816 @ SY815 )
| ~ ( in @ SY817 @ SY815 )
| ~ ( in @ ( ordered_pair @ SY816 @ SY817 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY817 @ SY816 ) @ SV141 )
| ( SY816 = SY817 ) ) ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2728,plain,
! [SV336: $i] :
( ( ( ~ ! [SY1175: $i,SY1176: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SY1175 @ SY1176 ) )
| ~ ( in @ ( sK108_B @ SV336 ) @ SV336 ) )
= $false )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2729,plain,
! [SV337: $i] :
( ( ( relation @ SV337 )
= $false )
| ( ( ! [SY1177: $i] :
( ( SY1177
= ( ordered_pair @ ( sK106_C @ SY1177 @ SV337 ) @ ( sK107_SY668 @ SY1177 @ SV337 ) ) )
| ~ ( in @ SY1177 @ SV337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2730,plain,
! [SV142: $i,SV282: $i] :
( ( ( ~ ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) ) )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2731,plain,
! [SV282: $i,SV142: $i] :
( ( ( ~ ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2460]) ).
thf(2732,plain,
! [SV338: $i] :
( ( ( empty @ SV338 )
= $false )
| ( ( empty @ ( relation_inverse @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2733,plain,
! [SV339: $i] :
( ( ( empty @ SV339 )
= $false )
| ( ( relation @ ( relation_inverse @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2734,plain,
! [SV283: $i,SV505: $i,SV143: $i] :
( ( ! [SY1323: $i] :
( ~ ( in @ SV143 @ SV505 )
| ~ ( in @ SV283 @ SY1323 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SY1323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2735,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) )
| ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2736,plain,
! [SV144: $i,SV433: $i] :
( ( ( ~ ( subset @ SV433 @ ( sK87_B @ SV144 ) )
| ( are_equipotent @ SV433 @ ( sK87_B @ SV144 ) ) )
= $true )
| ( ( in @ SV433 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2737,plain,
! [SV144: $i] :
( ( ~ ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2738,plain,
! [SV144: $i] :
( ( ~ ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2739,plain,
! [SV340: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV340 )
| ~ ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 ) ) )
= $true )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2740,plain,
! [SV435: $i,SV341: $i] :
( ( ( ~ ( subset @ SV341 @ SV435 ) )
= $true )
| ( ( ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SV341 )
| ( in @ SY1261 @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2741,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
| ~ ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
| ( SV506
= ( set_union2 @ SV145 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2742,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( SV507
!= ( set_union2 @ SV145 @ SV437 ) )
| ~ ( ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) )
| ~ ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2743,plain,
! [SV146: $i] :
( ( ( ! [SY846: $i] :
( ~ ( ~ ( ! [SY847: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ SY847 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SY846 @ SV146 ) @ ( sK98_SY665 @ SY846 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SY846 @ SV146 ) @ SY846 ) ) )
| ( SY846
= ( relation_dom @ SV146 ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2744,plain,
! [SV146: $i] :
( ( ( ! [SY848: $i] :
( ( SY848
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY849: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY849 @ SY850 ) @ SV146 )
| ( in @ SY849 @ SY848 ) )
| ~ ! [SY851: $i] :
( ~ ( in @ SY851 @ SY848 )
| ( in @ ( ordered_pair @ SY851 @ ( sK96_D @ SY851 @ SY848 @ SV146 ) ) @ SV146 ) ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2472]) ).
thf(2745,plain,
! [SV147: $i] :
( ( ( ! [SY852: $i] :
( ~ ( ~ ( in @ ( sK53_C @ SY852 @ SV147 ) @ SY852 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SY852 @ SV147 ) @ ( sK53_C @ SY852 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SY852 ) ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2746,plain,
! [SV147: $i] :
( ( ( ! [SY853: $i] :
( ~ ( is_reflexive_in @ SV147 @ SY853 )
| ! [SY854: $i] :
( ~ ( in @ SY854 @ SY853 )
| ( in @ ( ordered_pair @ SY854 @ SY854 ) @ SV147 ) ) ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2747,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( function @ SV438 )
| ~ ( relation @ SV438 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 )
| ( SV438
= ( identity_relation @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2748,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)],[2476]) ).
thf(2749,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( function @ SX1 )
| ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ( ( relation_dom @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2750,plain,
! [SV148: $i] :
( ( ( empty @ ( sK10_B @ SV148 ) )
= $false )
| ( ( empty @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2751,plain,
! [SV149: $i] :
( ( ( ! [SY855: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SY855 @ SV149 ) @ SY855 )
| ~ ( in @ ( sK14_SY611 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( sK15_SY613 @ SY855 @ SV149 ) @ SY855 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK14_SY611 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SY855 @ SV149 ) @ ( sK15_SY613 @ SY855 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SY855 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2752,plain,
! [SV149: $i] :
( ( ( ! [SY856: $i] :
( ~ ( is_transitive_in @ SV149 @ SY856 )
| ! [SY857: $i,SY858: $i,SY859: $i] :
( ~ ( in @ SY857 @ SY856 )
| ~ ( in @ SY858 @ SY856 )
| ~ ( in @ SY859 @ SY856 )
| ~ ( in @ ( ordered_pair @ SY857 @ SY858 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY858 @ SY859 ) @ SV149 )
| ( in @ ( ordered_pair @ SY857 @ SY859 ) @ SV149 ) ) ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2753,plain,
! [SV439: $i,SV150: $i] :
( ( ( ~ ( subset @ SV150 @ SV439 ) )
= $true )
| ( ( ! [SY1267: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY1267 ) @ ( cartesian_product2 @ SV439 @ SY1267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2754,plain,
! [SV440: $i,SV150: $i] :
( ( ( ~ ( subset @ SV150 @ SV440 ) )
= $true )
| ( ( ! [SY1268: $i] : ( subset @ ( cartesian_product2 @ SY1268 @ SV150 ) @ ( cartesian_product2 @ SY1268 @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2755,plain,
! [SV441: $i,SV343: $i] :
( ( ( ( ( set_difference @ SV343 @ SV441 )
!= empty_set ) )
= $true )
| ( ( subset @ SV343 @ SV441 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2756,plain,
! [SV442: $i,SV344: $i] :
( ( ( ~ ( subset @ SV344 @ SV442 ) )
= $true )
| ( ( ( set_difference @ SV344 @ SV442 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2757,plain,
! [SV151: $i] :
( ( ( ! [SY864: $i] :
( ~ ( relation @ SY864 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY864 @ SV151 ) @ ( sK23_SY620 @ SY864 @ SV151 ) ) @ SY864 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SY864 @ SV151 ) @ ( sK22_C @ SY864 @ SV151 ) ) @ SV151 ) ) )
| ( SY864
= ( relation_inverse @ SV151 ) ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2758,plain,
! [SV151: $i] :
( ( ( ! [SY865: $i] :
( ~ ( relation @ SY865 )
| ( SY865
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY866: $i,SY867: $i] :
( ~ ( in @ ( ordered_pair @ SY866 @ SY867 ) @ SY865 )
| ( in @ ( ordered_pair @ SY867 @ SY866 ) @ SV151 ) )
| ~ ! [SY868: $i,SY869: $i] :
( ~ ( in @ ( ordered_pair @ SY869 @ SY868 ) @ SV151 )
| ( in @ ( ordered_pair @ SY868 @ SY869 ) @ SY865 ) ) ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2759,plain,
! [SV443: $i,SV345: $i] :
( ( ( ( ( set_difference @ SV345 @ ( singleton @ SV443 ) )
!= SV345 ) )
= $true )
| ( ( ~ ( in @ SV443 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2760,plain,
! [SV346: $i,SV444: $i] :
( ( ( in @ SV444 @ SV346 )
= $true )
| ( ( ( set_difference @ SV346 @ ( singleton @ SV444 ) )
= SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2489]) ).
thf(2761,plain,
! [SV445: $i,SV347: $i] :
( ( ( ( ( set_difference @ SV347 @ SV445 )
!= SV347 ) )
= $true )
| ( ( disjoint @ SV347 @ SV445 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2762,plain,
! [SV446: $i,SV348: $i] :
( ( ( ~ ( disjoint @ SV348 @ SV446 ) )
= $true )
| ( ( ( set_difference @ SV348 @ SV446 )
= SV348 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2763,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2764,plain,
! [SV152: $i,SV284: $i] :
( ( ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
| ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2765,plain,
! [SV447: $i,SV349: $i] :
( ( ( ~ ( empty @ SV349 )
| ~ ( relation @ SV447 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV447 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2766,plain,
! [SV448: $i,SV350: $i] :
( ( ( ~ ( empty @ SV350 )
| ~ ( relation @ SV448 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV448 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2767,plain,
( ( function @ sK91_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2768,plain,
( ( relation @ sK91_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2497]) ).
thf(2769,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ~ ( ~ ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) )
| ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) ) )
| ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2770,plain,
! [SV450: $i,SV153: $i,SV509: $i] :
( ( ( SV509
!= ( cartesian_product2 @ SV153 @ SV450 ) )
| ~ ( ~ ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) )
| ~ ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2771,plain,
! [SV451: $i,SV351: $i] :
( ( ( ( ( set_intersection2 @ SV351 @ SV451 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV351 @ SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2772,plain,
! [SV452: $i,SV352: $i] :
( ( ( ~ ( disjoint @ SV352 @ SV452 ) )
= $true )
| ( ( ( set_intersection2 @ SV352 @ SV452 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2773,plain,
! [SV354: $i] :
( ( ( SV354 = empty_set )
= $false )
| ( ( ! [SY1192: $i] :
~ ( in @ SY1192 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2774,plain,
! [SV453: $i,SV355: $i] :
( ( ( ~ ( subset @ SV355 @ ( singleton @ SV453 ) ) )
= $true )
| ( ( ( SV355 = empty_set )
| ( SV355
= ( singleton @ SV453 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2775,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2776,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2777,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
| ~ ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) ) ) )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2778,plain,
! [SV357: $i,SV455: $i] :
( ( ( ( SV455
!= ( powerset @ SV357 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) )
| ~ ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2779,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)],[2509]) ).
thf(2780,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2781,plain,
! [SV456: $i,SV358: $i] :
( ( ( ~ ( ordinal @ SV358 )
| ~ ( ordinal @ SV456 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV358 @ SV456 )
| ( subset @ SV358 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2782,plain,
! [SV457: $i,SV359: $i] :
( ( ( ~ ( ordinal @ SV359 )
| ~ ( ordinal @ SV457 ) )
= $true )
| ( ( ~ ( subset @ SV359 @ SV457 )
| ( ordinal_subset @ SV359 @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2783,plain,
! [SV360: $i,SV458: $i] :
( ( ( ~ ( function @ SV458 )
| ~ ( relation @ SV458 ) )
= $true )
| ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 )
| ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2784,plain,
! [SV361: $i,SV459: $i] :
( ( ( ~ ( function @ SV459 )
| ~ ( relation @ SV459 ) )
= $true )
| ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2785,plain,
! [SV154: $i] :
( ( ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) )
| ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2786,plain,
! [SV362: $i] :
( ( ( relation @ SV362 )
= $false )
| ( ( ( ( relation_dom @ SV362 )
!= empty_set )
| ( SV362 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2787,plain,
! [SV363: $i] :
( ( ( relation @ SV363 )
= $false )
| ( ( ( ( relation_rng @ SV363 )
!= empty_set )
| ( SV363 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2788,plain,
! [SV364: $i] :
( ( ( ~ ( function @ SV364 ) )
= $true )
| ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
| ( one_to_one @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2789,plain,
! [SV365: $i] :
( ( ( ~ ( function @ SV365 ) )
= $true )
| ( ( ~ ( relation @ SV365 ) )
= $true )
| ( ( ~ ( one_to_one @ SV365 )
| ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2790,plain,
! [SV460: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV460 ) )
= $true )
| ( ( subset @ ( singleton @ SV366 ) @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2791,plain,
! [SV461: $i,SV367: $i] :
( ( ( ~ ( subset @ ( singleton @ SV367 ) @ SV461 ) )
= $true )
| ( ( in @ SV367 @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2792,plain,
! [SV368: $i] :
( ( ( relation @ SV368 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
| ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) )
| ( antisymmetric @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2793,plain,
! [SV369: $i] :
( ( ( relation @ SV369 )
= $false )
| ( ( ~ ( antisymmetric @ SV369 )
| ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ ( ordered_pair @ SY1206 @ SY1207 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV369 )
| ( SY1206 = SY1207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2794,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) ) )
| ( SV510
= ( set_difference @ SV155 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2795,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( SV511
!= ( set_difference @ SV155 @ SV463 ) )
| ~ ( ~ ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) )
| ~ ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2796,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ~ ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) ) ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2797,plain,
! [SV371: $i,SV465: $i] :
( ( ( ( SV465
!= ( union @ SV371 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) )
| ~ ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2798,plain,
! [SV285: $i,SV512: $i,SV156: $i] :
( ( ! [SY1336: $i] :
( ~ ( relation @ SY1336 )
| ~ ( in @ SV156 @ SV512 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1336 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SY1336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2799,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) )
| ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2800,plain,
! [SV372: $i,SV466: $i] :
( ( ( ~ ( ~ ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
| ~ ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) ) ) )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2801,plain,
! [SV373: $i,SV467: $i] :
( ( ( ( SV467
!= ( singleton @ SV373 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) )
| ~ ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2802,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2532]) ).
thf(2803,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2804,plain,
! [SV374: $i] :
( ( ( ordinal @ SV374 )
= $false )
| ( ( ordinal @ ( union @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2805,plain,
! [SV468: $i,SV375: $i] :
( ( ( ( ( set_difference @ SV375 @ SV468 )
!= empty_set ) )
= $true )
| ( ( subset @ SV375 @ SV468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2806,plain,
! [SV469: $i,SV376: $i] :
( ( ( ~ ( subset @ SV376 @ SV469 ) )
= $true )
| ( ( ( set_difference @ SV376 @ SV469 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2807,plain,
! [SV157: $i] :
( ( ( ~ ( one_to_one @ SV157 ) )
= $true )
| ( ( ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2808,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)],[2538]) ).
thf(2809,plain,
( ( epsilon_connected @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2810,plain,
! [SV377: $i] :
( ( ( relation @ SV377 )
= $false )
| ( ( ( relation_rng @ SV377 )
= ( relation_dom @ ( relation_inverse @ SV377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2811,plain,
! [SV378: $i] :
( ( ( relation @ SV378 )
= $false )
| ( ( ( relation_dom @ SV378 )
= ( relation_rng @ ( relation_inverse @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2812,plain,
! [SV158: $i] :
( ( ( ! [SY914: $i] :
( ~ ( ordinal @ SY914 )
| ~ ( in @ SV158 @ SY914 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SY914 ) ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2813,plain,
! [SV158: $i] :
( ( ( ! [SY915: $i] :
( ~ ( ordinal @ SY915 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SY915 )
| ( in @ SV158 @ SY915 ) ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2543]) ).
thf(2814,plain,
! [SV470: $i,SV159: $i,SV513: $i] :
( ( ~ ( relation @ SV513 )
| ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY1337 ) @ SV513 )
| ~ ( in @ SY1337 @ SV470 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2815,plain,
! [SV471: $i,SV159: $i,SV514: $i] :
( ( ~ ( relation @ SV514 )
| ~ ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2816,plain,
! [SV379: $i] :
( ( ( empty @ SV379 )
= $false )
| ( ( empty @ ( relation_rng @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2817,plain,
! [SV380: $i] :
( ( ( empty @ SV380 )
= $false )
| ( ( relation @ ( relation_rng @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2818,plain,
! [SV160: $i] :
( ( ( ! [SY921: $i] :
( ~ ( relation @ SY921 )
| ~ ( subset @ SV160 @ SY921 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SY921 ) ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2819,plain,
! [SV160: $i] :
( ( ( ! [SY922: $i] :
( ~ ( relation @ SY922 )
| ~ ( subset @ SV160 @ SY922 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SY922 ) ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2820,plain,
! [SV472: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ SV472 ) )
= $true )
| ( ( subset @ ( singleton @ SV381 ) @ SV472 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2821,plain,
! [SV473: $i,SV382: $i] :
( ( ( ~ ( subset @ ( singleton @ SV382 ) @ SV473 ) )
= $true )
| ( ( in @ SV382 @ SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2822,plain,
! [SV383: $i] :
( ( ( relation @ SV383 )
= $false )
| ( ( ( ( relation_dom @ SV383 )
!= empty_set )
| ( ( relation_rng @ SV383 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2823,plain,
! [SV384: $i] :
( ( ( relation @ SV384 )
= $false )
| ( ( ( ( relation_rng @ SV384 )
!= empty_set )
| ( ( relation_dom @ SV384 )
= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2824,plain,
! [SV474: $i,SV385: $i] :
( ( ( ( SV385 = SV474 )
| ~ ( subset @ SV385 @ SV474 ) )
= $true )
| ( ( proper_subset @ SV385 @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2825,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2826,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2827,plain,
! [SV475: $i,SV386: $i] :
( ( ( ~ ( subset @ SV386 @ ( singleton @ SV475 ) ) )
= $true )
| ( ( ( SV386 = empty_set )
| ( SV386
= ( singleton @ SV475 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2828,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2829,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2830,plain,
! [SV476: $i,SV161: $i,SV515: $i] :
( ( ~ ( relation @ SV515 )
| ~ ( in @ SV161 @ SV515 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) )
| ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2831,plain,
! [SV161: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2832,plain,
! [SV161: $i] :
( ( ~ ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2833,plain,
! [SV477: $i,SV162: $i,SV516: $i] :
( ( ~ ( relation @ SV516 )
| ~ ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SV516 )
| ( in @ SV162 @ ( relation_field @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2834,plain,
! [SV478: $i,SV162: $i,SV517: $i] :
( ( ~ ( relation @ SV517 )
| ~ ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SV517 )
| ( in @ SV478 @ ( relation_field @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(2835,plain,
! [SV518: $i,SV286: $i,SV163: $i] :
( ( ! [SY1338: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV518 @ SY1338 ) )
| ( SV163 = SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2836,plain,
! [SV519: $i,SV286: $i,SV163: $i] :
( ( ! [SY1339: $i] :
( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV519 @ SY1339 ) )
| ( SV286 = SY1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2837,plain,
! [SV479: $i,SV387: $i] :
( ( ( ~ ( element @ SV387 @ ( powerset @ SV479 ) ) )
= $true )
| ( ( subset @ SV387 @ SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2838,plain,
! [SV480: $i,SV388: $i] :
( ( ( ~ ( subset @ SV388 @ SV480 ) )
= $true )
| ( ( element @ SV388 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2839,plain,
! [SV164: $i,SV481: $i,SV520: $i] :
( ( ~ ( function @ SV520 )
| ~ ( relation @ SV520 )
| ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2840,plain,
! [SV164: $i] :
( ( ~ ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2841,plain,
! [SV164: $i] :
( ( ~ ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2842,plain,
! [SV165: $i,SV287: $i] :
( ( ( ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV287 )
| ~ ( in @ SY1142 @ ( sK3_C @ SV287 @ SV165 ) ) ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2843,plain,
! [SV165: $i,SV287: $i] :
( ( ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2844,plain,
! [SV482: $i,SV166: $i,SV521: $i] :
( ( ~ ( relation @ SV521 )
| ~ ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SV521 )
| ( in @ SV166 @ ( relation_dom @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(2845,plain,
! [SV483: $i,SV166: $i,SV522: $i] :
( ( ~ ( relation @ SV522 )
| ~ ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SV522 )
| ( in @ SV483 @ ( relation_rng @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2846,plain,
! [SV167: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ ( sK80_B @ SV167 ) )
| ( are_equipotent @ SV484 @ ( sK80_B @ SV167 ) ) )
= $true )
| ( ( in @ SV484 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2847,plain,
! [SV167: $i] :
( ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2848,plain,
! [SV167: $i] :
( ( ~ ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2849,plain,
! [SV389: $i] :
( ( ( ~ ( in @ ( sK104_B @ SV389 ) @ SV389 )
| ~ ~ ( subset @ ( sK104_B @ SV389 ) @ SV389 ) )
= $false )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2850,plain,
! [SV390: $i] :
( ( ( epsilon_transitive @ SV390 )
= $false )
| ( ( ! [SY1226: $i] :
( ~ ( in @ SY1226 @ SV390 )
| ( subset @ SY1226 @ SV390 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(2851,plain,
! [SV168: $i,SV485: $i,SV523: $i] :
( ( ~ ( function @ SV523 )
| ~ ( relation @ SV523 )
| ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(2852,plain,
! [SV168: $i] :
( ( ~ ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2853,plain,
! [SV168: $i] :
( ( ~ ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2854,plain,
( ( empty @ sK93_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2855,plain,
( ( relation @ sK93_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2856,plain,
! [SV169: $i] :
( ( ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) )
| ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2582]) ).
thf(2857,plain,
! [SV486: $i,SV391: $i] :
( ( ( disjoint @ SV391 @ SV486 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV391 )
| ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV486 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2858,plain,
! [SV487: $i,SV392: $i] :
( ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV392 )
| ~ ( in @ SY1300 @ SV487 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV392 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2859,plain,
! [SV170: $i] :
( ( ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
| ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2860,plain,
( ( epsilon_connected @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2861,plain,
( ( epsilon_transitive @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2862,plain,
! [SV488: $i,SV171: $i,SV524: $i] :
( ( ~ ( relation @ SV524 )
| ~ ( in @ SV171 @ SV488 )
| ~ ( in @ SV171 @ ( relation_dom @ SV524 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2863,plain,
! [SV171: $i] :
( ( ~ ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2864,plain,
! [SV171: $i] :
( ( ~ ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2865,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2866,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2867,plain,
! [SV395: $i] :
( ( ( SV395
= ( union @ SV395 ) )
= $false )
| ( ( being_limit_ordinal @ SV395 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2868,plain,
! [SV396: $i] :
( ( ( being_limit_ordinal @ SV396 )
= $false )
| ( ( SV396
= ( union @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2869,plain,
! [SV172: $i,SV397: $i] :
( ( ( relation @ SV397 )
= $false )
| ( ( ~ ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) )
| ~ ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2870,plain,
! [SV173: $i] :
( ( ( ! [SY990: $i] :
( ~ ( ~ ( ! [SY991: $i] :
~ ( in @ ( ordered_pair @ SY991 @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SY990 @ SV173 ) @ ( sK27_C @ SY990 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SY990 @ SV173 ) @ SY990 ) ) )
| ( SY990
= ( relation_rng @ SV173 ) ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2871,plain,
! [SV173: $i] :
( ( ( ! [SY992: $i] :
( ( SY992
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY993: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY993 ) @ SV173 )
| ( in @ SY993 @ SY992 ) )
| ~ ! [SY995: $i] :
( ~ ( in @ SY995 @ SY992 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY995 @ SY992 @ SV173 ) @ SY995 ) @ SV173 ) ) ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2872,plain,
! [SV174: $i,SV288: $i,SV525: $i] :
( ( ! [SY1340: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 ) @ SY1340 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 ) @ SY1340 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 ) @ SY1340 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 ) @ SY1340 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SY1340 @ SV525 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SY1340
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2873,plain,
! [SV526: $i,SV288: $i,SV174: $i] :
( ( ! [SY1341: $i] :
( ( SY1341
!= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
| ~ ( ~ ! [SY1342: $i] :
( ~ ( in @ SY1342 @ SY1341 )
| ( SY1342 = SV526 )
| ( SY1342 = SV174 )
| ( SY1342 = SV288 ) )
| ~ ~ ( ~ ! [SY1343: $i] :
( ( SY1343 != SV526 )
| ( in @ SY1343 @ SY1341 ) )
| ~ ~ ( ~ ! [SY1003: $i] :
( ( SY1003 != SV174 )
| ( in @ SY1003 @ SY1341 ) )
| ~ ! [SY1150: $i] :
( ( SY1150 != SV288 )
| ( in @ SY1150 @ SY1341 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2874,plain,
! [SV398: $i] :
( ( ( ~ ( relation @ SV398 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV398 ) )
= $true )
| ( ( ! [SY1238: $i] : ( relation @ ( relation_dom_restriction @ SV398 @ SY1238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2875,plain,
! [SV399: $i] :
( ( ( ~ ( relation @ SV399 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV399 ) )
= $true )
| ( ( ! [SY1239: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2876,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ ( sK52_SY636 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK51_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2601]) ).
thf(2877,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK50_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2878,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2879,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2880,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) )
| ~ ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) ) )
| ( SV527
= ( unordered_pair @ SV175 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(2881,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( SV528
!= ( unordered_pair @ SV175 @ SV490 ) )
| ~ ( ~ ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) )
| ~ ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2882,plain,
! [SV400: $i] :
( ( ( relation @ SV400 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ( transitive @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2883,plain,
! [SV401: $i] :
( ( ( relation @ SV401 )
= $false )
| ( ( ~ ( transitive @ SV401 )
| ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( in @ ( ordered_pair @ SY1240 @ SY1241 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1241 @ SY1242 ) @ SV401 )
| ( in @ ( ordered_pair @ SY1240 @ SY1242 ) @ SV401 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2884,plain,
! [SV402: $i] :
( ( ( empty @ SV402 )
= $false )
| ( ( empty @ ( relation_dom @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2885,plain,
! [SV403: $i] :
( ( ( empty @ SV403 )
= $false )
| ( ( relation @ ( relation_dom @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2886,plain,
! [SV176: $i,SV289: $i] :
( ( ( relation @ SV289 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( ~ ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2887,plain,
! [SV491: $i,SV404: $i] :
( ( ( ~ ( subset @ SV404 @ SV491 )
| ~ ( subset @ SV491 @ SV404 ) )
= $true )
| ( ( SV404 = SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2888,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2614]) ).
thf(2890,plain,
! [SV405: $i] :
( ( ( ~ ( function @ SV405 ) )
= $true )
| ( ( ~ ( relation @ SV405 ) )
= $true )
| ( ( function @ ( function_inverse @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2891,plain,
! [SV406: $i] :
( ( ( ~ ( function @ SV406 ) )
= $true )
| ( ( ~ ( relation @ SV406 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2892,plain,
! [SV492: $i,SV529: $i,SV177: $i] :
( ( ~ ( in @ SV177 @ SV529 )
| ~ ( in @ SV492 @ SV529 )
| ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2893,plain,
! [SV177: $i] :
( ( ~ ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2894,plain,
! [SV177: $i] :
( ( ~ ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2895,plain,
! [SV178: $i,SV290: $i] :
( ( ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
| ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2896,plain,
! [SV291: $i,SV179: $i] :
( ( ( ~ ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2897,plain,
! [SV291: $i,SV179: $i] :
( ( ( ~ ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2620]) ).
thf(2898,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2899,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2622]) ).
thf(2900,plain,
! [SV407: $i] :
( ( ( empty @ SV407 )
= $false )
| ( ( ordinal @ SV407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2901,plain,
! [SV181: $i] :
( ( ( ! [SY1027: $i] :
( ~ ( relation @ SY1027 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SY1027 @ SV181 ) @ ( sK103_SY667 @ SY1027 @ SV181 ) ) @ SY1027 ) ) )
| ( SV181 = SY1027 ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2902,plain,
! [SV181: $i] :
( ( ( ! [SY1028: $i] :
( ~ ( relation @ SY1028 )
| ( SV181 != SY1028 )
| ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1029 @ SY1030 ) @ SY1028 ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SY1028 )
| ( in @ ( ordered_pair @ SY1031 @ SY1032 ) @ SV181 ) ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2625]) ).
thf(2903,plain,
! [SV493: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 )
| ~ ( relation @ SV493 )
| ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2904,plain,
! [SV494: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 )
| ~ ( relation @ SV494 )
| ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2905,plain,
! [SV182: $i] :
( ( ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) )
| ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2906,plain,
! [SV183: $i] :
( ( ( ~ ( ordinal @ ( sK111_B @ SV183 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) )
= $true )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2907,plain,
! [SV184: $i,SV292: $i] :
( ( ( relation @ SV292 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( ~ ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2908,plain,
( ( relation @ sK89_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2909,plain,
( ( relation_empty_yielding @ sK89_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2910,plain,
! [SV410: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
| ~ ~ ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2911,plain,
! [SV411: $i] :
( ( ( epsilon_connected @ SV411 )
= $false )
| ( ( ! [SY1246: $i,SY1247: $i] :
( ( SY1246 = SY1247 )
| ~ ( in @ SY1246 @ SV411 )
| ~ ( in @ SY1247 @ SV411 )
| ( in @ SY1246 @ SY1247 )
| ( in @ SY1247 @ SY1246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2912,plain,
! [SV185: $i] :
( ( ( ! [SY1044: $i,SY1045: $i] :
( ~ ( relation @ SY1045 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ SY1044 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1045 @ SY1044 @ SV185 ) @ ( sK66_SY644 @ SY1045 @ SY1044 @ SV185 ) ) @ SY1045 ) ) ) )
| ( SY1045
= ( relation_dom_restriction @ SV185 @ SY1044 ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2913,plain,
! [SV185: $i] :
( ( ( ! [SY1046: $i,SY1047: $i] :
( ~ ( relation @ SY1047 )
| ( SY1047
!= ( relation_dom_restriction @ SV185 @ SY1046 ) )
| ~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SY1048 @ SY1046 )
| ~ ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1048 @ SY1049 ) @ SY1047 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY1047 )
| ( in @ SX3 @ SY1046 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1047 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2914,plain,
! [SV412: $i] :
( ( ( ordinal @ SV412 )
= $false )
| ( ( epsilon_connected @ SV412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2915,plain,
! [SV413: $i] :
( ( ( ordinal @ SV413 )
= $false )
| ( ( epsilon_transitive @ SV413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2916,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2917,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( function @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2918,plain,
! [SV414: $i] :
( ( ( ~ ( empty @ SV414 )
| ~ ( relation @ SV414 ) )
= $true )
| ( ( ~ ( function @ SV414 ) )
= $true )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2919,plain,
! [SV495: $i,SV186: $i,SV530: $i] :
( ( ~ ( relation @ SV530 )
| ~ ( in @ SV186 @ SV495 )
| ~ ( in @ SV186 @ ( relation_rng @ SV530 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(2920,plain,
! [SV186: $i] :
( ( ~ ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2921,plain,
! [SV186: $i] :
( ( ~ ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2644]) ).
thf(2922,plain,
! [SV496: $i,SV415: $i] :
( ( ( ~ ( empty @ SV415 )
| ~ ( relation @ SV496 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV415 @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2923,plain,
! [SV497: $i,SV416: $i] :
( ( ( ~ ( empty @ SV416 )
| ~ ( relation @ SV497 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV416 @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2924,plain,
! [SV498: $i,SV187: $i,SV531: $i] :
( ( ~ ( relation @ SV531 )
| ! [SY1349: $i] :
( ~ ( in @ SY1349 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SY1349 @ SV187 ) @ SV531 )
| ~ ( in @ SY1349 @ SV498 ) )
| ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(2925,plain,
! [SV499: $i,SV187: $i,SV532: $i] :
( ( ~ ( relation @ SV532 )
| ~ ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2926,plain,
! [SV188: $i] :
( ( ( ! [SY1065: $i] :
( ~ ( relation @ SY1065 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SY1065 @ SV188 ) @ ( sK101_SY666 @ SY1065 @ SV188 ) ) @ SY1065 ) )
| ( subset @ SV188 @ SY1065 ) ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2927,plain,
! [SV188: $i] :
( ( ( ! [SY1066: $i] :
( ~ ( relation @ SY1066 )
| ~ ( subset @ SV188 @ SY1066 )
| ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1066 ) ) ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2928,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) ) )
| ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(2929,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( SV534
!= ( set_intersection2 @ SV189 @ SV501 ) )
| ~ ( ~ ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) )
| ~ ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2930,plain,
! [SV419: $i] :
( ( ( ~ ( epsilon_connected @ SV419 ) )
= $true )
| ( ( ~ ( epsilon_transitive @ SV419 ) )
= $true )
| ( ( ordinal @ SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2931,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2932,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2933,plain,
! [SV293: $i,SV535: $i,SV190: $i] :
( ( ! [SY1353: $i] :
( ~ ( in @ SV190 @ SV535 )
| ~ ( in @ SV293 @ SY1353 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SY1353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2934,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) )
| ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2935,plain,
( ( ~ ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2658]) ).
thf(2936,plain,
( ( epsilon_connected @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2659]) ).
thf(2937,plain,
! [SV191: $i,SV294: $i] :
( ( ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV191 )
= $true )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2660]) ).
thf(2938,plain,
! [SV191: $i,SV294: $i] :
( ( ( ~ ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 ) )
= $true )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2661]) ).
thf(2939,plain,
! [SV420: $i] :
( ( ( ~ ( function @ SV420 ) )
= $true )
| ( ( ~ ( relation @ SV420 ) )
= $true )
| ( ( ! [SY1250: $i] : ( function @ ( relation_dom_restriction @ SV420 @ SY1250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2940,plain,
! [SV421: $i] :
( ( ( ~ ( function @ SV421 ) )
= $true )
| ( ( ~ ( relation @ SV421 ) )
= $true )
| ( ( ! [SY1251: $i] : ( relation @ ( relation_dom_restriction @ SV421 @ SY1251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2941,plain,
! [SV192: $i] :
( ( ( ! [SY1084: $i,SY1085: $i] :
( ~ ( ~ ( ! [SY1086: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1086 ) @ SV192 )
| ~ ( in @ SY1086 @ SY1084 ) )
| ~ ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1085 @ SY1084 @ SV192 ) @ SY1084 ) )
| ( in @ ( sK56_D @ SY1085 @ SY1084 @ SV192 ) @ SY1085 ) ) )
| ( SY1085
= ( relation_inverse_image @ SV192 @ SY1084 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2942,plain,
! [SV192: $i] :
( ( ( ! [SY1087: $i,SY1088: $i] :
( ( SY1088
!= ( relation_inverse_image @ SV192 @ SY1087 ) )
| ~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i] :
( ~ ( in @ ( ordered_pair @ SY1089 @ SY1090 ) @ SV192 )
| ~ ( in @ SY1090 @ SY1087 ) )
| ( in @ SY1089 @ SY1088 ) )
| ~ ! [SY1091: $i] :
( ~ ( in @ SY1091 @ SY1088 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1091 @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1091 @ SY1088 @ SY1087 @ SV192 ) @ SY1087 ) ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2665]) ).
thf(2943,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( relation @ SV502 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
| ( SV502
= ( identity_relation @ SV422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2944,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ( relation @ SV503 ) )
= $true )
| ( ( ( SV503
!= ( identity_relation @ SV423 ) )
| ~ ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2945,plain,
! [SV315: $i,SV295: $i,SV198: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV198 )
= $false )
| ( ( ~ ( subset @ SV295 @ SV315 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2946,plain,
! [SV297: $i,SV205: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV205 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV297 @ SV14 ) @ ( relation_inverse_image @ SV297 @ SV205 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2947,plain,
! [SV209: $i,SV298: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV298 )
= $false )
| ( ( subset @ SV18 @ SV209 )
= $false )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV209 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2948,plain,
! [SV19: $i,SV299: $i,SV210: $i] :
( ( ( subset @ SV210 @ SV299 )
= $false )
| ( ( subset @ SV19 @ SV210 )
= $false )
| ( ( subset @ SV19 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2949,plain,
! [SV318: $i,SV30: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SV318 ) ) )
= $true )
| ( ( ( relation_dom @ ( relation_composition @ SV30 @ SV318 ) )
= ( relation_dom @ SV30 ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2950,plain,
! [SV319: $i,SV31: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SV319 ) ) )
= $true )
| ( ( ( relation_rng @ ( relation_composition @ SV319 @ SV31 ) )
= ( relation_rng @ SV31 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2951,plain,
! [SV300: $i,SV217: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV217 )
= $false )
| ( ( disjoint @ SV217 @ SV300 )
= $false )
| ( ( disjoint @ SV33 @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2952,plain,
! [SV37: $i,SV221: $i,SV301: $i] :
( ( ( subset @ SV301 @ SV221 )
= $false )
| ( ( subset @ SV37 @ SV221 )
= $false )
| ( ( subset @ ( set_union2 @ SV37 @ SV301 ) @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2953,plain,
! [SV59: $i,SV233: $i,SV426: $i] :
( ( ( in @ SV426 @ SV233 )
= $false )
| ( ( in @ SV426 @ SV59 )
= $true )
| ( ( element @ SV233 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2954,plain,
! [SV322: $i,SV302: $i,SV235: $i,SV62: $i] :
( ( ( ( unordered_pair @ SV62 @ SV235 )
= ( unordered_pair @ SV302 @ SV322 ) )
= $false )
| ( ( SV62 = SV302 )
= $true )
| ( ( SV62 = SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2955,plain,
! [SV237: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ ( relation_rng @ SV237 ) ) )
= $true )
| ( ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 )
= $true )
| ( ( function @ SV237 )
= $false )
| ( ( relation @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2956,plain,
! [SV238: $i,SV66: $i] :
( ( ( subset @ SV66 @ ( relation_rng @ SV238 ) )
= $false )
| ( ( SV66 = empty_set )
= $true )
| ( ( ( ( relation_inverse_image @ SV238 @ SV66 )
!= empty_set ) )
= $true )
| ( ( relation @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2957,plain,
! [SV324: $i,SV67: $i] :
( ( ( ~ ( proper_subset @ SV67 @ SV324 ) )
= $true )
| ( ( in @ SV67 @ SV324 )
= $true )
| ( ( ordinal @ SV324 )
= $false )
| ( ( epsilon_transitive @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2690]) ).
thf(2958,plain,
! [SV239: $i,SV68: $i,SV536: $i] :
( ( ( ~ ( function @ SV536 )
| ~ ( relation @ SV536 )
| ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) ) )
= $true )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(2959,plain,
! [SV240: $i,SV69: $i,SV537: $i] :
( ( ( ~ ( function @ SV537 )
| ~ ( relation @ SV537 )
| ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(2960,plain,
! [SV325: $i,SV71: $i] :
( ( ( ( in @ SV71 @ SV325 )
| ( SV71 = SV325 ) )
= $true )
| ( ( in @ SV325 @ SV71 )
= $true )
| ( ( ordinal @ SV325 )
= $false )
| ( ( ordinal @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2694]) ).
thf(2961,plain,
! [SV74: $i,SV303: $i,SV244: $i] :
( ( ( in @ SV244 @ SV303 )
= $false )
| ( ( in @ SV74 @ SV244 )
= $false )
| ( ( ~ ( in @ SV303 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2962,plain,
! [SV304: $i,SV79: $i,SV504: $i] :
( ( ( ~ ( element @ SV504 @ SV79 ) )
= $true )
| ( ( ( in @ SV504 @ SV304 )
| ( in @ SV504 @ ( subset_complement @ SV79 @ SV304 ) ) )
= $true )
| ( ( element @ SV304 @ ( powerset @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2697]) ).
thf(2963,plain,
! [SV305: $i,SV80: $i,SV249: $i] :
( ( ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) )
= $false )
| ( ( ~ ( in @ SV249 @ SV305 ) )
= $true )
| ( ( element @ SV305 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2964,plain,
! [SV82: $i] :
( ( ( one_to_one @ SV82 )
= $false )
| ( ( one_to_one @ ( function_inverse @ SV82 ) )
= $true )
| ( ( function @ SV82 )
= $false )
| ( ( relation @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2965,plain,
! [SV84: $i,SV250: $i,SV306: $i] :
( ( ( relation @ SV306 )
= $false )
| ( ( function @ SV306 )
= $false )
| ( ( ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
| ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2966,plain,
! [SV85: $i,SV251: $i,SV307: $i] :
( ( ( relation @ SV307 )
= $false )
| ( ( function @ SV307 )
= $false )
| ( ( ~ ( in @ SV251 @ SV85 )
| ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2967,plain,
! [SV260: $i,SV97: $i] :
( ( ( ordinal_subset @ SV97 @ SV260 )
= $true )
| ( ( ordinal_subset @ SV260 @ SV97 )
= $true )
| ( ( ordinal @ SV97 )
= $false )
| ( ( ordinal @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2968,plain,
! [SV103: $i] :
( ( ( one_to_one @ SV103 )
= $false )
| ( ( ( function_inverse @ SV103 )
= ( relation_inverse @ SV103 ) )
= $true )
| ( ( function @ SV103 )
= $false )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2969,plain,
! [SV266: $i,SV108: $i,SV309: $i] :
( ( ( element @ SV309 @ ( powerset @ SV108 ) )
= $false )
| ( ( element @ SV266 @ ( powerset @ SV108 ) )
= $false )
| ( ( element @ ( subset_difference @ SV108 @ SV266 @ SV309 ) @ ( powerset @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2970,plain,
! [SV274: $i,SV125: $i,SV312: $i] :
( ( ( element @ SV312 @ ( powerset @ SV125 ) )
= $false )
| ( ( element @ SV274 @ ( powerset @ SV125 ) )
= $false )
| ( ( ( subset_difference @ SV125 @ SV274 @ SV312 )
= ( set_difference @ SV274 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2971,plain,
! [SV313: $i,SV278: $i,SV134: $i] :
( ( ( in @ SV134 @ SV278 )
= $false )
| ( ( element @ SV278 @ ( powerset @ SV313 ) )
= $false )
| ( ( element @ SV134 @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2972,plain,
! [SV314: $i,SV279: $i,SV135: $i] :
( ( ( in @ SV135 @ SV279 )
= $false )
| ( ( element @ SV279 @ ( powerset @ SV314 ) )
= $false )
| ( ( ~ ( empty @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2973,plain,
! [SV430: $i,SV329: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ ( set_intersection2 @ SV329 @ SV430 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV329 @ SV430 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(2974,plain,
! [SV330: $i,SV431: $i] :
( ( ( ~ ( function @ SV431 ) )
= $true )
| ( ( ~ ( relation @ SV431 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV330 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2975,plain,
! [SV331: $i,SV432: $i] :
( ( ( ~ ( function @ SV432 ) )
= $true )
| ( ( ~ ( relation @ SV432 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV331 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2976,plain,
! [SV332: $i] :
( ( ( function @ SV332 )
= $false )
| ( ( ~ ( relation @ SV332 ) )
= $true )
| ( ( ~ ( one_to_one @ SV332 )
| ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2977,plain,
! [SV333: $i] :
( ( ( function @ SV333 )
= $false )
| ( ( ~ ( relation @ SV333 ) )
= $true )
| ( ( ~ ( one_to_one @ SV333 )
| ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2978,plain,
! [SV539: $i] :
( ( ( empty @ SV539 )
| ! [SY1354: $i] :
( ~ ( element @ SY1354 @ SV539 )
| ( in @ SY1354 @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(2979,plain,
! [SV540: $i] :
( ( ( empty @ SV540 )
| ! [SY1355: $i] :
( ~ ( in @ SY1355 @ SV540 )
| ( element @ SY1355 @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(2980,plain,
! [SV541: $i] :
( ( ~ ( empty @ SV541 )
| ! [SY1356: $i] :
( ~ ( element @ SY1356 @ SV541 )
| ( empty @ SY1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(2981,plain,
! [SV542: $i] :
( ( ~ ( empty @ SV542 )
| ! [SY1357: $i] :
( ~ ( empty @ SY1357 )
| ( element @ SY1357 @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(2982,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 ) )
| ( is_connected_in @ SV139 @ SV543 ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(2983,plain,
! [SV544: $i,SV139: $i] :
( ( ( ~ ( is_connected_in @ SV139 @ SV544 )
| ! [SY1358: $i,SY1359: $i] :
( ( SY1358 = SY1359 )
| ~ ( in @ SY1358 @ SV544 )
| ~ ( in @ SY1359 @ SV544 )
| ( in @ ( ordered_pair @ SY1358 @ SY1359 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1359 @ SY1358 ) @ SV139 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(2984,plain,
! [SV140: $i,SV545: $i] :
( ( ( ! [SY1360: $i] :
( ~ ( ~ ( ! [SY1361: $i] :
( ~ ( in @ ( ordered_pair @ SY1361 @ ( sK59_D @ SY1360 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1361 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SY1360 @ SV545 @ SV140 ) @ SY1360 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SY1360 @ SV545 @ SV140 ) @ ( sK59_D @ SY1360 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SY1360 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SY1360 @ SV545 @ SV140 ) @ SY1360 ) ) )
| ( SY1360
= ( relation_image @ SV140 @ SV545 ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(2985,plain,
! [SV546: $i,SV140: $i] :
( ( ( ! [SY1362: $i] :
( ( SY1362
!= ( relation_image @ SV140 @ SV546 ) )
| ~ ( ~ ! [SY1363: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1363 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1363 @ SY1362 ) )
| ~ ! [SY1365: $i] :
( ~ ( in @ SY1365 @ SY1362 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1365 @ SY1362 @ SV546 @ SV140 ) @ SY1365 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1365 @ SY1362 @ SV546 @ SV140 ) @ SV546 ) ) ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(2986,plain,
! [SV334: $i] :
( ( ( ~ ( function @ SV334 ) )
= $true )
| ( ( ~ ( relation @ SV334 ) )
= $true )
| ( ( ~ ( one_to_one @ SV334 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2987,plain,
! [SV335: $i] :
( ( ( ~ ( function @ SV335 ) )
= $true )
| ( ( ~ ( relation @ SV335 ) )
= $true )
| ( ( ~ ( one_to_one @ SV335 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2988,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SV547 @ SV141 )
!= ( sK37_SY628 @ SV547 @ SV141 ) ) ) )
| ( is_antisymmetric_in @ SV141 @ SV547 ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2989,plain,
! [SV548: $i,SV141: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV141 @ SV548 )
| ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1366 @ SV548 )
| ~ ( in @ SY1367 @ SV548 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY1367 @ SY1366 ) @ SV141 )
| ( SY1366 = SY1367 ) ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(2990,plain,
! [SV336: $i] :
( ( ( ~ ! [SY1175: $i,SY1176: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SY1175 @ SY1176 ) ) )
= $false )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2991,plain,
! [SV336: $i] :
( ( ( ~ ( in @ ( sK108_B @ SV336 ) @ SV336 ) )
= $false )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2728]) ).
thf(2992,plain,
! [SV337: $i,SV549: $i] :
( ( ( ( SV549
= ( ordered_pair @ ( sK106_C @ SV549 @ SV337 ) @ ( sK107_SY668 @ SV549 @ SV337 ) ) )
| ~ ( in @ SV549 @ SV337 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2993,plain,
! [SV142: $i,SV282: $i] :
( ( ( ! [SY1118: $i] :
( ~ ( relation @ SY1118 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SY1118 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SY1118 @ SV282 @ SV142 ) ) @ SY1118 ) ) ) )
| ( SY1118
= ( relation_rng_restriction @ SV142 @ SV282 ) ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2730]) ).
thf(2994,plain,
! [SV282: $i,SV142: $i] :
( ( ( ! [SY1119: $i] :
( ~ ( relation @ SY1119 )
| ( SY1119
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1120: $i,SY1121: $i] :
( ~ ( in @ SY1121 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1120 @ SY1121 ) @ SY1119 ) )
| ~ ~ ( ~ ! [SY823: $i,SY824: $i] :
( ~ ( in @ ( ordered_pair @ SY823 @ SY824 ) @ SY1119 )
| ( in @ SY824 @ SV142 ) )
| ~ ! [SY1124: $i,SY1125: $i] :
( ~ ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SY1119 )
| ( in @ ( ordered_pair @ SY1124 @ SY1125 ) @ SV282 ) ) ) ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2995,plain,
! [SV550: $i,SV283: $i,SV505: $i,SV143: $i] :
( ( ~ ( in @ SV143 @ SV505 )
| ~ ( in @ SV283 @ SV550 )
| ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(2996,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2997,plain,
! [SV283: $i,SV143: $i] :
( ( ~ ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2735]) ).
thf(2998,plain,
! [SV144: $i,SV433: $i] :
( ( ( ~ ( subset @ SV433 @ ( sK87_B @ SV144 ) ) )
= $true )
| ( ( are_equipotent @ SV433 @ ( sK87_B @ SV144 ) )
= $true )
| ( ( in @ SV433 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(2999,plain,
! [SV144: $i] :
( ( ! [SY835: $i] :
( ~ ( ~ ! [SY836: $i] :
( ~ ( subset @ SY836 @ SY835 )
| ( in @ SY836 @ ( sK88_SY659 @ SY835 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SY835 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SY835 @ ( sK87_B @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(3000,plain,
! [SV144: $i] :
( ( ~ ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2738]) ).
thf(3001,plain,
! [SV340: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV340 )
| ~ ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 ) )
= $false )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(3002,plain,
! [SV435: $i,SV341: $i] :
( ( ( subset @ SV341 @ SV435 )
= $false )
| ( ( ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SV341 )
| ( in @ SY1261 @ SV435 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(3003,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
| ~ ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(3004,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( ( SV507
!= ( set_union2 @ SV145 @ SV437 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) )
| ~ ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(3005,plain,
! [SV146: $i,SV551: $i] :
( ( ( ~ ( ~ ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) ) )
| ( SV551
= ( relation_dom @ SV146 ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3006,plain,
! [SV146: $i,SV552: $i] :
( ( ( ( SV552
!= ( relation_dom @ SV146 ) )
| ~ ( ~ ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) )
| ~ ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3007,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_C @ SV553 @ SV147 ) @ SV553 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 ) )
| ( is_reflexive_in @ SV147 @ SV553 ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3008,plain,
! [SV554: $i,SV147: $i] :
( ( ( ~ ( is_reflexive_in @ SV147 @ SV554 )
| ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV554 )
| ( in @ ( ordered_pair @ SY1372 @ SY1372 ) @ SV147 ) ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3009,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( function @ SV438 ) )
= $true )
| ( ( ~ ( relation @ SV438 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 )
| ( SV438
= ( identity_relation @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(3010,plain,
! [SV555: $i] :
( ( ! [SY1373: $i] :
( ~ ( function @ SY1373 )
| ~ ( relation @ SY1373 )
| ( SY1373
!= ( identity_relation @ SV555 ) )
| ! [SY1374: $i] :
( ~ ( in @ SY1374 @ SV555 )
| ( ( apply @ SY1373 @ SY1374 )
= SY1374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3011,plain,
! [SV556: $i] :
( ( ! [SY1375: $i] :
( ~ ( function @ SY1375 )
| ~ ( relation @ SY1375 )
| ( SY1375
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SY1375 )
= SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3012,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
| ( is_transitive_in @ SV149 @ SV557 ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3013,plain,
! [SV558: $i,SV149: $i] :
( ( ( ~ ( is_transitive_in @ SV149 @ SV558 )
| ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( in @ SY1376 @ SV558 )
| ~ ( in @ SY1377 @ SV558 )
| ~ ( in @ SY1378 @ SV558 )
| ~ ( in @ ( ordered_pair @ SY1376 @ SY1377 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY1377 @ SY1378 ) @ SV149 )
| ( in @ ( ordered_pair @ SY1376 @ SY1378 ) @ SV149 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3014,plain,
! [SV439: $i,SV150: $i] :
( ( ( subset @ SV150 @ SV439 )
= $false )
| ( ( ! [SY1267: $i] : ( subset @ ( cartesian_product2 @ SV150 @ SY1267 ) @ ( cartesian_product2 @ SV439 @ SY1267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3015,plain,
! [SV440: $i,SV150: $i] :
( ( ( subset @ SV150 @ SV440 )
= $false )
| ( ( ! [SY1268: $i] : ( subset @ ( cartesian_product2 @ SY1268 @ SV150 ) @ ( cartesian_product2 @ SY1268 @ SV440 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3016,plain,
! [SV441: $i,SV343: $i] :
( ( ( ( set_difference @ SV343 @ SV441 )
= empty_set )
= $false )
| ( ( subset @ SV343 @ SV441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(3017,plain,
! [SV442: $i,SV344: $i] :
( ( ( subset @ SV344 @ SV442 )
= $false )
| ( ( ( set_difference @ SV344 @ SV442 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(3018,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( relation @ SV559 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
| ( SV559
= ( relation_inverse @ SV151 ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3019,plain,
! [SV151: $i,SV560: $i] :
( ( ( ~ ( relation @ SV560 )
| ( SV560
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3020,plain,
! [SV443: $i,SV345: $i] :
( ( ( ( set_difference @ SV345 @ ( singleton @ SV443 ) )
= SV345 )
= $false )
| ( ( ~ ( in @ SV443 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(3021,plain,
! [SV445: $i,SV347: $i] :
( ( ( ( set_difference @ SV347 @ SV445 )
= SV347 )
= $false )
| ( ( disjoint @ SV347 @ SV445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(3022,plain,
! [SV446: $i,SV348: $i] :
( ( ( disjoint @ SV348 @ SV446 )
= $false )
| ( ( ( set_difference @ SV348 @ SV446 )
= SV348 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3023,plain,
! [SV152: $i,SV284: $i] :
( ( ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 ) )
= $true )
| ( ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(3024,plain,
! [SV152: $i,SV284: $i] :
( ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
= $true )
| ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(3025,plain,
! [SV447: $i,SV349: $i] :
( ( ( ~ ( empty @ SV349 ) )
= $true )
| ( ( ~ ( relation @ SV447 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV447 @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(3026,plain,
! [SV448: $i,SV350: $i] :
( ( ( ~ ( empty @ SV350 ) )
= $true )
| ( ( ~ ( relation @ SV448 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV448 @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(3027,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ( ~ ( ~ ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) )
| ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) ) ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(3028,plain,
! [SV450: $i,SV153: $i,SV509: $i] :
( ( ( ( SV509
!= ( cartesian_product2 @ SV153 @ SV450 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) )
| ~ ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(3029,plain,
! [SV451: $i,SV351: $i] :
( ( ( ( set_intersection2 @ SV351 @ SV451 )
= empty_set )
= $false )
| ( ( disjoint @ SV351 @ SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3030,plain,
! [SV452: $i,SV352: $i] :
( ( ( disjoint @ SV352 @ SV452 )
= $false )
| ( ( ( set_intersection2 @ SV352 @ SV452 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3031,plain,
! [SV354: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV354 ) )
= $true )
| ( ( SV354 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3032,plain,
! [SV453: $i,SV355: $i] :
( ( ( subset @ SV355 @ ( singleton @ SV453 ) )
= $false )
| ( ( ( SV355 = empty_set )
| ( SV355
= ( singleton @ SV453 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(3033,plain,
! [SV562: $i] :
( ( ( SV562 != empty_set )
| ! [SY1383: $i] : ( subset @ SV562 @ ( singleton @ SY1383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3034,plain,
! [SV563: $i] :
( ( ! [SY1384: $i] :
( ( SV563
!= ( singleton @ SY1384 ) )
| ( subset @ SV563 @ ( singleton @ SY1384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3035,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
| ~ ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) ) )
= $false )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(3036,plain,
! [SV357: $i,SV455: $i] :
( ( ( SV455
= ( powerset @ SV357 ) )
= $false )
| ( ( ~ ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) )
| ~ ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(3037,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)],[2779]) ).
thf(3038,plain,
! [SV456: $i,SV358: $i] :
( ( ( ~ ( ordinal @ SV358 ) )
= $true )
| ( ( ~ ( ordinal @ SV456 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV358 @ SV456 )
| ( subset @ SV358 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3039,plain,
! [SV457: $i,SV359: $i] :
( ( ( ~ ( ordinal @ SV359 ) )
= $true )
| ( ( ~ ( ordinal @ SV457 ) )
= $true )
| ( ( ~ ( subset @ SV359 @ SV457 )
| ( ordinal_subset @ SV359 @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3040,plain,
! [SV360: $i,SV458: $i] :
( ( ( ~ ( function @ SV458 ) )
= $true )
| ( ( ~ ( relation @ SV458 ) )
= $true )
| ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 )
| ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3041,plain,
! [SV361: $i,SV459: $i] :
( ( ( ~ ( function @ SV459 ) )
= $true )
| ( ( ~ ( relation @ SV459 ) )
= $true )
| ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(3042,plain,
! [SV154: $i] :
( ( ( ~ ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(3043,plain,
! [SV154: $i] :
( ( ( ~ ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(3044,plain,
! [SV362: $i] :
( ( ( ( ( relation_dom @ SV362 )
!= empty_set ) )
= $true )
| ( ( SV362 = empty_set )
= $true )
| ( ( relation @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(3045,plain,
! [SV363: $i] :
( ( ( ( ( relation_rng @ SV363 )
!= empty_set ) )
= $true )
| ( ( SV363 = empty_set )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(3046,plain,
! [SV364: $i] :
( ( ( function @ SV364 )
= $false )
| ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
| ( one_to_one @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(3047,plain,
! [SV365: $i] :
( ( ( function @ SV365 )
= $false )
| ( ( ~ ( relation @ SV365 ) )
= $true )
| ( ( ~ ( one_to_one @ SV365 )
| ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3048,plain,
! [SV460: $i,SV366: $i] :
( ( ( in @ SV366 @ SV460 )
= $false )
| ( ( subset @ ( singleton @ SV366 ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3049,plain,
! [SV461: $i,SV367: $i] :
( ( ( subset @ ( singleton @ SV367 ) @ SV461 )
= $false )
| ( ( in @ SV367 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3050,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
| ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(3051,plain,
! [SV369: $i] :
( ( ( ~ ( antisymmetric @ SV369 ) )
= $true )
| ( ( ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ ( ordered_pair @ SY1206 @ SY1207 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV369 )
| ( SY1206 = SY1207 ) ) )
= $true )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(3052,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) ) ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(3053,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ( SV511
!= ( set_difference @ SV155 @ SV463 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) )
| ~ ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3054,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
| ~ ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) ) )
= $false )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(3055,plain,
! [SV371: $i,SV465: $i] :
( ( ( SV465
= ( union @ SV371 ) )
= $false )
| ( ( ~ ( ~ ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) )
| ~ ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3056,plain,
! [SV285: $i,SV512: $i,SV156: $i,SV564: $i] :
( ( ~ ( relation @ SV564 )
| ~ ( in @ SV156 @ SV512 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3057,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(3058,plain,
! [SV285: $i,SV156: $i] :
( ( ~ ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(3059,plain,
! [SV372: $i,SV466: $i] :
( ( ( ~ ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
| ~ ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) ) )
= $false )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3060,plain,
! [SV373: $i,SV467: $i] :
( ( ( SV467
= ( singleton @ SV373 ) )
= $false )
| ( ( ~ ( ~ ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) )
| ~ ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3061,plain,
! [SV565: $i] :
( ( ~ ( ordinal @ SV565 )
| ( epsilon_connected @ ( union @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3062,plain,
! [SV566: $i] :
( ( ~ ( ordinal @ SV566 )
| ( epsilon_transitive @ ( union @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3063,plain,
! [SV468: $i,SV375: $i] :
( ( ( ( set_difference @ SV375 @ SV468 )
= empty_set )
= $false )
| ( ( subset @ SV375 @ SV468 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(3064,plain,
! [SV469: $i,SV376: $i] :
( ( ( subset @ SV376 @ SV469 )
= $false )
| ( ( ( set_difference @ SV376 @ SV469 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(3065,plain,
! [SV157: $i] :
( ( ( one_to_one @ SV157 )
= $false )
| ( ( ~ ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(3066,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)],[2808]) ).
thf(3067,plain,
! [SV158: $i,SV567: $i] :
( ( ( ~ ( ordinal @ SV567 )
| ~ ( in @ SV158 @ SV567 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SV567 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3068,plain,
! [SV158: $i,SV568: $i] :
( ( ( ~ ( ordinal @ SV568 )
| ~ ( ordinal_subset @ ( succ @ SV158 ) @ SV568 )
| ( in @ SV158 @ SV568 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3069,plain,
! [SV470: $i,SV159: $i,SV513: $i] :
( ( ( ~ ( relation @ SV513 ) )
= $true )
| ( ( ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY1337 ) @ SV513 )
| ~ ( in @ SY1337 @ SV470 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(3070,plain,
! [SV471: $i,SV159: $i,SV514: $i] :
( ( ( ~ ( relation @ SV514 ) )
= $true )
| ( ( ~ ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(3071,plain,
! [SV160: $i,SV569: $i] :
( ( ( ~ ( relation @ SV569 )
| ~ ( subset @ SV160 @ SV569 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SV569 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3072,plain,
! [SV160: $i,SV570: $i] :
( ( ( ~ ( relation @ SV570 )
| ~ ( subset @ SV160 @ SV570 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SV570 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3073,plain,
! [SV472: $i,SV381: $i] :
( ( ( in @ SV381 @ SV472 )
= $false )
| ( ( subset @ ( singleton @ SV381 ) @ SV472 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3074,plain,
! [SV473: $i,SV382: $i] :
( ( ( subset @ ( singleton @ SV382 ) @ SV473 )
= $false )
| ( ( in @ SV382 @ SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3075,plain,
! [SV383: $i] :
( ( ( ( ( relation_dom @ SV383 )
!= empty_set ) )
= $true )
| ( ( ( relation_rng @ SV383 )
= empty_set )
= $true )
| ( ( relation @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(3076,plain,
! [SV384: $i] :
( ( ( ( ( relation_rng @ SV384 )
!= empty_set ) )
= $true )
| ( ( ( relation_dom @ SV384 )
= empty_set )
= $true )
| ( ( relation @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3077,plain,
! [SV474: $i,SV385: $i] :
( ( ( SV385 = SV474 )
= $true )
| ( ( ~ ( subset @ SV385 @ SV474 ) )
= $true )
| ( ( proper_subset @ SV385 @ SV474 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3078,plain,
! [SV571: $i] :
( ( ! [SY1385: $i] :
( ~ ( proper_subset @ SV571 @ SY1385 )
| ( SV571 != SY1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3079,plain,
! [SV572: $i] :
( ( ! [SY1386: $i] :
( ~ ( proper_subset @ SV572 @ SY1386 )
| ( subset @ SV572 @ SY1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3080,plain,
! [SV475: $i,SV386: $i] :
( ( ( subset @ SV386 @ ( singleton @ SV475 ) )
= $false )
| ( ( ( SV386 = empty_set )
| ( SV386
= ( singleton @ SV475 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(3081,plain,
! [SV573: $i] :
( ( ( SV573 != empty_set )
| ! [SY1387: $i] : ( subset @ SV573 @ ( singleton @ SY1387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3082,plain,
! [SV574: $i] :
( ( ! [SY1388: $i] :
( ( SV574
!= ( singleton @ SY1388 ) )
| ( subset @ SV574 @ ( singleton @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3083,plain,
! [SV476: $i,SV161: $i,SV515: $i] :
( ( ( ~ ( relation @ SV515 ) )
= $true )
| ( ( ~ ( in @ SV161 @ SV515 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) )
| ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(3084,plain,
! [SV161: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ~ ( relation @ SY926 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY926 @ SY925 ) )
| ( in @ SV161 @ SY926 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(3085,plain,
! [SV161: $i] :
( ( ! [SY927: $i,SY928: $i] :
( ~ ( relation @ SY928 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY928 @ SY927 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SY927 @ SY927 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2832]) ).
thf(3086,plain,
! [SV477: $i,SV162: $i,SV516: $i] :
( ( ( ~ ( relation @ SV516 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SV516 )
| ( in @ SV162 @ ( relation_field @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(3087,plain,
! [SV478: $i,SV162: $i,SV517: $i] :
( ( ( ~ ( relation @ SV517 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SV517 )
| ( in @ SV478 @ ( relation_field @ SV517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3088,plain,
! [SV518: $i,SV286: $i,SV163: $i] :
( ( ( ! [SY1338: $i] :
( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV518 @ SY1338 ) ) )
= $true )
| ( ( SV163 = SV518 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(3089,plain,
! [SV575: $i,SV519: $i,SV286: $i,SV163: $i] :
( ( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV519 @ SV575 ) )
| ( SV286 = SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3090,plain,
! [SV479: $i,SV387: $i] :
( ( ( element @ SV387 @ ( powerset @ SV479 ) )
= $false )
| ( ( subset @ SV387 @ SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3091,plain,
! [SV480: $i,SV388: $i] :
( ( ( subset @ SV388 @ SV480 )
= $false )
| ( ( element @ SV388 @ ( powerset @ SV480 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3092,plain,
! [SV164: $i,SV481: $i,SV520: $i] :
( ( ( ~ ( function @ SV520 )
| ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3093,plain,
! [SV164: $i] :
( ( ! [SY940: $i,SY941: $i] :
( ~ ( function @ SY941 )
| ~ ( relation @ SY941 )
| ~ ( in @ SY940 @ ( relation_dom @ ( relation_dom_restriction @ SY941 @ SV164 ) ) )
| ( in @ SY940 @ ( relation_dom @ SY941 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(3094,plain,
! [SV164: $i] :
( ( ! [SY942: $i,SY943: $i] :
( ~ ( function @ SY943 )
| ~ ( relation @ SY943 )
| ~ ( in @ SY942 @ ( relation_dom @ ( relation_dom_restriction @ SY943 @ SV164 ) ) )
| ( in @ SY942 @ SV164 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(3095,plain,
! [SV165: $i,SV287: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV287 )
| ~ ( in @ SV576 @ ( sK3_C @ SV287 @ SV165 ) ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3096,plain,
! [SV287: $i,SV165: $i] :
( ( ( in @ SV165 @ SV287 )
= $false )
| ( ( in @ ( sK3_C @ SV287 @ SV165 ) @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3097,plain,
! [SV482: $i,SV166: $i,SV521: $i] :
( ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SV521 )
| ( in @ SV166 @ ( relation_dom @ SV521 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3098,plain,
! [SV483: $i,SV166: $i,SV522: $i] :
( ( ( ~ ( relation @ SV522 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SV522 )
| ( in @ SV483 @ ( relation_rng @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3099,plain,
! [SV167: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ ( sK80_B @ SV167 ) ) )
= $true )
| ( ( are_equipotent @ SV484 @ ( sK80_B @ SV167 ) )
= $true )
| ( ( in @ SV484 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(3100,plain,
! [SV167: $i] :
( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SY951 ) @ ( sK80_B @ SV167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(3101,plain,
! [SV167: $i] :
( ( ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(3102,plain,
! [SV389: $i] :
( ( ( ~ ( in @ ( sK104_B @ SV389 ) @ SV389 ) )
= $false )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(3103,plain,
! [SV389: $i] :
( ( ( ~ ~ ( subset @ ( sK104_B @ SV389 ) @ SV389 ) )
= $false )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(3104,plain,
! [SV390: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV390 )
| ( subset @ SV577 @ SV390 ) )
= $true )
| ( ( epsilon_transitive @ SV390 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3105,plain,
! [SV168: $i,SV485: $i,SV523: $i] :
( ( ( ~ ( function @ SV523 )
| ~ ( relation @ SV523 ) )
= $true )
| ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3106,plain,
! [SV168: $i] :
( ( ! [SY956: $i,SY957: $i] :
( ~ ( function @ SY957 )
| ~ ( relation @ SY957 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY956 ) @ SY957 )
| ( SY956
= ( apply @ SY957 @ SV168 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2852]) ).
thf(3107,plain,
! [SV168: $i] :
( ( ! [SY958: $i,SY959: $i] :
( ~ ( function @ SY959 )
| ~ ( relation @ SY959 )
| ~ ( in @ ( ordered_pair @ SV168 @ SY958 ) @ SY959 )
| ( in @ SV168 @ ( relation_dom @ SY959 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2853]) ).
thf(3108,plain,
! [SV169: $i] :
( ( ( ~ ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(3109,plain,
! [SV169: $i] :
( ( ( ~ ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(3110,plain,
! [SV391: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV391 )
| ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV486 ) )
= $false )
| ( ( disjoint @ SV391 @ SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3111,plain,
! [SV487: $i,SV392: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV392 )
| ~ ( in @ SV578 @ SV487 ) )
= $true )
| ( ( ~ ( disjoint @ SV392 @ SV487 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3112,plain,
! [SV170: $i] :
( ( ( ~ ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2859]) ).
thf(3113,plain,
! [SV170: $i] :
( ( ( ~ ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2859]) ).
thf(3114,plain,
! [SV488: $i,SV171: $i,SV524: $i] :
( ( ( ~ ( relation @ SV524 ) )
= $true )
| ( ( ~ ( in @ SV171 @ SV488 )
| ~ ( in @ SV171 @ ( relation_dom @ SV524 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(3115,plain,
! [SV171: $i] :
( ( ! [SY977: $i,SY978: $i] :
( ~ ( relation @ SY978 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY978 @ SY977 ) ) )
| ( in @ SV171 @ SY977 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(3116,plain,
! [SV171: $i] :
( ( ! [SY979: $i,SY980: $i] :
( ~ ( relation @ SY980 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY980 @ SY979 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY980 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2864]) ).
thf(3117,plain,
! [SV172: $i,SV397: $i] :
( ( ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) )
| ~ ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3118,plain,
! [SV173: $i,SV579: $i] :
( ( ( ~ ( ~ ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) ) )
| ( SV579
= ( relation_rng @ SV173 ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3119,plain,
! [SV173: $i,SV580: $i] :
( ( ( ( SV580
!= ( relation_rng @ SV173 ) )
| ~ ( ~ ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) )
| ~ ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3120,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) ) )
| ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3121,plain,
! [SV526: $i,SV288: $i,SV174: $i,SV582: $i] :
( ( ( SV582
!= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
| ~ ( ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) )
| ~ ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3122,plain,
! [SV398: $i] :
( ( ( relation @ SV398 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV398 ) )
= $true )
| ( ( ! [SY1238: $i] : ( relation @ ( relation_dom_restriction @ SV398 @ SY1238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3123,plain,
! [SV399: $i] :
( ( ( relation @ SV399 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV399 ) )
= $true )
| ( ( ! [SY1239: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(3124,plain,
! [SV583: $i] :
( ( ( SV583 = empty_set )
| ! [SY1397: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SY1397 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SY1397 @ SV583 ) @ ( sK52_SY636 @ SY1397 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1397 ) )
| ~ ( ! [SY1398: $i] :
( ~ ( in @ SY1398 @ SV583 )
| ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1398 ) )
| ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1397 ) ) )
| ( SY1397
= ( set_meet @ SV583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3125,plain,
! [SV584: $i] :
( ( ( SV584 = empty_set )
| ! [SY1399: $i] :
( ( SY1399
!= ( set_meet @ SV584 ) )
| ~ ( ~ ! [SY1400: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1400 @ SY1399 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1400 @ ( sK50_D @ SY1400 @ SY1399 @ SV584 ) ) )
| ( in @ SY1400 @ SY1399 ) )
| ~ ! [SY1401: $i] :
( ~ ( in @ SY1401 @ SY1399 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1401 @ SY1402 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3126,plain,
! [SV585: $i] :
( ( ( SV585 != empty_set )
| ! [SY1403: $i] :
( ( SY1403
!= ( set_meet @ SV585 ) )
| ( SY1403 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3127,plain,
! [SV586: $i] :
( ( ( SV586 != empty_set )
| ! [SY1404: $i] :
( ( SY1404 != empty_set )
| ( SY1404
= ( set_meet @ SV586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3128,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) )
| ~ ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) ) ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3129,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( ( SV528
!= ( unordered_pair @ SV175 @ SV490 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) )
| ~ ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3130,plain,
! [SV400: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) ) )
= $true )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3131,plain,
! [SV401: $i] :
( ( ( ~ ( transitive @ SV401 ) )
= $true )
| ( ( ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( in @ ( ordered_pair @ SY1240 @ SY1241 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1241 @ SY1242 ) @ SV401 )
| ( in @ ( ordered_pair @ SY1240 @ SY1242 ) @ SV401 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3132,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) )
| ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3133,plain,
! [SV491: $i,SV404: $i] :
( ( ( ~ ( subset @ SV404 @ SV491 ) )
= $true )
| ( ( ~ ( subset @ SV491 @ SV404 ) )
= $true )
| ( ( SV404 = SV491 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3134,plain,
! [SV587: $i] :
( ( ! [SY1405: $i] :
( ( SV587 != SY1405 )
| ( subset @ SV587 @ SY1405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3135,plain,
! [SV588: $i] :
( ( ! [SY1406: $i] :
( ( SV588 != SY1406 )
| ( subset @ SY1406 @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3136,plain,
! [SV405: $i] :
( ( ( function @ SV405 )
= $false )
| ( ( ~ ( relation @ SV405 ) )
= $true )
| ( ( function @ ( function_inverse @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(3137,plain,
! [SV406: $i] :
( ( ( function @ SV406 )
= $false )
| ( ( ~ ( relation @ SV406 ) )
= $true )
| ( ( relation @ ( function_inverse @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(3138,plain,
! [SV492: $i,SV529: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV529 )
| ~ ( in @ SV492 @ SV529 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SV529 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2892]) ).
thf(3139,plain,
! [SV177: $i] :
( ( ! [SY1018: $i,SY1019: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1018 ) @ SY1019 )
| ( in @ SV177 @ SY1019 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(3140,plain,
! [SV177: $i] :
( ( ! [SY1020: $i,SY1021: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SY1020 ) @ SY1021 )
| ( in @ SY1020 @ SY1021 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(3141,plain,
! [SV178: $i,SV290: $i] :
( ( ( ~ ( ordinal @ ( sK77_C @ SV290 @ SV178 ) ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(3142,plain,
! [SV290: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2895]) ).
thf(3143,plain,
! [SV291: $i,SV179: $i] :
( ( ( ! [SY1155: $i] :
( ~ ( element @ SY1155 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SY1155 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1155 ) ) ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2896]) ).
thf(3144,plain,
! [SV291: $i,SV179: $i] :
( ( ( ! [SY1156: $i] :
( ~ ( element @ SY1156 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SY1156 ) )
| ( disjoint @ SV291 @ SY1156 ) ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(3145,plain,
! [SV589: $i] :
( ( ~ ( empty @ SV589 )
| ( epsilon_connected @ SV589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3146,plain,
! [SV590: $i] :
( ( ~ ( empty @ SV590 )
| ( epsilon_transitive @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3147,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( relation @ SV591 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
| ( SV181 = SV591 ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3148,plain,
! [SV181: $i,SV592: $i] :
( ( ( ~ ( relation @ SV592 )
| ( SV181 != SV592 )
| ~ ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3149,plain,
! [SV493: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 )
| ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2903]) ).
thf(3150,plain,
! [SV494: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 )
| ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(3151,plain,
! [SV182: $i] :
( ( ( ~ ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3152,plain,
! [SV182: $i] :
( ( ( ~ ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3153,plain,
! [SV183: $i] :
( ( ( ordinal @ ( sK111_B @ SV183 ) )
= $false )
| ( ( ~ ( subset @ ( sK111_B @ SV183 ) @ SV183 ) )
= $true )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3154,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) )
| ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3155,plain,
! [SV410: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(3156,plain,
! [SV410: $i] :
( ( ( ~ ~ ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2910]) ).
thf(3157,plain,
! [SV411: $i,SV593: $i] :
( ( ( ! [SY1411: $i] :
( ( SV593 = SY1411 )
| ~ ( in @ SV593 @ SV411 )
| ~ ( in @ SY1411 @ SV411 )
| ( in @ SV593 @ SY1411 )
| ( in @ SY1411 @ SV593 ) ) )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3158,plain,
! [SV185: $i,SV594: $i] :
( ( ( ! [SY1412: $i] :
( ~ ( relation @ SY1412 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SY1412 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SY1412 @ SV594 @ SV185 ) ) @ SY1412 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SY1412 @ SV594 @ SV185 ) ) @ SY1412 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SY1412 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SY1412 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SY1412 @ SV594 @ SV185 ) ) @ SY1412 ) ) ) )
| ( SY1412
= ( relation_dom_restriction @ SV185 @ SV594 ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3159,plain,
! [SV595: $i,SV185: $i] :
( ( ( ! [SY1413: $i] :
( ~ ( relation @ SY1413 )
| ( SY1413
!= ( relation_dom_restriction @ SV185 @ SV595 ) )
| ~ ( ~ ! [SY1414: $i,SY1415: $i] :
( ~ ( in @ SY1414 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1414 @ SY1415 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1414 @ SY1415 ) @ SY1413 ) )
| ~ ~ ( ~ ! [SY1416: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY1416 @ SX4 ) @ SY1413 )
| ( in @ SY1416 @ SV595 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SY1413 )
| ( in @ ( ordered_pair @ SY1052 @ SY1053 ) @ SV185 ) ) ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3160,plain,
! [SV596: $i] :
( ( ~ ( empty @ SV596 )
| ~ ( relation @ SV596 )
| ~ ( function @ SV596 )
| ( function @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3161,plain,
! [SV597: $i] :
( ( ~ ( empty @ SV597 )
| ~ ( relation @ SV597 )
| ~ ( function @ SV597 )
| ( relation @ SV597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3162,plain,
! [SV414: $i] :
( ( ( ~ ( empty @ SV414 ) )
= $true )
| ( ( ~ ( relation @ SV414 ) )
= $true )
| ( ( ~ ( function @ SV414 ) )
= $true )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3163,plain,
! [SV495: $i,SV186: $i,SV530: $i] :
( ( ( ~ ( relation @ SV530 ) )
= $true )
| ( ( ~ ( in @ SV186 @ SV495 )
| ~ ( in @ SV186 @ ( relation_rng @ SV530 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(3164,plain,
! [SV186: $i] :
( ( ! [SY1056: $i,SY1057: $i] :
( ~ ( relation @ SY1057 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1056 @ SY1057 ) ) )
| ( in @ SV186 @ SY1056 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(3165,plain,
! [SV186: $i] :
( ( ! [SY1058: $i,SY1059: $i] :
( ~ ( relation @ SY1059 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SY1058 @ SY1059 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1059 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2921]) ).
thf(3166,plain,
! [SV496: $i,SV415: $i] :
( ( ( ~ ( empty @ SV415 ) )
= $true )
| ( ( ~ ( relation @ SV496 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV415 @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3167,plain,
! [SV497: $i,SV416: $i] :
( ( ( ~ ( empty @ SV416 ) )
= $true )
| ( ( ~ ( relation @ SV497 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV416 @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3168,plain,
! [SV498: $i,SV187: $i,SV531: $i] :
( ( ( ~ ( relation @ SV531 ) )
= $true )
| ( ( ! [SY1349: $i] :
( ~ ( in @ SY1349 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SY1349 @ SV187 ) @ SV531 )
| ~ ( in @ SY1349 @ SV498 ) )
| ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3169,plain,
! [SV499: $i,SV187: $i,SV532: $i] :
( ( ( ~ ( relation @ SV532 ) )
= $true )
| ( ( ~ ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3170,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( relation @ SV598 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
| ( subset @ SV188 @ SV598 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3171,plain,
! [SV188: $i,SV599: $i] :
( ( ( ~ ( relation @ SV599 )
| ~ ( subset @ SV188 @ SV599 )
| ! [SY1420: $i,SY1421: $i] :
( ~ ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV599 ) ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3172,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) ) ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3173,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ( SV534
!= ( set_intersection2 @ SV189 @ SV501 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) )
| ~ ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3174,plain,
! [SV419: $i] :
( ( ( epsilon_connected @ SV419 )
= $false )
| ( ( ~ ( epsilon_transitive @ SV419 ) )
= $true )
| ( ( ordinal @ SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3175,plain,
! [SV600: $i] :
( ( ~ ( ordinal @ SV600 )
| ( epsilon_connected @ SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3176,plain,
! [SV601: $i] :
( ( ~ ( ordinal @ SV601 )
| ( epsilon_transitive @ SV601 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3177,plain,
! [SV602: $i,SV293: $i,SV535: $i,SV190: $i] :
( ( ~ ( in @ SV190 @ SV535 )
| ~ ( in @ SV293 @ SV602 )
| ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3178,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3179,plain,
! [SV293: $i,SV190: $i] :
( ( ~ ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3180,plain,
( ( ~ ~ ( empty @ sK5_A )
| ~ ( epsilon_transitive @ sK5_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2935]) ).
thf(3181,plain,
! [SV191: $i,SV294: $i] :
( ( ( in @ ( sK81_C @ SV294 @ SV191 ) @ SV294 )
= $false )
| ( ( element @ SV191 @ ( powerset @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3182,plain,
! [SV420: $i] :
( ( ( function @ SV420 )
= $false )
| ( ( ~ ( relation @ SV420 ) )
= $true )
| ( ( ! [SY1250: $i] : ( function @ ( relation_dom_restriction @ SV420 @ SY1250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3183,plain,
! [SV421: $i] :
( ( ( function @ SV421 )
= $false )
| ( ( ~ ( relation @ SV421 ) )
= $true )
| ( ( ! [SY1251: $i] : ( relation @ ( relation_dom_restriction @ SV421 @ SY1251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3184,plain,
! [SV192: $i,SV603: $i] :
( ( ( ! [SY1422: $i] :
( ~ ( ~ ( ! [SY1423: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1422 @ SV603 @ SV192 ) @ SY1423 ) @ SV192 )
| ~ ( in @ SY1423 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SY1422 @ SV603 @ SV192 ) @ SY1422 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SY1422 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SY1422 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SY1422 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SY1422 @ SV603 @ SV192 ) @ SY1422 ) ) )
| ( SY1422
= ( relation_inverse_image @ SV192 @ SV603 ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3185,plain,
! [SV604: $i,SV192: $i] :
( ( ( ! [SY1424: $i] :
( ( SY1424
!= ( relation_inverse_image @ SV192 @ SV604 ) )
| ~ ( ~ ! [SY1425: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1425 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1425 @ SY1424 ) )
| ~ ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SY1424 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1427 @ ( sK55_E @ SY1427 @ SY1424 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1427 @ SY1424 @ SV604 @ SV192 ) @ SV604 ) ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3186,plain,
! [SV422: $i,SV502: $i] :
( ( ( relation @ SV502 )
= $false )
| ( ( ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
| ( SV502
= ( identity_relation @ SV422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3187,plain,
! [SV423: $i,SV503: $i] :
( ( ( relation @ SV503 )
= $false )
| ( ( ( SV503
!= ( identity_relation @ SV423 ) )
| ~ ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(3188,plain,
! [SV198: $i,SV6: $i,SV315: $i,SV295: $i] :
( ( ( subset @ SV295 @ SV315 )
= $false )
| ( ( subset @ SV6 @ SV198 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV6 @ SV295 ) @ ( cartesian_product2 @ SV198 @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3189,plain,
! [SV318: $i,SV30: $i] :
( ( ( subset @ ( relation_rng @ SV30 ) @ ( relation_dom @ SV318 ) )
= $false )
| ( ( ( relation_dom @ ( relation_composition @ SV30 @ SV318 ) )
= ( relation_dom @ SV30 ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3190,plain,
! [SV319: $i,SV31: $i] :
( ( ( subset @ ( relation_dom @ SV31 ) @ ( relation_rng @ SV319 ) )
= $false )
| ( ( ( relation_rng @ ( relation_composition @ SV319 @ SV31 ) )
= ( relation_rng @ SV31 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(3191,plain,
! [SV237: $i,SV64: $i] :
( ( ( subset @ SV64 @ ( relation_rng @ SV237 ) )
= $false )
| ( ( ( relation_image @ SV237 @ ( relation_inverse_image @ SV237 @ SV64 ) )
= SV64 )
= $true )
| ( ( function @ SV237 )
= $false )
| ( ( relation @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3192,plain,
! [SV66: $i,SV238: $i] :
( ( ( ( relation_inverse_image @ SV238 @ SV66 )
= empty_set )
= $false )
| ( ( SV66 = empty_set )
= $true )
| ( ( subset @ SV66 @ ( relation_rng @ SV238 ) )
= $false )
| ( ( relation @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3193,plain,
! [SV324: $i,SV67: $i] :
( ( ( proper_subset @ SV67 @ SV324 )
= $false )
| ( ( in @ SV67 @ SV324 )
= $true )
| ( ( ordinal @ SV324 )
= $false )
| ( ( epsilon_transitive @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3194,plain,
! [SV239: $i,SV68: $i,SV536: $i] :
( ( ( ~ ( function @ SV536 )
| ~ ( relation @ SV536 ) )
= $true )
| ( ( ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) ) )
= $true )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3195,plain,
! [SV240: $i,SV69: $i,SV537: $i] :
( ( ( ~ ( function @ SV537 )
| ~ ( relation @ SV537 ) )
= $true )
| ( ( ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3196,plain,
! [SV325: $i,SV71: $i] :
( ( ( in @ SV71 @ SV325 )
= $true )
| ( ( SV71 = SV325 )
= $true )
| ( ( in @ SV325 @ SV71 )
= $true )
| ( ( ordinal @ SV325 )
= $false )
| ( ( ordinal @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2960]) ).
thf(3197,plain,
! [SV244: $i,SV74: $i,SV303: $i] :
( ( ( in @ SV303 @ SV74 )
= $false )
| ( ( in @ SV74 @ SV244 )
= $false )
| ( ( in @ SV244 @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3198,plain,
! [SV304: $i,SV79: $i,SV504: $i] :
( ( ( element @ SV504 @ SV79 )
= $false )
| ( ( ( in @ SV504 @ SV304 )
| ( in @ SV504 @ ( subset_complement @ SV79 @ SV304 ) ) )
= $true )
| ( ( element @ SV304 @ ( powerset @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3199,plain,
! [SV80: $i,SV305: $i,SV249: $i] :
( ( ( in @ SV249 @ SV305 )
= $false )
| ( ( in @ SV249 @ ( subset_complement @ SV80 @ SV305 ) )
= $false )
| ( ( element @ SV305 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3200,plain,
! [SV84: $i,SV306: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) )
= $true )
| ( ( function @ SV306 )
= $false )
| ( ( relation @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3201,plain,
! [SV307: $i,SV85: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV85 ) )
= $true )
| ( ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) )
= $true )
| ( ( function @ SV307 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3202,plain,
! [SV135: $i,SV279: $i,SV314: $i] :
( ( ( empty @ SV314 )
= $false )
| ( ( element @ SV279 @ ( powerset @ SV314 ) )
= $false )
| ( ( in @ SV135 @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3203,plain,
! [SV430: $i,SV329: $i,SV538: $i] :
( ( ( in @ SV538 @ ( set_intersection2 @ SV329 @ SV430 ) )
= $false )
| ( ( ~ ( disjoint @ SV329 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3204,plain,
! [SV330: $i,SV431: $i] :
( ( ( function @ SV431 )
= $false )
| ( ( ~ ( relation @ SV431 ) )
= $true )
| ( ( function @ ( relation_rng_restriction @ SV330 @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3205,plain,
! [SV331: $i,SV432: $i] :
( ( ( function @ SV432 )
= $false )
| ( ( ~ ( relation @ SV432 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV331 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3206,plain,
! [SV332: $i] :
( ( ( relation @ SV332 )
= $false )
| ( ( function @ SV332 )
= $false )
| ( ( ~ ( one_to_one @ SV332 )
| ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3207,plain,
! [SV333: $i] :
( ( ( relation @ SV333 )
= $false )
| ( ( function @ SV333 )
= $false )
| ( ( ~ ( one_to_one @ SV333 )
| ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3208,plain,
! [SV539: $i] :
( ( ( empty @ SV539 )
= $true )
| ( ( ! [SY1354: $i] :
( ~ ( element @ SY1354 @ SV539 )
| ( in @ SY1354 @ SV539 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3209,plain,
! [SV540: $i] :
( ( ( empty @ SV540 )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( in @ SY1355 @ SV540 )
| ( element @ SY1355 @ SV540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3210,plain,
! [SV541: $i] :
( ( ( ~ ( empty @ SV541 ) )
= $true )
| ( ( ! [SY1356: $i] :
( ~ ( element @ SY1356 @ SV541 )
| ( empty @ SY1356 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3211,plain,
! [SV542: $i] :
( ( ( ~ ( empty @ SV542 ) )
= $true )
| ( ( ! [SY1357: $i] :
( ~ ( empty @ SY1357 )
| ( element @ SY1357 @ SV542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3212,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3213,plain,
! [SV544: $i,SV139: $i] :
( ( ( ~ ( is_connected_in @ SV139 @ SV544 ) )
= $true )
| ( ( ! [SY1358: $i,SY1359: $i] :
( ( SY1358 = SY1359 )
| ~ ( in @ SY1358 @ SV544 )
| ~ ( in @ SY1359 @ SV544 )
| ( in @ ( ordered_pair @ SY1358 @ SY1359 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1359 @ SY1358 ) @ SV139 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3214,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ~ ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) ) )
| ( SV605
= ( relation_image @ SV140 @ SV545 ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3215,plain,
! [SV546: $i,SV140: $i,SV606: $i] :
( ( ( ( SV606
!= ( relation_image @ SV140 @ SV546 ) )
| ~ ( ~ ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) )
| ~ ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3216,plain,
! [SV334: $i] :
( ( ( function @ SV334 )
= $false )
| ( ( ~ ( relation @ SV334 ) )
= $true )
| ( ( ~ ( one_to_one @ SV334 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3217,plain,
! [SV335: $i] :
( ( ( function @ SV335 )
= $false )
| ( ( ~ ( relation @ SV335 ) )
= $true )
| ( ( ~ ( one_to_one @ SV335 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3218,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SV547 @ SV141 )
!= ( sK37_SY628 @ SV547 @ SV141 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(3219,plain,
! [SV548: $i,SV141: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV141 @ SV548 ) )
= $true )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1366 @ SV548 )
| ~ ( in @ SY1367 @ SV548 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY1367 @ SY1366 ) @ SV141 )
| ( SY1366 = SY1367 ) ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2989]) ).
thf(3220,plain,
! [SV336: $i] :
( ( ( ! [SY1175: $i,SY1176: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SY1175 @ SY1176 ) ) )
= $true )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2990]) ).
thf(3221,plain,
! [SV336: $i] :
( ( ( in @ ( sK108_B @ SV336 ) @ SV336 )
= $true )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2991]) ).
thf(3222,plain,
! [SV337: $i,SV549: $i] :
( ( ( SV549
= ( ordered_pair @ ( sK106_C @ SV549 @ SV337 ) @ ( sK107_SY668 @ SV549 @ SV337 ) ) )
= $true )
| ( ( ~ ( in @ SV549 @ SV337 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3223,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( relation @ SV607 )
| ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
| ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3224,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ( relation @ SV608 )
| ( SV608
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3225,plain,
! [SV550: $i,SV283: $i,SV505: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV505 )
| ~ ( in @ SV283 @ SV550 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3226,plain,
! [SV283: $i,SV143: $i] :
( ( ! [SY1128: $i] :
( ! [SY1129: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1128 @ SY1129 ) )
| ( in @ SV143 @ SY1128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2996]) ).
thf(3227,plain,
! [SV283: $i,SV143: $i] :
( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SY1130 @ SY1131 ) )
| ( in @ SV283 @ SY1131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3228,plain,
! [SV144: $i,SV433: $i] :
( ( ( subset @ SV433 @ ( sK87_B @ SV144 ) )
= $false )
| ( ( are_equipotent @ SV433 @ ( sK87_B @ SV144 ) )
= $true )
| ( ( in @ SV433 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3229,plain,
! [SV144: $i,SV609: $i] :
( ( ~ ( ~ ! [SY1438: $i] :
( ~ ( subset @ SY1438 @ SV609 )
| ( in @ SY1438 @ ( sK88_SY659 @ SV609 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3230,plain,
! [SV144: $i] :
( ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) )
| ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3231,plain,
! [SV340: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV340 ) )
= $false )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3232,plain,
! [SV340: $i,SV434: $i] :
( ( ( ~ ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 ) )
= $false )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3233,plain,
! [SV435: $i,SV341: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV341 )
| ( in @ SV610 @ SV435 ) )
= $true )
| ( ( subset @ SV341 @ SV435 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3234,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
| ~ ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3235,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false )
| ( ( ~ ( ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) )
| ~ ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3236,plain,
! [SV146: $i,SV551: $i] :
( ( ( ~ ( ~ ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) ) ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3237,plain,
! [SV146: $i,SV552: $i] :
( ( ( ( SV552
!= ( relation_dom @ SV146 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) )
| ~ ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3238,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_C @ SV553 @ SV147 ) @ SV553 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 ) ) )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3239,plain,
! [SV554: $i,SV147: $i] :
( ( ( ~ ( is_reflexive_in @ SV147 @ SV554 ) )
= $true )
| ( ( ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV554 )
| ( in @ ( ordered_pair @ SY1372 @ SY1372 ) @ SV147 ) ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3240,plain,
! [SV342: $i,SV438: $i] :
( ( ( function @ SV438 )
= $false )
| ( ( ~ ( relation @ SV438 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 )
| ( SV438
= ( identity_relation @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3241,plain,
! [SV555: $i,SV611: $i] :
( ( ~ ( function @ SV611 )
| ~ ( relation @ SV611 )
| ( SV611
!= ( identity_relation @ SV555 ) )
| ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3242,plain,
! [SV556: $i,SV612: $i] :
( ( ~ ( function @ SV612 )
| ~ ( relation @ SV612 )
| ( SV612
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SV612 )
= SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3243,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3244,plain,
! [SV558: $i,SV149: $i] :
( ( ( ~ ( is_transitive_in @ SV149 @ SV558 ) )
= $true )
| ( ( ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( in @ SY1376 @ SV558 )
| ~ ( in @ SY1377 @ SV558 )
| ~ ( in @ SY1378 @ SV558 )
| ~ ( in @ ( ordered_pair @ SY1376 @ SY1377 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY1377 @ SY1378 ) @ SV149 )
| ( in @ ( ordered_pair @ SY1376 @ SY1378 ) @ SV149 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3245,plain,
! [SV439: $i,SV613: $i,SV150: $i] :
( ( ( subset @ ( cartesian_product2 @ SV150 @ SV613 ) @ ( cartesian_product2 @ SV439 @ SV613 ) )
= $true )
| ( ( subset @ SV150 @ SV439 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3246,plain,
! [SV440: $i,SV150: $i,SV614: $i] :
( ( ( subset @ ( cartesian_product2 @ SV614 @ SV150 ) @ ( cartesian_product2 @ SV614 @ SV440 ) )
= $true )
| ( ( subset @ SV150 @ SV440 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3247,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( relation @ SV559 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
| ( SV559
= ( relation_inverse @ SV151 ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3248,plain,
! [SV151: $i,SV560: $i] :
( ( ( ~ ( relation @ SV560 ) )
= $true )
| ( ( ( SV560
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3249,plain,
! [SV345: $i,SV443: $i] :
( ( ( in @ SV443 @ SV345 )
= $false )
| ( ( ( set_difference @ SV345 @ ( singleton @ SV443 ) )
= SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3250,plain,
! [SV152: $i,SV284: $i] :
( ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
= $false )
| ( ( ~ ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 ) )
= $true )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3251,plain,
! [SV447: $i,SV349: $i] :
( ( ( empty @ SV349 )
= $false )
| ( ( ~ ( relation @ SV447 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV447 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3252,plain,
! [SV448: $i,SV350: $i] :
( ( ( empty @ SV350 )
= $false )
| ( ( ~ ( relation @ SV448 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV448 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3253,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ( ~ ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) )
| ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) ) )
= $false )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3254,plain,
! [SV450: $i,SV153: $i,SV509: $i] :
( ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false )
| ( ( ~ ( ~ ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) )
| ~ ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3255,plain,
! [SV354: $i,SV561: $i] :
( ( ( in @ SV561 @ SV354 )
= $false )
| ( ( SV354 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3256,plain,
! [SV453: $i,SV355: $i] :
( ( ( SV355 = empty_set )
= $true )
| ( ( SV355
= ( singleton @ SV453 ) )
= $true )
| ( ( subset @ SV355 @ ( singleton @ SV453 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3257,plain,
! [SV562: $i] :
( ( ( ( SV562 != empty_set ) )
= $true )
| ( ( ! [SY1383: $i] : ( subset @ SV562 @ ( singleton @ SY1383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3258,plain,
! [SV615: $i,SV563: $i] :
( ( ( SV563
!= ( singleton @ SV615 ) )
| ( subset @ SV563 @ ( singleton @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3259,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) ) )
= $false )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3260,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) ) )
= $false )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3261,plain,
! [SV357: $i,SV455: $i] :
( ( ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) )
| ~ ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) )
= $false )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3262,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)],[3037]) ).
thf(3263,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3264,plain,
! [SV456: $i,SV358: $i] :
( ( ( ordinal @ SV358 )
= $false )
| ( ( ~ ( ordinal @ SV456 ) )
= $true )
| ( ( ~ ( ordinal_subset @ SV358 @ SV456 )
| ( subset @ SV358 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3265,plain,
! [SV457: $i,SV359: $i] :
( ( ( ordinal @ SV359 )
= $false )
| ( ( ~ ( ordinal @ SV457 ) )
= $true )
| ( ( ~ ( subset @ SV359 @ SV457 )
| ( ordinal_subset @ SV359 @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3266,plain,
! [SV360: $i,SV458: $i] :
( ( ( function @ SV458 )
= $false )
| ( ( ~ ( relation @ SV458 ) )
= $true )
| ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 )
| ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3267,plain,
! [SV361: $i,SV459: $i] :
( ( ( function @ SV459 )
= $false )
| ( ( ~ ( relation @ SV459 ) )
= $true )
| ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3268,plain,
! [SV154: $i] :
( ( ( ! [SY881: $i,SY882: $i] :
( ~ ( ~ ( ! [SY883: $i] :
( ~ ( in @ SY883 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY883 @ SY881 )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ SY883 ) ) )
| ~ ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) @ SY881 ) )
| ( ( sK63_D @ SY882 @ SY881 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY882 @ SY881 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY882 @ SY881 @ SV154 ) @ SY882 ) ) )
| ( SY882
= ( relation_image @ SV154 @ SY881 ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3042]) ).
thf(3269,plain,
! [SV154: $i] :
( ( ( ! [SY884: $i,SY885: $i] :
( ( SY885
!= ( relation_image @ SV154 @ SY884 ) )
| ~ ( ~ ! [SY886: $i] :
( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY887 @ SY884 )
| ( SY886
!= ( apply @ SV154 @ SY887 ) ) )
| ( in @ SY886 @ SY885 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SY885 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) @ SY884 ) )
| ( SY888
!= ( apply @ SV154 @ ( sK62_E @ SY888 @ SY885 @ SY884 @ SV154 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3043]) ).
thf(3270,plain,
! [SV362: $i] :
( ( ( ( relation_dom @ SV362 )
= empty_set )
= $false )
| ( ( SV362 = empty_set )
= $true )
| ( ( relation @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3271,plain,
! [SV363: $i] :
( ( ( ( relation_rng @ SV363 )
= empty_set )
= $false )
| ( ( SV363 = empty_set )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3272,plain,
! [SV364: $i] :
( ( ( relation @ SV364 )
= $false )
| ( ( function @ SV364 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
| ( one_to_one @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3273,plain,
! [SV365: $i] :
( ( ( relation @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( ~ ( one_to_one @ SV365 )
| ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3274,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
| ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3275,plain,
! [SV369: $i] :
( ( ( antisymmetric @ SV369 )
= $false )
| ( ( ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ ( ordered_pair @ SY1206 @ SY1207 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1207 @ SY1206 ) @ SV369 )
| ( SY1206 = SY1207 ) ) )
= $true )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3276,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ~ ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3277,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false )
| ( ( ~ ( ~ ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) )
| ~ ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3278,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) ) )
= $false )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3279,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) ) )
= $false )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3054]) ).
thf(3280,plain,
! [SV465: $i,SV371: $i] :
( ( ( ~ ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) )
| ~ ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3281,plain,
! [SV285: $i,SV512: $i,SV156: $i,SV564: $i] :
( ( ( ~ ( relation @ SV564 ) )
= $true )
| ( ( ~ ( in @ SV156 @ SV512 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3282,plain,
! [SV285: $i,SV156: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ~ ( relation @ SY1135 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1134 ) @ SY1135 ) )
| ( in @ SV156 @ SY1134 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3057]) ).
thf(3283,plain,
! [SV285: $i,SV156: $i] :
( ( ! [SY1136: $i,SY1137: $i] :
( ~ ( relation @ SY1137 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SY1136 ) @ SY1137 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3058]) ).
thf(3284,plain,
! [SV372: $i,SV466: $i] :
( ( ( ~ ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) ) )
= $false )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3285,plain,
! [SV372: $i,SV466: $i] :
( ( ( ~ ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) ) )
= $false )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3286,plain,
! [SV467: $i,SV373: $i] :
( ( ( ~ ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) )
| ~ ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) )
= $false )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3287,plain,
! [SV565: $i] :
( ( ( ~ ( ordinal @ SV565 ) )
= $true )
| ( ( epsilon_connected @ ( union @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3288,plain,
! [SV566: $i] :
( ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( epsilon_transitive @ ( union @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3289,plain,
! [SV157: $i] :
( ( ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) )
| ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3290,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3291,plain,
( ( ~ ( epsilon_transitive @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3292,plain,
! [SV158: $i,SV567: $i] :
( ( ( ~ ( ordinal @ SV567 ) )
= $true )
| ( ( ~ ( in @ SV158 @ SV567 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SV567 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3293,plain,
! [SV158: $i,SV568: $i] :
( ( ( ~ ( ordinal @ SV568 ) )
= $true )
| ( ( ~ ( ordinal_subset @ ( succ @ SV158 ) @ SV568 )
| ( in @ SV158 @ SV568 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3294,plain,
! [SV470: $i,SV159: $i,SV513: $i] :
( ( ( relation @ SV513 )
= $false )
| ( ( ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY1337 ) @ SV513 )
| ~ ( in @ SY1337 @ SV470 ) )
| ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3295,plain,
! [SV471: $i,SV159: $i,SV514: $i] :
( ( ( relation @ SV514 )
= $false )
| ( ( ~ ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3296,plain,
! [SV160: $i,SV569: $i] :
( ( ( ~ ( relation @ SV569 ) )
= $true )
| ( ( ~ ( subset @ SV160 @ SV569 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SV569 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3297,plain,
! [SV160: $i,SV570: $i] :
( ( ( ~ ( relation @ SV570 ) )
= $true )
| ( ( ~ ( subset @ SV160 @ SV570 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SV570 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3298,plain,
! [SV383: $i] :
( ( ( ( relation_dom @ SV383 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV383 )
= empty_set )
= $true )
| ( ( relation @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3299,plain,
! [SV384: $i] :
( ( ( ( relation_rng @ SV384 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV384 )
= empty_set )
= $true )
| ( ( relation @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3300,plain,
! [SV474: $i,SV385: $i] :
( ( ( subset @ SV385 @ SV474 )
= $false )
| ( ( SV385 = SV474 )
= $true )
| ( ( proper_subset @ SV385 @ SV474 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3301,plain,
! [SV616: $i,SV571: $i] :
( ( ~ ( proper_subset @ SV571 @ SV616 )
| ( SV571 != SV616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3302,plain,
! [SV617: $i,SV572: $i] :
( ( ~ ( proper_subset @ SV572 @ SV617 )
| ( subset @ SV572 @ SV617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3303,plain,
! [SV475: $i,SV386: $i] :
( ( ( SV386 = empty_set )
= $true )
| ( ( SV386
= ( singleton @ SV475 ) )
= $true )
| ( ( subset @ SV386 @ ( singleton @ SV475 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3304,plain,
! [SV573: $i] :
( ( ( ( SV573 != empty_set ) )
= $true )
| ( ( ! [SY1387: $i] : ( subset @ SV573 @ ( singleton @ SY1387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3305,plain,
! [SV618: $i,SV574: $i] :
( ( ( SV574
!= ( singleton @ SV618 ) )
| ( subset @ SV574 @ ( singleton @ SV618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3306,plain,
! [SV476: $i,SV161: $i,SV515: $i] :
( ( ( relation @ SV515 )
= $false )
| ( ( ~ ( in @ SV161 @ SV515 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) )
| ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3307,plain,
! [SV619: $i,SV161: $i] :
( ( ! [SY1440: $i] :
( ~ ( relation @ SY1440 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY1440 @ SV619 ) )
| ( in @ SV161 @ SY1440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3308,plain,
! [SV620: $i,SV161: $i] :
( ( ! [SY1441: $i] :
( ~ ( relation @ SY1441 )
| ~ ( in @ SV161 @ ( relation_restriction @ SY1441 @ SV620 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3309,plain,
! [SV477: $i,SV162: $i,SV516: $i] :
( ( ( relation @ SV516 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SV516 )
| ( in @ SV162 @ ( relation_field @ SV516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3310,plain,
! [SV478: $i,SV162: $i,SV517: $i] :
( ( ( relation @ SV517 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SV517 )
| ( in @ SV478 @ ( relation_field @ SV517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3087]) ).
thf(3311,plain,
! [SV621: $i,SV518: $i,SV286: $i,SV163: $i] :
( ( ( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV518 @ SV621 ) ) )
= $true )
| ( ( SV163 = SV518 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3312,plain,
! [SV575: $i,SV519: $i,SV286: $i,SV163: $i] :
( ( ( ( ( ordered_pair @ SV163 @ SV286 )
!= ( ordered_pair @ SV519 @ SV575 ) ) )
= $true )
| ( ( SV286 = SV575 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3313,plain,
! [SV164: $i,SV481: $i,SV520: $i] :
( ( ( ~ ( function @ SV520 ) )
= $true )
| ( ( ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3314,plain,
! [SV164: $i,SV622: $i] :
( ( ! [SY1442: $i] :
( ~ ( function @ SY1442 )
| ~ ( relation @ SY1442 )
| ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SY1442 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SY1442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3315,plain,
! [SV164: $i,SV623: $i] :
( ( ! [SY1443: $i] :
( ~ ( function @ SY1443 )
| ~ ( relation @ SY1443 )
| ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SY1443 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3316,plain,
! [SV165: $i,SV287: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV287 ) )
= $true )
| ( ( ~ ( in @ SV576 @ ( sK3_C @ SV287 @ SV165 ) ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3317,plain,
! [SV482: $i,SV166: $i,SV521: $i] :
( ( ( relation @ SV521 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SV521 )
| ( in @ SV166 @ ( relation_dom @ SV521 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3318,plain,
! [SV483: $i,SV166: $i,SV522: $i] :
( ( ( relation @ SV522 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SV522 )
| ( in @ SV483 @ ( relation_rng @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3319,plain,
! [SV167: $i,SV484: $i] :
( ( ( subset @ SV484 @ ( sK80_B @ SV167 ) )
= $false )
| ( ( are_equipotent @ SV484 @ ( sK80_B @ SV167 ) )
= $true )
| ( ( in @ SV484 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3320,plain,
! [SV167: $i,SV624: $i] :
( ( ~ ( in @ SV624 @ ( sK80_B @ SV167 ) )
| ( in @ ( powerset @ SV624 ) @ ( sK80_B @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3321,plain,
! [SV167: $i] :
( ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) )
| ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3322,plain,
! [SV389: $i] :
( ( ( in @ ( sK104_B @ SV389 ) @ SV389 )
= $true )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3102]) ).
thf(3323,plain,
! [SV389: $i] :
( ( ( ~ ( subset @ ( sK104_B @ SV389 ) @ SV389 ) )
= $true )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3324,plain,
! [SV390: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV390 ) )
= $true )
| ( ( subset @ SV577 @ SV390 )
= $true )
| ( ( epsilon_transitive @ SV390 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3325,plain,
! [SV168: $i,SV485: $i,SV523: $i] :
( ( ( ~ ( function @ SV523 ) )
= $true )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3326,plain,
! [SV625: $i,SV168: $i] :
( ( ! [SY1444: $i] :
( ~ ( function @ SY1444 )
| ~ ( relation @ SY1444 )
| ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SY1444 )
| ( SV625
= ( apply @ SY1444 @ SV168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3327,plain,
! [SV626: $i,SV168: $i] :
( ( ! [SY1445: $i] :
( ~ ( function @ SY1445 )
| ~ ( relation @ SY1445 )
| ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SY1445 )
| ( in @ SV168 @ ( relation_dom @ SY1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3328,plain,
! [SV169: $i] :
( ( ( ! [SY960: $i,SY961: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ~ ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY961 @ SY960 @ SV169 ) ) @ SY960 )
| ( in @ ( sK61_D @ SY961 @ SY960 @ SV169 ) @ SY961 ) ) ) )
| ( SY961
= ( relation_inverse_image @ SV169 @ SY960 ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3329,plain,
! [SV169: $i] :
( ( ( ! [SY962: $i,SY963: $i] :
( ( SY963
!= ( relation_inverse_image @ SV169 @ SY962 ) )
| ~ ( ~ ! [SY964: $i] :
( ~ ( in @ SY964 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY964 ) @ SY962 )
| ( in @ SY964 @ SY963 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY963 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SY963 )
| ( in @ ( apply @ SV169 @ SY966 ) @ SY962 ) ) ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3109]) ).
thf(3330,plain,
! [SV391: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV391 ) )
= $false )
| ( ( disjoint @ SV391 @ SV486 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3331,plain,
! [SV391: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV486 ) )
= $false )
| ( ( disjoint @ SV391 @ SV486 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3332,plain,
! [SV487: $i,SV392: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV392 ) )
= $true )
| ( ( ~ ( in @ SV578 @ SV487 ) )
= $true )
| ( ( ~ ( disjoint @ SV392 @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3333,plain,
! [SV170: $i] :
( ( ( ~ ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3334,plain,
! [SV170: $i] :
( ( ( ~ ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3335,plain,
! [SV488: $i,SV171: $i,SV524: $i] :
( ( ( relation @ SV524 )
= $false )
| ( ( ~ ( in @ SV171 @ SV488 )
| ~ ( in @ SV171 @ ( relation_dom @ SV524 ) )
| ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3336,plain,
! [SV627: $i,SV171: $i] :
( ( ! [SY1446: $i] :
( ~ ( relation @ SY1446 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY1446 @ SV627 ) ) )
| ( in @ SV171 @ SV627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3337,plain,
! [SV628: $i,SV171: $i] :
( ( ! [SY1447: $i] :
( ~ ( relation @ SY1447 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SY1447 @ SV628 ) ) )
| ( in @ SV171 @ ( relation_dom @ SY1447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3338,plain,
! [SV172: $i,SV397: $i] :
( ( ( ~ ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) ) )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3117]) ).
thf(3339,plain,
! [SV397: $i,SV172: $i] :
( ( ( ~ ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3117]) ).
thf(3340,plain,
! [SV173: $i,SV579: $i] :
( ( ( ~ ( ~ ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) ) ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3341,plain,
! [SV173: $i,SV580: $i] :
( ( ( ( SV580
!= ( relation_rng @ SV173 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) )
| ~ ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3342,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) ) ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3120]) ).
thf(3343,plain,
! [SV526: $i,SV288: $i,SV174: $i,SV582: $i] :
( ( ( ( SV582
!= ( unordered_triple @ SV174 @ SV288 @ SV526 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) )
| ~ ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3344,plain,
! [SV398: $i] :
( ( ( relation_empty_yielding @ SV398 )
= $false )
| ( ( relation @ SV398 )
= $false )
| ( ( ! [SY1238: $i] : ( relation @ ( relation_dom_restriction @ SV398 @ SY1238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3345,plain,
! [SV399: $i] :
( ( ( relation_empty_yielding @ SV399 )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( ! [SY1239: $i] : ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SY1239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3346,plain,
! [SV583: $i] :
( ( ( SV583 = empty_set )
= $true )
| ( ( ! [SY1397: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SY1397 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SY1397 @ SV583 ) @ ( sK52_SY636 @ SY1397 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1397 ) )
| ~ ( ! [SY1398: $i] :
( ~ ( in @ SY1398 @ SV583 )
| ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1398 ) )
| ( in @ ( sK51_C @ SY1397 @ SV583 ) @ SY1397 ) ) )
| ( SY1397
= ( set_meet @ SV583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3347,plain,
! [SV584: $i] :
( ( ( SV584 = empty_set )
= $true )
| ( ( ! [SY1399: $i] :
( ( SY1399
!= ( set_meet @ SV584 ) )
| ~ ( ~ ! [SY1400: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1400 @ SY1399 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1400 @ ( sK50_D @ SY1400 @ SY1399 @ SV584 ) ) )
| ( in @ SY1400 @ SY1399 ) )
| ~ ! [SY1401: $i] :
( ~ ( in @ SY1401 @ SY1399 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1401 @ SY1402 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3348,plain,
! [SV585: $i] :
( ( ( ( SV585 != empty_set ) )
= $true )
| ( ( ! [SY1403: $i] :
( ( SY1403
!= ( set_meet @ SV585 ) )
| ( SY1403 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3126]) ).
thf(3349,plain,
! [SV586: $i] :
( ( ( ( SV586 != empty_set ) )
= $true )
| ( ( ! [SY1404: $i] :
( ( SY1404 != empty_set )
| ( SY1404
= ( set_meet @ SV586 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3350,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) )
| ~ ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3351,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false )
| ( ( ~ ( ~ ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) )
| ~ ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3352,plain,
! [SV400: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3353,plain,
! [SV401: $i] :
( ( ( transitive @ SV401 )
= $false )
| ( ( ! [SY1240: $i,SY1241: $i,SY1242: $i] :
( ~ ( in @ ( ordered_pair @ SY1240 @ SY1241 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1241 @ SY1242 ) @ SV401 )
| ( in @ ( ordered_pair @ SY1240 @ SY1242 ) @ SV401 ) ) )
= $true )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3354,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3355,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3132]) ).
thf(3356,plain,
! [SV491: $i,SV404: $i] :
( ( ( subset @ SV404 @ SV491 )
= $false )
| ( ( ~ ( subset @ SV491 @ SV404 ) )
= $true )
| ( ( SV404 = SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3357,plain,
! [SV629: $i,SV587: $i] :
( ( ( SV587 != SV629 )
| ( subset @ SV587 @ SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3358,plain,
! [SV630: $i,SV588: $i] :
( ( ( SV588 != SV630 )
| ( subset @ SV630 @ SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3359,plain,
! [SV405: $i] :
( ( ( relation @ SV405 )
= $false )
| ( ( function @ SV405 )
= $false )
| ( ( function @ ( function_inverse @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3360,plain,
! [SV406: $i] :
( ( ( relation @ SV406 )
= $false )
| ( ( function @ SV406 )
= $false )
| ( ( relation @ ( function_inverse @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3361,plain,
! [SV492: $i,SV529: $i,SV177: $i] :
( ( ( ~ ( in @ SV177 @ SV529 ) )
= $true )
| ( ( ~ ( in @ SV492 @ SV529 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SV529 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3362,plain,
! [SV631: $i,SV177: $i] :
( ( ! [SY1448: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SV631 ) @ SY1448 )
| ( in @ SV177 @ SY1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3363,plain,
! [SV632: $i,SV177: $i] :
( ( ! [SY1449: $i] :
( ~ ( subset @ ( unordered_pair @ SV177 @ SV632 ) @ SY1449 )
| ( in @ SV632 @ SY1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3364,plain,
! [SV178: $i,SV290: $i] :
( ( ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3365,plain,
! [SV290: $i,SV178: $i] :
( ( ( ~ ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3142]) ).
thf(3366,plain,
! [SV291: $i,SV179: $i,SV633: $i] :
( ( ( ~ ( element @ SV633 @ ( powerset @ SV179 ) )
| ~ ( disjoint @ SV291 @ SV633 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SV633 ) ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3367,plain,
! [SV291: $i,SV179: $i,SV634: $i] :
( ( ( ~ ( element @ SV634 @ ( powerset @ SV179 ) )
| ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SV634 ) )
| ( disjoint @ SV291 @ SV634 ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3368,plain,
! [SV589: $i] :
( ( ( ~ ( empty @ SV589 ) )
= $true )
| ( ( epsilon_connected @ SV589 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3369,plain,
! [SV590: $i] :
( ( ( ~ ( empty @ SV590 ) )
= $true )
| ( ( epsilon_transitive @ SV590 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3370,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( relation @ SV591 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
| ( SV181 = SV591 ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3371,plain,
! [SV181: $i,SV592: $i] :
( ( ( ~ ( relation @ SV592 ) )
= $true )
| ( ( ( SV181 != SV592 )
| ~ ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3372,plain,
! [SV493: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 )
| ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3373,plain,
! [SV494: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 )
| ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3374,plain,
! [SV182: $i] :
( ( ( ! [SY1033: $i] :
( ~ ( ~ ( ! [SY1034: $i] :
( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ SY1034 ) )
| ~ ( in @ SY1034 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) )
| ~ ( ~ ( ( ( sK30_C @ SY1033 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SY1033 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SY1033 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SY1033 @ SV182 ) @ SY1033 ) ) )
| ( SY1033
= ( relation_rng @ SV182 ) ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3375,plain,
! [SV182: $i] :
( ( ( ! [SY1035: $i] :
( ( SY1035
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1036: $i] :
( ! [SY1037: $i] :
( ( SY1036
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1036 @ SY1035 ) )
| ~ ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SY1035 )
| ~ ( ( SY1038
!= ( apply @ SV182 @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1038 @ SY1035 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3152]) ).
thf(3376,plain,
! [SV183: $i] :
( ( ( subset @ ( sK111_B @ SV183 ) @ SV183 )
= $false )
| ( ( ordinal @ ( sK111_B @ SV183 ) )
= $false )
| ( ( ordinal @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3377,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3378,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3154]) ).
thf(3379,plain,
! [SV410: $i] :
( ( ( ~ ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3155]) ).
thf(3380,plain,
! [SV410: $i] :
( ( ( ~ ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3381,plain,
! [SV411: $i,SV635: $i,SV593: $i] :
( ( ( ( SV593 = SV635 )
| ~ ( in @ SV593 @ SV411 )
| ~ ( in @ SV635 @ SV411 )
| ( in @ SV593 @ SV635 )
| ( in @ SV635 @ SV593 ) )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3382,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( relation @ SV636 )
| ~ ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
| ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3383,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( ~ ( relation @ SV637 )
| ( SV637
!= ( relation_dom_restriction @ SV185 @ SV595 ) )
| ~ ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3384,plain,
! [SV596: $i] :
( ( ( ~ ( empty @ SV596 )
| ~ ( relation @ SV596 )
| ~ ( function @ SV596 ) )
= $true )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3385,plain,
! [SV597: $i] :
( ( ( ~ ( empty @ SV597 )
| ~ ( relation @ SV597 )
| ~ ( function @ SV597 ) )
= $true )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3161]) ).
thf(3386,plain,
! [SV414: $i] :
( ( ( empty @ SV414 )
= $false )
| ( ( ~ ( relation @ SV414 ) )
= $true )
| ( ( ~ ( function @ SV414 ) )
= $true )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3387,plain,
! [SV495: $i,SV186: $i,SV530: $i] :
( ( ( relation @ SV530 )
= $false )
| ( ( ~ ( in @ SV186 @ SV495 )
| ~ ( in @ SV186 @ ( relation_rng @ SV530 ) )
| ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3388,plain,
! [SV638: $i,SV186: $i] :
( ( ! [SY1456: $i] :
( ~ ( relation @ SY1456 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SY1456 ) ) )
| ( in @ SV186 @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3389,plain,
! [SV639: $i,SV186: $i] :
( ( ! [SY1457: $i] :
( ~ ( relation @ SY1457 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SY1457 ) ) )
| ( in @ SV186 @ ( relation_rng @ SY1457 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3390,plain,
! [SV496: $i,SV415: $i] :
( ( ( empty @ SV415 )
= $false )
| ( ( ~ ( relation @ SV496 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV415 @ SV496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3391,plain,
! [SV497: $i,SV416: $i] :
( ( ( empty @ SV416 )
= $false )
| ( ( ~ ( relation @ SV497 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV416 @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3392,plain,
! [SV498: $i,SV187: $i,SV531: $i] :
( ( ( relation @ SV531 )
= $false )
| ( ( ! [SY1349: $i] :
( ~ ( in @ SY1349 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SY1349 @ SV187 ) @ SV531 )
| ~ ( in @ SY1349 @ SV498 ) )
| ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3393,plain,
! [SV499: $i,SV187: $i,SV532: $i] :
( ( ( relation @ SV532 )
= $false )
| ( ( ~ ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3169]) ).
thf(3394,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( relation @ SV598 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
| ( subset @ SV188 @ SV598 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3395,plain,
! [SV188: $i,SV599: $i] :
( ( ( ~ ( relation @ SV599 ) )
= $true )
| ( ( ~ ( subset @ SV188 @ SV599 )
| ! [SY1420: $i,SY1421: $i] :
( ~ ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV599 ) ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3396,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ~ ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3397,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false )
| ( ( ~ ( ~ ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) )
| ~ ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3398,plain,
! [SV419: $i] :
( ( ( epsilon_transitive @ SV419 )
= $false )
| ( ( epsilon_connected @ SV419 )
= $false )
| ( ( ordinal @ SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3399,plain,
! [SV600: $i] :
( ( ( ~ ( ordinal @ SV600 ) )
= $true )
| ( ( epsilon_connected @ SV600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3400,plain,
! [SV601: $i] :
( ( ( ~ ( ordinal @ SV601 ) )
= $true )
| ( ( epsilon_transitive @ SV601 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3176]) ).
thf(3401,plain,
! [SV602: $i,SV293: $i,SV535: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ SV535 )
| ~ ( in @ SV293 @ SV602 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3402,plain,
! [SV293: $i,SV190: $i] :
( ( ! [SY1163: $i] :
( ! [SY1164: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1163 @ SY1164 ) )
| ( in @ SV190 @ SY1163 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3403,plain,
! [SV293: $i,SV190: $i] :
( ( ! [SY1165: $i,SY1166: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SY1165 @ SY1166 ) )
| ( in @ SV293 @ SY1166 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3404,plain,
( ( ~ ~ ( empty @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3405,plain,
( ( ~ ( epsilon_transitive @ sK5_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3406,plain,
! [SV420: $i] :
( ( ( relation @ SV420 )
= $false )
| ( ( function @ SV420 )
= $false )
| ( ( ! [SY1250: $i] : ( function @ ( relation_dom_restriction @ SV420 @ SY1250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3407,plain,
! [SV421: $i] :
( ( ( relation @ SV421 )
= $false )
| ( ( function @ SV421 )
= $false )
| ( ( ! [SY1251: $i] : ( relation @ ( relation_dom_restriction @ SV421 @ SY1251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3408,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ~ ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) ) )
| ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3409,plain,
! [SV604: $i,SV192: $i,SV641: $i] :
( ( ( ( SV641
!= ( relation_inverse_image @ SV192 @ SV604 ) )
| ~ ( ~ ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) )
| ~ ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3410,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3411,plain,
! [SV423: $i,SV503: $i] :
( ( ( ( SV503
!= ( identity_relation @ SV423 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) ) )
= $true )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3412,plain,
! [SV239: $i,SV68: $i,SV536: $i] :
( ( ( ~ ( function @ SV536 ) )
= $true )
| ( ( ~ ( relation @ SV536 ) )
= $true )
| ( ( ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) ) )
= $true )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3413,plain,
! [SV240: $i,SV69: $i,SV537: $i] :
( ( ( ~ ( function @ SV537 ) )
= $true )
| ( ( ~ ( relation @ SV537 ) )
= $true )
| ( ( ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3414,plain,
! [SV79: $i,SV304: $i,SV504: $i] :
( ( ( in @ SV504 @ SV304 )
= $true )
| ( ( in @ SV504 @ ( subset_complement @ SV79 @ SV304 ) )
= $true )
| ( ( element @ SV504 @ SV79 )
= $false )
| ( ( element @ SV304 @ ( powerset @ SV79 ) )
= $false )
| ( ( SV79 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3415,plain,
! [SV84: $i,SV306: $i,SV250: $i] :
( ( ( in @ SV250 @ ( relation_dom @ ( relation_dom_restriction @ SV306 @ SV84 ) ) )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV306 @ SV84 ) @ SV250 )
= ( apply @ SV306 @ SV250 ) )
= $true )
| ( ( function @ SV306 )
= $false )
| ( ( relation @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3416,plain,
! [SV307: $i,SV85: $i,SV251: $i] :
( ( ( in @ SV251 @ SV85 )
= $false )
| ( ( ( apply @ ( relation_dom_restriction @ SV307 @ SV85 ) @ SV251 )
= ( apply @ SV307 @ SV251 ) )
= $true )
| ( ( function @ SV307 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3417,plain,
! [SV538: $i,SV430: $i,SV329: $i] :
( ( ( disjoint @ SV329 @ SV430 )
= $false )
| ( ( in @ SV538 @ ( set_intersection2 @ SV329 @ SV430 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3418,plain,
! [SV330: $i,SV431: $i] :
( ( ( relation @ SV431 )
= $false )
| ( ( function @ SV431 )
= $false )
| ( ( function @ ( relation_rng_restriction @ SV330 @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3419,plain,
! [SV331: $i,SV432: $i] :
( ( ( relation @ SV432 )
= $false )
| ( ( function @ SV432 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV331 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3420,plain,
! [SV332: $i] :
( ( ( ~ ( one_to_one @ SV332 ) )
= $true )
| ( ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) )
= $true )
| ( ( function @ SV332 )
= $false )
| ( ( relation @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3421,plain,
! [SV333: $i] :
( ( ( ~ ( one_to_one @ SV333 ) )
= $true )
| ( ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) )
= $true )
| ( ( function @ SV333 )
= $false )
| ( ( relation @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3422,plain,
! [SV539: $i,SV642: $i] :
( ( ( ~ ( element @ SV642 @ SV539 )
| ( in @ SV642 @ SV539 ) )
= $true )
| ( ( empty @ SV539 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3423,plain,
! [SV540: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV540 )
| ( element @ SV643 @ SV540 ) )
= $true )
| ( ( empty @ SV540 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3424,plain,
! [SV541: $i] :
( ( ( empty @ SV541 )
= $false )
| ( ( ! [SY1356: $i] :
( ~ ( element @ SY1356 @ SV541 )
| ( empty @ SY1356 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3425,plain,
! [SV542: $i] :
( ( ( empty @ SV542 )
= $false )
| ( ( ! [SY1357: $i] :
( ~ ( empty @ SY1357 )
| ( element @ SY1357 @ SV542 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3426,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3427,plain,
! [SV544: $i,SV139: $i] :
( ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( ! [SY1358: $i,SY1359: $i] :
( ( SY1358 = SY1359 )
| ~ ( in @ SY1358 @ SV544 )
| ~ ( in @ SY1359 @ SV544 )
| ( in @ ( ordered_pair @ SY1358 @ SY1359 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1359 @ SY1358 ) @ SV139 ) ) )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3428,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ~ ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) ) ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3429,plain,
! [SV546: $i,SV140: $i,SV606: $i] :
( ( ( ( SV606
!= ( relation_image @ SV140 @ SV546 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) )
| ~ ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3430,plain,
! [SV334: $i] :
( ( ( relation @ SV334 )
= $false )
| ( ( function @ SV334 )
= $false )
| ( ( ~ ( one_to_one @ SV334 ) )
= $true )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3431,plain,
! [SV335: $i] :
( ( ( relation @ SV335 )
= $false )
| ( ( function @ SV335 )
= $false )
| ( ( ~ ( one_to_one @ SV335 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3432,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( ( ( sK36_C @ SV547 @ SV141 )
!= ( sK37_SY628 @ SV547 @ SV141 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3433,plain,
! [SV548: $i,SV141: $i] :
( ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( ! [SY1366: $i,SY1367: $i] :
( ~ ( in @ SY1366 @ SV548 )
| ~ ( in @ SY1367 @ SV548 )
| ~ ( in @ ( ordered_pair @ SY1366 @ SY1367 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY1367 @ SY1366 ) @ SV141 )
| ( SY1366 = SY1367 ) ) )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3434,plain,
! [SV644: $i,SV336: $i] :
( ( ( ! [SY1462: $i] :
( ( sK108_B @ SV336 )
!= ( ordered_pair @ SV644 @ SY1462 ) ) )
= $true )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3435,plain,
! [SV337: $i,SV549: $i] :
( ( ( in @ SV549 @ SV337 )
= $false )
| ( ( SV549
= ( ordered_pair @ ( sK106_C @ SV549 @ SV337 ) @ ( sK107_SY668 @ SV549 @ SV337 ) ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3436,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( relation @ SV607 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
| ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3437,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ( relation @ SV608 ) )
= $true )
| ( ( ( SV608
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3438,plain,
! [SV550: $i,SV283: $i,SV505: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV505 ) )
= $true )
| ( ( ~ ( in @ SV283 @ SV550 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3439,plain,
! [SV645: $i,SV283: $i,SV143: $i] :
( ( ! [SY1463: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV645 @ SY1463 ) )
| ( in @ SV143 @ SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3440,plain,
! [SV646: $i,SV283: $i,SV143: $i] :
( ( ! [SY1464: $i] :
( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV646 @ SY1464 ) )
| ( in @ SV283 @ SY1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3441,plain,
! [SV144: $i,SV609: $i] :
( ( ( ~ ( ~ ! [SY1438: $i] :
( ~ ( subset @ SY1438 @ SV609 )
| ( in @ SY1438 @ ( sK88_SY659 @ SV609 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) ) ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3442,plain,
! [SV144: $i] :
( ( ~ ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3230]) ).
thf(3443,plain,
! [SV144: $i] :
( ( ~ ( in @ SV144 @ ( sK87_B @ SV144 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3230]) ).
thf(3444,plain,
! [SV340: $i,SV434: $i] :
( ( ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV340 )
= $true )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3231]) ).
thf(3445,plain,
! [SV340: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 ) )
= $true )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3232]) ).
thf(3446,plain,
! [SV435: $i,SV341: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV341 ) )
= $true )
| ( ( in @ SV610 @ SV435 )
= $true )
| ( ( subset @ SV341 @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3447,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3448,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3449,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) )
| ~ ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3450,plain,
! [SV146: $i,SV551: $i] :
( ( ( ~ ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) ) )
= $false )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3451,plain,
! [SV146: $i,SV552: $i] :
( ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( ~ ( ~ ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) )
| ~ ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3452,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK53_C @ SV553 @ SV147 ) @ SV553 )
| ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 ) )
= $false )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3453,plain,
! [SV554: $i,SV147: $i] :
( ( ( is_reflexive_in @ SV147 @ SV554 )
= $false )
| ( ( ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV554 )
| ( in @ ( ordered_pair @ SY1372 @ SY1372 ) @ SV147 ) ) )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3454,plain,
! [SV342: $i,SV438: $i] :
( ( ( relation @ SV438 )
= $false )
| ( ( function @ SV438 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 )
| ( SV438
= ( identity_relation @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3455,plain,
! [SV555: $i,SV611: $i] :
( ( ( ~ ( function @ SV611 )
| ~ ( relation @ SV611 ) )
= $true )
| ( ( ( SV611
!= ( identity_relation @ SV555 ) )
| ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3241]) ).
thf(3456,plain,
! [SV556: $i,SV612: $i] :
( ( ( ~ ( function @ SV612 )
| ~ ( relation @ SV612 ) )
= $true )
| ( ( ( SV612
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SV612 )
= SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3457,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3458,plain,
! [SV558: $i,SV149: $i] :
( ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( ! [SY1376: $i,SY1377: $i,SY1378: $i] :
( ~ ( in @ SY1376 @ SV558 )
| ~ ( in @ SY1377 @ SV558 )
| ~ ( in @ SY1378 @ SV558 )
| ~ ( in @ ( ordered_pair @ SY1376 @ SY1377 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY1377 @ SY1378 ) @ SV149 )
| ( in @ ( ordered_pair @ SY1376 @ SY1378 ) @ SV149 ) ) )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3459,plain,
! [SV151: $i,SV559: $i] :
( ( ( relation @ SV559 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
| ( SV559
= ( relation_inverse @ SV151 ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3460,plain,
! [SV151: $i,SV560: $i] :
( ( ( relation @ SV560 )
= $false )
| ( ( ( SV560
!= ( relation_inverse @ SV151 ) )
| ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) ) )
= $true )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3461,plain,
! [SV152: $i,SV284: $i] :
( ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV284 )
= $false )
| ( ( in @ ( sK4_C @ SV284 @ SV152 ) @ SV152 )
= $false )
| ( ( SV152 = SV284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3462,plain,
! [SV349: $i,SV447: $i] :
( ( ( relation @ SV447 )
= $false )
| ( ( empty @ SV349 )
= $false )
| ( ( empty @ ( relation_composition @ SV447 @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3463,plain,
! [SV350: $i,SV448: $i] :
( ( ( relation @ SV448 )
= $false )
| ( ( empty @ SV350 )
= $false )
| ( ( relation @ ( relation_composition @ SV448 @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3464,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ( ~ ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) )
| ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) ) )
= $false )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3465,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) ) )
= $false )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3253]) ).
thf(3466,plain,
! [SV509: $i,SV450: $i,SV153: $i] :
( ( ( ~ ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) )
| ~ ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3467,plain,
! [SV562: $i] :
( ( ( SV562 = empty_set )
= $false )
| ( ( ! [SY1383: $i] : ( subset @ SV562 @ ( singleton @ SY1383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3468,plain,
! [SV615: $i,SV563: $i] :
( ( ( ( SV563
!= ( singleton @ SV615 ) ) )
= $true )
| ( ( subset @ SV563 @ ( singleton @ SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3469,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3259]) ).
thf(3470,plain,
! [SV356: $i,SV454: $i] :
( ( ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
| ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3471,plain,
! [SV357: $i,SV455: $i] :
( ( ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) ) )
= $false )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3472,plain,
! [SV455: $i,SV357: $i] :
( ( ( ~ ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) )
= $false )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3473,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)],[3262]) ).
thf(3474,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3263]) ).
thf(3475,plain,
! [SV358: $i,SV456: $i] :
( ( ( ordinal @ SV456 )
= $false )
| ( ( ordinal @ SV358 )
= $false )
| ( ( ~ ( ordinal_subset @ SV358 @ SV456 )
| ( subset @ SV358 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3476,plain,
! [SV359: $i,SV457: $i] :
( ( ( ordinal @ SV457 )
= $false )
| ( ( ordinal @ SV359 )
= $false )
| ( ( ~ ( subset @ SV359 @ SV457 )
| ( ordinal_subset @ SV359 @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3477,plain,
! [SV360: $i,SV458: $i] :
( ( ( relation @ SV458 )
= $false )
| ( ( function @ SV458 )
= $false )
| ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 )
| ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3478,plain,
! [SV361: $i,SV459: $i] :
( ( ( relation @ SV459 )
= $false )
| ( ( function @ SV459 )
= $false )
| ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 )
| ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3479,plain,
! [SV647: $i,SV154: $i] :
( ( ( ! [SY1465: $i] :
( ~ ( ~ ( ! [SY1466: $i] :
( ~ ( in @ SY1466 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1466 @ SV647 )
| ( ( sK63_D @ SY1465 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1466 ) ) )
| ~ ( in @ ( sK63_D @ SY1465 @ SV647 @ SV154 ) @ SY1465 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SY1465 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SY1465 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SY1465 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SY1465 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SY1465 @ SV647 @ SV154 ) @ SY1465 ) ) )
| ( SY1465
= ( relation_image @ SV154 @ SV647 ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3480,plain,
! [SV648: $i,SV154: $i] :
( ( ( ! [SY1467: $i] :
( ( SY1467
!= ( relation_image @ SV154 @ SV648 ) )
| ~ ( ~ ! [SY1468: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1468
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1468 @ SY1467 ) )
| ~ ! [SY1470: $i] :
( ~ ( in @ SY1470 @ SY1467 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1470 @ SY1467 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1470 @ SY1467 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1470
!= ( apply @ SV154 @ ( sK62_E @ SY1470 @ SY1467 @ SV648 @ SV154 ) ) ) ) ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3481,plain,
! [SV364: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3482,plain,
! [SV365: $i] :
( ( ( ~ ( one_to_one @ SV365 ) )
= $true )
| ( ( ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3483,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3484,plain,
! [SV368: $i] :
( ( ( ~ ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3485,plain,
! [SV369: $i,SV649: $i] :
( ( ( ! [SY1471: $i] :
( ~ ( in @ ( ordered_pair @ SV649 @ SY1471 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SY1471 @ SV649 ) @ SV369 )
| ( SV649 = SY1471 ) ) )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3486,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3276]) ).
thf(3487,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3276]) ).
thf(3488,plain,
! [SV511: $i,SV463: $i,SV155: $i] :
( ( ( ~ ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) )
| ~ ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3489,plain,
! [SV370: $i,SV464: $i] :
( ( ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) )
| ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3278]) ).
thf(3490,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
| ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3279]) ).
thf(3491,plain,
! [SV465: $i,SV371: $i] :
( ( ( ~ ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) ) )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3492,plain,
! [SV371: $i,SV465: $i] :
( ( ( ~ ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3493,plain,
! [SV285: $i,SV512: $i,SV156: $i,SV564: $i] :
( ( ( relation @ SV564 )
= $false )
| ( ( ~ ( in @ SV156 @ SV512 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3494,plain,
! [SV650: $i,SV285: $i,SV156: $i] :
( ( ! [SY1472: $i] :
( ~ ( relation @ SY1472 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SY1472 ) )
| ( in @ SV156 @ SV650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3495,plain,
! [SV651: $i,SV285: $i,SV156: $i] :
( ( ! [SY1473: $i] :
( ~ ( relation @ SY1473 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SY1473 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SY1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3496,plain,
! [SV372: $i,SV466: $i] :
( ( ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 )
| ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3497,plain,
! [SV372: $i,SV466: $i] :
( ( ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
| ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3285]) ).
thf(3498,plain,
! [SV467: $i,SV373: $i] :
( ( ( ~ ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) ) )
= $false )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3499,plain,
! [SV373: $i,SV467: $i] :
( ( ( ~ ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) )
= $false )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3500,plain,
! [SV565: $i] :
( ( ( ordinal @ SV565 )
= $false )
| ( ( epsilon_connected @ ( union @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3501,plain,
! [SV566: $i] :
( ( ( ordinal @ SV566 )
= $false )
| ( ( epsilon_transitive @ ( union @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3502,plain,
! [SV157: $i] :
( ( ( ~ ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3289]) ).
thf(3503,plain,
! [SV157: $i] :
( ( ( ~ ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3289]) ).
thf(3504,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3290]) ).
thf(3505,plain,
( ( epsilon_transitive @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3291]) ).
thf(3506,plain,
! [SV158: $i,SV567: $i] :
( ( ( ordinal @ SV567 )
= $false )
| ( ( ~ ( in @ SV158 @ SV567 )
| ( ordinal_subset @ ( succ @ SV158 ) @ SV567 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3507,plain,
! [SV158: $i,SV568: $i] :
( ( ( ordinal @ SV568 )
= $false )
| ( ( ~ ( ordinal_subset @ ( succ @ SV158 ) @ SV568 )
| ( in @ SV158 @ SV568 ) )
= $true )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3508,plain,
! [SV470: $i,SV159: $i,SV513: $i] :
( ( ( ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SY1337 ) @ SV513 )
| ~ ( in @ SY1337 @ SV470 ) ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3509,plain,
! [SV471: $i,SV514: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) ) )
= $true )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3295]) ).
thf(3510,plain,
! [SV160: $i,SV569: $i] :
( ( ( relation @ SV569 )
= $false )
| ( ( ~ ( subset @ SV160 @ SV569 )
| ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SV569 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3511,plain,
! [SV160: $i,SV570: $i] :
( ( ( relation @ SV570 )
= $false )
| ( ( ~ ( subset @ SV160 @ SV570 )
| ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SV570 ) ) )
= $true )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3512,plain,
! [SV616: $i,SV571: $i] :
( ( ( ~ ( proper_subset @ SV571 @ SV616 ) )
= $true )
| ( ( ( SV571 != SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3513,plain,
! [SV617: $i,SV572: $i] :
( ( ( ~ ( proper_subset @ SV572 @ SV617 ) )
= $true )
| ( ( subset @ SV572 @ SV617 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3514,plain,
! [SV573: $i] :
( ( ( SV573 = empty_set )
= $false )
| ( ( ! [SY1387: $i] : ( subset @ SV573 @ ( singleton @ SY1387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3304]) ).
thf(3515,plain,
! [SV618: $i,SV574: $i] :
( ( ( ( SV574
!= ( singleton @ SV618 ) ) )
= $true )
| ( ( subset @ SV574 @ ( singleton @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3516,plain,
! [SV476: $i,SV515: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV515 )
| ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) ) )
= $true )
| ( ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3517,plain,
! [SV619: $i,SV161: $i,SV652: $i] :
( ( ~ ( relation @ SV652 )
| ~ ( in @ SV161 @ ( relation_restriction @ SV652 @ SV619 ) )
| ( in @ SV161 @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3518,plain,
! [SV620: $i,SV161: $i,SV653: $i] :
( ( ~ ( relation @ SV653 )
| ~ ( in @ SV161 @ ( relation_restriction @ SV653 @ SV620 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3519,plain,
! [SV516: $i,SV477: $i,SV162: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SV516 ) )
= $true )
| ( ( in @ SV162 @ ( relation_field @ SV516 ) )
= $true )
| ( ( relation @ SV516 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3520,plain,
! [SV517: $i,SV478: $i,SV162: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SV517 ) )
= $true )
| ( ( in @ SV478 @ ( relation_field @ SV517 ) )
= $true )
| ( ( relation @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3310]) ).
thf(3521,plain,
! [SV621: $i,SV518: $i,SV286: $i,SV163: $i] :
( ( ( ( ordered_pair @ SV163 @ SV286 )
= ( ordered_pair @ SV518 @ SV621 ) )
= $false )
| ( ( SV163 = SV518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3522,plain,
! [SV575: $i,SV519: $i,SV286: $i,SV163: $i] :
( ( ( ( ordered_pair @ SV163 @ SV286 )
= ( ordered_pair @ SV519 @ SV575 ) )
= $false )
| ( ( SV286 = SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3523,plain,
! [SV164: $i,SV481: $i,SV520: $i] :
( ( ( function @ SV520 )
= $false )
| ( ( ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3524,plain,
! [SV164: $i,SV622: $i,SV654: $i] :
( ( ~ ( function @ SV654 )
| ~ ( relation @ SV654 )
| ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3525,plain,
! [SV164: $i,SV623: $i,SV655: $i] :
( ( ~ ( function @ SV655 )
| ~ ( relation @ SV655 )
| ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3526,plain,
! [SV165: $i,SV287: $i,SV576: $i] :
( ( ( in @ SV576 @ SV287 )
= $false )
| ( ( ~ ( in @ SV576 @ ( sK3_C @ SV287 @ SV165 ) ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3527,plain,
! [SV521: $i,SV482: $i,SV166: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SV521 ) )
= $true )
| ( ( in @ SV166 @ ( relation_dom @ SV521 ) )
= $true )
| ( ( relation @ SV521 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3317]) ).
thf(3528,plain,
! [SV522: $i,SV483: $i,SV166: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SV522 ) )
= $true )
| ( ( in @ SV483 @ ( relation_rng @ SV522 ) )
= $true )
| ( ( relation @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3529,plain,
! [SV167: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ ( sK80_B @ SV167 ) ) )
= $true )
| ( ( in @ ( powerset @ SV624 ) @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3320]) ).
thf(3530,plain,
! [SV167: $i] :
( ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3321]) ).
thf(3531,plain,
! [SV167: $i] :
( ( ~ ( in @ SV167 @ ( sK80_B @ SV167 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3321]) ).
thf(3532,plain,
! [SV389: $i] :
( ( ( subset @ ( sK104_B @ SV389 ) @ SV389 )
= $false )
| ( ( epsilon_transitive @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3533,plain,
! [SV390: $i,SV577: $i] :
( ( ( in @ SV577 @ SV390 )
= $false )
| ( ( subset @ SV577 @ SV390 )
= $true )
| ( ( epsilon_transitive @ SV390 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3534,plain,
! [SV168: $i,SV485: $i,SV523: $i] :
( ( ( function @ SV523 )
= $false )
| ( ( ~ ( relation @ SV523 ) )
= $true )
| ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3535,plain,
! [SV625: $i,SV168: $i,SV656: $i] :
( ( ~ ( function @ SV656 )
| ~ ( relation @ SV656 )
| ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
| ( SV625
= ( apply @ SV656 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3536,plain,
! [SV626: $i,SV168: $i,SV657: $i] :
( ( ~ ( function @ SV657 )
| ~ ( relation @ SV657 )
| ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
| ( in @ SV168 @ ( relation_dom @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(3537,plain,
! [SV169: $i,SV658: $i] :
( ( ( ! [SY1474: $i] :
( ~ ( ~ ( ~ ( in @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) @ SY1474 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) @ SY1474 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SY1474 @ SV658 @ SV169 ) @ SY1474 ) ) ) )
| ( SY1474
= ( relation_inverse_image @ SV169 @ SV658 ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(3538,plain,
! [SV659: $i,SV169: $i] :
( ( ( ! [SY1475: $i] :
( ( SY1475
!= ( relation_inverse_image @ SV169 @ SV659 ) )
| ~ ( ~ ! [SY1476: $i] :
( ~ ( in @ SY1476 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1476 ) @ SV659 )
| ( in @ SY1476 @ SY1475 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ~ ( in @ SY965 @ SY1475 )
| ( in @ SY965 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1478: $i] :
( ~ ( in @ SY1478 @ SY1475 )
| ( in @ ( apply @ SV169 @ SY1478 ) @ SV659 ) ) ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3539,plain,
! [SV391: $i,SV486: $i] :
( ( ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV391 )
= $true )
| ( ( disjoint @ SV391 @ SV486 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3540,plain,
! [SV391: $i,SV486: $i] :
( ( ( in @ ( sK75_C @ SV486 @ SV391 ) @ SV486 )
= $true )
| ( ( disjoint @ SV391 @ SV486 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3331]) ).
thf(3541,plain,
! [SV487: $i,SV392: $i,SV578: $i] :
( ( ( in @ SV578 @ SV392 )
= $false )
| ( ( ~ ( in @ SV578 @ SV487 ) )
= $true )
| ( ( ~ ( disjoint @ SV392 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3542,plain,
! [SV170: $i] :
( ( ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) )
| ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3543,plain,
! [SV170: $i] :
( ( ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) )
| ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3544,plain,
! [SV524: $i,SV488: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV488 )
| ~ ( in @ SV171 @ ( relation_dom @ SV524 ) ) )
= $true )
| ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) )
= $true )
| ( ( relation @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3545,plain,
! [SV627: $i,SV171: $i,SV660: $i] :
( ( ~ ( relation @ SV660 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV660 @ SV627 ) ) )
| ( in @ SV171 @ SV627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3546,plain,
! [SV628: $i,SV171: $i,SV661: $i] :
( ( ~ ( relation @ SV661 )
| ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV661 @ SV628 ) ) )
| ( in @ SV171 @ ( relation_dom @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3547,plain,
! [SV172: $i,SV397: $i] :
( ( ( ! [SY1230: $i] :
( ~ ( relation @ SY1230 )
| ~ ( ~ ( ! [SY1231: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ SY1231 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1231 @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SY1230 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SY1230 @ SV397 @ SV172 ) ) @ SY1230 ) ) )
| ( SY1230
= ( relation_composition @ SV172 @ SV397 ) ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3338]) ).
thf(3548,plain,
! [SV397: $i,SV172: $i] :
( ( ( ! [SY1232: $i] :
( ~ ( relation @ SY1232 )
| ( SY1232
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1233: $i,SY1234: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1233 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1234 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1233 @ SY1234 ) @ SY1232 ) )
| ~ ! [SY1236: $i,SY1237: $i] :
( ~ ( in @ ( ordered_pair @ SY1236 @ SY1237 ) @ SY1232 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1236 @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1237 @ SY1236 @ SY1232 @ SV397 @ SV172 ) @ SY1237 ) @ SV397 ) ) ) ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3339]) ).
thf(3549,plain,
! [SV173: $i,SV579: $i] :
( ( ( ~ ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) ) )
= $false )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3550,plain,
! [SV173: $i,SV580: $i] :
( ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( ~ ( ~ ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) )
| ~ ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3551,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
| ~ ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3552,plain,
! [SV526: $i,SV288: $i,SV174: $i,SV582: $i] :
( ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) )
| ~ ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3553,plain,
! [SV662: $i,SV398: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV398 @ SV662 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation_empty_yielding @ SV398 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3554,plain,
! [SV663: $i,SV399: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV399 @ SV663 ) )
= $true )
| ( ( relation @ SV399 )
= $false )
| ( ( relation_empty_yielding @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3555,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
| ~ ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) ) )
| ( SV664
= ( set_meet @ SV583 ) ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3556,plain,
! [SV584: $i,SV665: $i] :
( ( ( ( SV665
!= ( set_meet @ SV584 ) )
| ~ ( ~ ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) )
| ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) ) )
= $true )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3557,plain,
! [SV585: $i] :
( ( ( SV585 = empty_set )
= $false )
| ( ( ! [SY1403: $i] :
( ( SY1403
!= ( set_meet @ SV585 ) )
| ( SY1403 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3558,plain,
! [SV586: $i] :
( ( ( SV586 = empty_set )
= $false )
| ( ( ! [SY1404: $i] :
( ( SY1404 != empty_set )
| ( SY1404
= ( set_meet @ SV586 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3559,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3350]) ).
thf(3560,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3350]) ).
thf(3561,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( ~ ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) )
| ~ ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3562,plain,
! [SV400: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3352]) ).
thf(3563,plain,
! [SV400: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3352]) ).
thf(3564,plain,
! [SV401: $i,SV666: $i] :
( ( ( ! [SY1483: $i,SY1484: $i] :
( ~ ( in @ ( ordered_pair @ SV666 @ SY1483 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SY1483 @ SY1484 ) @ SV401 )
| ( in @ ( ordered_pair @ SV666 @ SY1484 ) @ SV401 ) ) )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3565,plain,
! [SV289: $i,SV176: $i] :
( ( ( ! [SY1151: $i] :
( ~ ( function @ SY1151 )
| ~ ( relation @ SY1151 )
| ~ ( in @ SV176 @ ( relation_dom @ SY1151 ) )
| ~ ( in @ ( apply @ SY1151 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1151 @ SV289 ) ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3354]) ).
thf(3566,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3567,plain,
! [SV404: $i,SV491: $i] :
( ( ( subset @ SV491 @ SV404 )
= $false )
| ( ( subset @ SV404 @ SV491 )
= $false )
| ( ( SV404 = SV491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3568,plain,
! [SV629: $i,SV587: $i] :
( ( ( ( SV587 != SV629 ) )
= $true )
| ( ( subset @ SV587 @ SV629 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3569,plain,
! [SV630: $i,SV588: $i] :
( ( ( ( SV588 != SV630 ) )
= $true )
| ( ( subset @ SV630 @ SV588 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3570,plain,
! [SV492: $i,SV529: $i,SV177: $i] :
( ( ( in @ SV177 @ SV529 )
= $false )
| ( ( ~ ( in @ SV492 @ SV529 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SV529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3571,plain,
! [SV667: $i,SV631: $i,SV177: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV177 @ SV631 ) @ SV667 )
| ( in @ SV177 @ SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3572,plain,
! [SV668: $i,SV632: $i,SV177: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV177 @ SV632 ) @ SV668 )
| ( in @ SV632 @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3573,plain,
! [SV290: $i,SV178: $i] :
( ( ( SV178 = empty_set )
= $true )
| ( ( ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3574,plain,
! [SV290: $i,SV178: $i] :
( ( ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) )
| ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3365]) ).
thf(3575,plain,
! [SV291: $i,SV179: $i,SV633: $i] :
( ( ( ~ ( element @ SV633 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV291 @ SV633 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SV633 ) ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3576,plain,
! [SV291: $i,SV179: $i,SV634: $i] :
( ( ( ~ ( element @ SV634 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SV634 ) )
| ( disjoint @ SV291 @ SV634 ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3577,plain,
! [SV589: $i] :
( ( ( empty @ SV589 )
= $false )
| ( ( epsilon_connected @ SV589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3578,plain,
! [SV590: $i] :
( ( ( empty @ SV590 )
= $false )
| ( ( epsilon_transitive @ SV590 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3579,plain,
! [SV181: $i,SV591: $i] :
( ( ( relation @ SV591 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
| ( SV181 = SV591 ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3580,plain,
! [SV181: $i,SV592: $i] :
( ( ( relation @ SV592 )
= $false )
| ( ( ( SV181 != SV592 )
| ~ ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3581,plain,
! [SV493: $i,SV408: $i] :
( ( ( ~ ( function @ SV408 ) )
= $true )
| ( ( ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3582,plain,
! [SV494: $i,SV409: $i] :
( ( ( ~ ( function @ SV409 ) )
= $true )
| ( ( ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3583,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ~ ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
| ~ ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) ) )
| ( SV669
= ( relation_rng @ SV182 ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3584,plain,
! [SV182: $i,SV670: $i] :
( ( ( ( SV670
!= ( relation_rng @ SV182 ) )
| ~ ( ~ ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) )
| ~ ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3585,plain,
! [SV184: $i,SV292: $i] :
( ( ( ! [SY1157: $i] :
( ~ ( function @ SY1157 )
| ~ ( relation @ SY1157 )
| ~ ( ~ ( in @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) )
!= ( apply @ SY1157 @ ( sK69_D @ SY1157 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SY1157 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SY1157 @ SV184 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3377]) ).
thf(3586,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3378]) ).
thf(3587,plain,
! [SV410: $i] :
( ( ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3588,plain,
! [SV410: $i] :
( ( ( in @ ( sK40_SY629 @ SV410 ) @ ( sK39_B @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3589,plain,
! [SV411: $i,SV635: $i,SV593: $i] :
( ( ( ( SV593 = SV635 )
| ~ ( in @ SV593 @ SV411 )
| ~ ( in @ SV635 @ SV411 )
| ( in @ SV593 @ SV635 ) )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3590,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( relation @ SV636 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
| ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3591,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( ~ ( relation @ SV637 ) )
= $true )
| ( ( ( SV637
!= ( relation_dom_restriction @ SV185 @ SV595 ) )
| ~ ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3592,plain,
! [SV596: $i] :
( ( ( ~ ( empty @ SV596 )
| ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( function @ SV596 ) )
= $true )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3593,plain,
! [SV597: $i] :
( ( ( ~ ( empty @ SV597 )
| ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( function @ SV597 ) )
= $true )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3594,plain,
! [SV414: $i] :
( ( ( relation @ SV414 )
= $false )
| ( ( empty @ SV414 )
= $false )
| ( ( ~ ( function @ SV414 ) )
= $true )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3595,plain,
! [SV530: $i,SV495: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV495 )
| ~ ( in @ SV186 @ ( relation_rng @ SV530 ) ) )
= $true )
| ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) )
= $true )
| ( ( relation @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3596,plain,
! [SV638: $i,SV186: $i,SV671: $i] :
( ( ~ ( relation @ SV671 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SV671 ) ) )
| ( in @ SV186 @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3597,plain,
! [SV639: $i,SV186: $i,SV672: $i] :
( ( ~ ( relation @ SV672 )
| ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SV672 ) ) )
| ( in @ SV186 @ ( relation_rng @ SV672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3598,plain,
! [SV415: $i,SV496: $i] :
( ( ( relation @ SV496 )
= $false )
| ( ( empty @ SV415 )
= $false )
| ( ( empty @ ( relation_composition @ SV415 @ SV496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3599,plain,
! [SV416: $i,SV497: $i] :
( ( ( relation @ SV497 )
= $false )
| ( ( empty @ SV416 )
= $false )
| ( ( relation @ ( relation_composition @ SV416 @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3600,plain,
! [SV498: $i,SV187: $i,SV531: $i] :
( ( ( ! [SY1349: $i] :
( ~ ( in @ SY1349 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SY1349 @ SV187 ) @ SV531 )
| ~ ( in @ SY1349 @ SV498 ) ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3601,plain,
! [SV499: $i,SV532: $i,SV187: $i] :
( ( ( ~ ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) ) )
= $true )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3602,plain,
! [SV188: $i,SV598: $i] :
( ( ( relation @ SV598 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
| ( subset @ SV188 @ SV598 ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3603,plain,
! [SV188: $i,SV599: $i] :
( ( ( relation @ SV599 )
= $false )
| ( ( ~ ( subset @ SV188 @ SV599 )
| ! [SY1420: $i,SY1421: $i] :
( ~ ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV599 ) ) )
= $true )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3604,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3396]) ).
thf(3605,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3396]) ).
thf(3606,plain,
! [SV534: $i,SV501: $i,SV189: $i] :
( ( ( ~ ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) )
| ~ ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3607,plain,
! [SV600: $i] :
( ( ( ordinal @ SV600 )
= $false )
| ( ( epsilon_connected @ SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3608,plain,
! [SV601: $i] :
( ( ( ordinal @ SV601 )
= $false )
| ( ( epsilon_transitive @ SV601 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3609,plain,
! [SV602: $i,SV293: $i,SV535: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ SV535 ) )
= $true )
| ( ( ~ ( in @ SV293 @ SV602 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3401]) ).
thf(3610,plain,
! [SV673: $i,SV293: $i,SV190: $i] :
( ( ! [SY1489: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV673 @ SY1489 ) )
| ( in @ SV190 @ SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3611,plain,
! [SV674: $i,SV293: $i,SV190: $i] :
( ( ! [SY1490: $i] :
( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV674 @ SY1490 ) )
| ( in @ SV293 @ SY1490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3612,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3613,plain,
( ( epsilon_transitive @ sK5_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3405]) ).
thf(3614,plain,
! [SV675: $i,SV420: $i] :
( ( ( function @ ( relation_dom_restriction @ SV420 @ SV675 ) )
= $true )
| ( ( function @ SV420 )
= $false )
| ( ( relation @ SV420 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3615,plain,
! [SV676: $i,SV421: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV421 @ SV676 ) )
= $true )
| ( ( function @ SV421 )
= $false )
| ( ( relation @ SV421 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3616,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ~ ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) ) ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3617,plain,
! [SV604: $i,SV192: $i,SV641: $i] :
( ( ( ( SV641
!= ( relation_inverse_image @ SV192 @ SV604 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) )
| ~ ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3618,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3619,plain,
! [SV423: $i,SV503: $i] :
( ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( ~ ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) ) )
= $true )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3620,plain,
! [SV239: $i,SV68: $i,SV536: $i] :
( ( ( function @ SV536 )
= $false )
| ( ( ~ ( relation @ SV536 ) )
= $true )
| ( ( ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) ) )
= $true )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3621,plain,
! [SV240: $i,SV69: $i,SV537: $i] :
( ( ( function @ SV537 )
= $false )
| ( ( ~ ( relation @ SV537 ) )
= $true )
| ( ( ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3622,plain,
! [SV332: $i] :
( ( ( one_to_one @ SV332 )
= $false )
| ( ( ( relation_rng @ SV332 )
= ( relation_dom @ ( function_inverse @ SV332 ) ) )
= $true )
| ( ( function @ SV332 )
= $false )
| ( ( relation @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3420]) ).
thf(3623,plain,
! [SV333: $i] :
( ( ( one_to_one @ SV333 )
= $false )
| ( ( ( relation_dom @ SV333 )
= ( relation_rng @ ( function_inverse @ SV333 ) ) )
= $true )
| ( ( function @ SV333 )
= $false )
| ( ( relation @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3624,plain,
! [SV539: $i,SV642: $i] :
( ( ( ~ ( element @ SV642 @ SV539 ) )
= $true )
| ( ( in @ SV642 @ SV539 )
= $true )
| ( ( empty @ SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(3625,plain,
! [SV540: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV540 ) )
= $true )
| ( ( element @ SV643 @ SV540 )
= $true )
| ( ( empty @ SV540 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(3626,plain,
! [SV541: $i,SV677: $i] :
( ( ( ~ ( element @ SV677 @ SV541 )
| ( empty @ SV677 ) )
= $true )
| ( ( empty @ SV541 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3627,plain,
! [SV542: $i,SV678: $i] :
( ( ( ~ ( empty @ SV678 )
| ( element @ SV678 @ SV542 ) )
= $true )
| ( ( empty @ SV542 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3628,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3629,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3630,plain,
! [SV139: $i,SV544: $i,SV679: $i] :
( ( ( ! [SY1491: $i] :
( ( SV679 = SY1491 )
| ~ ( in @ SV679 @ SV544 )
| ~ ( in @ SY1491 @ SV544 )
| ( in @ ( ordered_pair @ SV679 @ SY1491 ) @ SV139 )
| ( in @ ( ordered_pair @ SY1491 @ SV679 ) @ SV139 ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3631,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) ) )
= $false )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3428]) ).
thf(3632,plain,
! [SV546: $i,SV140: $i,SV606: $i] :
( ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( ~ ( ~ ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) )
| ~ ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3633,plain,
! [SV334: $i] :
( ( ( one_to_one @ SV334 )
= $false )
| ( ( function @ SV334 )
= $false )
| ( ( relation @ SV334 )
= $false )
| ( ( function @ ( relation_inverse @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3634,plain,
! [SV335: $i] :
( ( ( one_to_one @ SV335 )
= $false )
| ( ( function @ SV335 )
= $false )
| ( ( relation @ SV335 )
= $false )
| ( ( relation @ ( relation_inverse @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3635,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3636,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ( ( sK36_C @ SV547 @ SV141 )
!= ( sK37_SY628 @ SV547 @ SV141 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3637,plain,
! [SV141: $i,SV548: $i,SV680: $i] :
( ( ( ! [SY1492: $i] :
( ~ ( in @ SV680 @ SV548 )
| ~ ( in @ SY1492 @ SV548 )
| ~ ( in @ ( ordered_pair @ SV680 @ SY1492 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SY1492 @ SV680 ) @ SV141 )
| ( SV680 = SY1492 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3638,plain,
! [SV681: $i,SV644: $i,SV336: $i] :
( ( ( ( ( sK108_B @ SV336 )
!= ( ordered_pair @ SV644 @ SV681 ) ) )
= $true )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3639,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( relation @ SV607 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
| ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3640,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( relation @ SV608 )
= $false )
| ( ( ( SV608
!= ( relation_rng_restriction @ SV142 @ SV282 ) )
| ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) ) )
= $true )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3641,plain,
! [SV550: $i,SV283: $i,SV505: $i,SV143: $i] :
( ( ( in @ SV143 @ SV505 )
= $false )
| ( ( ~ ( in @ SV283 @ SV550 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3642,plain,
! [SV645: $i,SV283: $i,SV143: $i] :
( ( ( ! [SY1463: $i] :
~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV645 @ SY1463 ) ) )
= $true )
| ( ( in @ SV143 @ SV645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(3643,plain,
! [SV682: $i,SV646: $i,SV283: $i,SV143: $i] :
( ( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV646 @ SV682 ) )
| ( in @ SV283 @ SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3644,plain,
! [SV144: $i,SV609: $i] :
( ( ( ~ ! [SY1438: $i] :
( ~ ( subset @ SY1438 @ SV609 )
| ( in @ SY1438 @ ( sK88_SY659 @ SV609 @ SV144 ) ) )
| ~ ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
= $false )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3441]) ).
thf(3645,plain,
! [SV144: $i] :
( ( ! [SY837: $i,SY838: $i] :
( ~ ( in @ SY837 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY838 @ SY837 )
| ( in @ SY838 @ ( sK87_B @ SV144 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3442]) ).
thf(3646,plain,
! [SV144: $i] :
( ( in @ SV144 @ ( sK87_B @ SV144 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3647,plain,
! [SV340: $i,SV434: $i] :
( ( ( in @ ( sK99_C @ SV434 @ SV340 ) @ SV434 )
= $false )
| ( ( subset @ SV340 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3648,plain,
! [SV435: $i,SV341: $i,SV610: $i] :
( ( ( in @ SV610 @ SV341 )
= $false )
| ( ( in @ SV610 @ SV435 )
= $true )
| ( ( subset @ SV341 @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3649,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3447]) ).
thf(3650,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3651,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3449]) ).
thf(3652,plain,
! [SV437: $i,SV507: $i,SV145: $i] :
( ( ( ~ ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3449]) ).
thf(3653,plain,
! [SV146: $i,SV551: $i] :
( ( ( ~ ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) ) )
= $false )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3450]) ).
thf(3654,plain,
! [SV146: $i,SV551: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) ) )
= $false )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3450]) ).
thf(3655,plain,
! [SV552: $i,SV146: $i] :
( ( ( ~ ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) )
| ~ ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) )
= $false )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3656,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK53_C @ SV553 @ SV147 ) @ SV553 ) )
= $false )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3452]) ).
thf(3657,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 ) )
= $false )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3452]) ).
thf(3658,plain,
! [SV147: $i,SV554: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV554 )
| ( in @ ( ordered_pair @ SV683 @ SV683 ) @ SV147 ) )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV554 )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3659,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
| ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3454]) ).
thf(3660,plain,
! [SV555: $i,SV611: $i] :
( ( ( ~ ( function @ SV611 ) )
= $true )
| ( ( ~ ( relation @ SV611 ) )
= $true )
| ( ( ( SV611
!= ( identity_relation @ SV555 ) )
| ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3661,plain,
! [SV556: $i,SV612: $i] :
( ( ( ~ ( function @ SV612 ) )
= $true )
| ( ( ~ ( relation @ SV612 ) )
= $true )
| ( ( ( SV612
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SV612 )
= SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3662,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3663,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3664,plain,
! [SV149: $i,SV558: $i,SV684: $i] :
( ( ( ! [SY1493: $i,SY1494: $i] :
( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SY1493 @ SV558 )
| ~ ( in @ SY1494 @ SV558 )
| ~ ( in @ ( ordered_pair @ SV684 @ SY1493 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SY1493 @ SY1494 ) @ SV149 )
| ( in @ ( ordered_pair @ SV684 @ SY1494 ) @ SV149 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3665,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) ) )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3666,plain,
! [SV151: $i,SV560: $i] :
( ( ( ( SV560
!= ( relation_inverse @ SV151 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) ) )
= $true )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3460]) ).
thf(3667,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) )
| ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3464]) ).
thf(3668,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
| ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3465]) ).
thf(3669,plain,
! [SV509: $i,SV450: $i,SV153: $i] :
( ( ( ~ ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) ) )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3466]) ).
thf(3670,plain,
! [SV153: $i,SV450: $i,SV509: $i] :
( ( ( ~ ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3466]) ).
thf(3671,plain,
! [SV685: $i,SV562: $i] :
( ( ( subset @ SV562 @ ( singleton @ SV685 ) )
= $true )
| ( ( SV562 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3672,plain,
! [SV615: $i,SV563: $i] :
( ( ( SV563
= ( singleton @ SV615 ) )
= $false )
| ( ( subset @ SV563 @ ( singleton @ SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3673,plain,
! [SV356: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 ) )
= $true )
| ( ( ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(3674,plain,
! [SV356: $i,SV454: $i] :
( ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
= $true )
| ( ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3675,plain,
! [SV357: $i,SV455: $i] :
( ( ( ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV455 )
| ( subset @ SY1277 @ SV357 ) ) )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3471]) ).
thf(3676,plain,
! [SV455: $i,SV357: $i] :
( ( ( ! [SY1278: $i] :
( ~ ( subset @ SY1278 @ SV357 )
| ( in @ SY1278 @ SV455 ) ) )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3472]) ).
thf(3677,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)],[3473]) ).
thf(3678,plain,
! [SV456: $i,SV358: $i] :
( ( ( ~ ( ordinal_subset @ SV358 @ SV456 ) )
= $true )
| ( ( subset @ SV358 @ SV456 )
= $true )
| ( ( ordinal @ SV358 )
= $false )
| ( ( ordinal @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(3679,plain,
! [SV457: $i,SV359: $i] :
( ( ( ~ ( subset @ SV359 @ SV457 ) )
= $true )
| ( ( ordinal_subset @ SV359 @ SV457 )
= $true )
| ( ( ordinal @ SV359 )
= $false )
| ( ( ordinal @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3476]) ).
thf(3680,plain,
! [SV458: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) )
| ~ ( one_to_one @ SV458 ) )
= $true )
| ( ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) )
= $true )
| ( ( function @ SV458 )
= $false )
| ( ( relation @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3477]) ).
thf(3681,plain,
! [SV459: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) )
| ~ ( one_to_one @ SV459 ) )
= $true )
| ( ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) )
= $true )
| ( ( function @ SV459 )
= $false )
| ( ( relation @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3478]) ).
thf(3682,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ~ ( ~ ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) )
| ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) ) )
| ( SV686
= ( relation_image @ SV154 @ SV647 ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3683,plain,
! [SV648: $i,SV154: $i,SV687: $i] :
( ( ( ( SV687
!= ( relation_image @ SV154 @ SV648 ) )
| ~ ( ~ ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) )
| ~ ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(3684,plain,
! [SV364: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
| ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3685,plain,
! [SV365: $i] :
( ( ( one_to_one @ SV365 )
= $false )
| ( ( ! [SY1202: $i,SY1203: $i] :
( ~ ( in @ SY1202 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1203 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SY1202 )
!= ( apply @ SV365 @ SY1203 ) )
| ( SY1202 = SY1203 ) ) )
= $true )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3686,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) ) )
= $true )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3483]) ).
thf(3687,plain,
! [SV368: $i] :
( ( ( ( ( sK82_B @ SV368 )
!= ( sK83_SY653 @ SV368 ) ) )
= $true )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3484]) ).
thf(3688,plain,
! [SV369: $i,SV688: $i,SV649: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV649 @ SV688 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SV688 @ SV649 ) @ SV369 )
| ( SV649 = SV688 ) )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(3689,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3486]) ).
thf(3690,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3691,plain,
! [SV511: $i,SV463: $i,SV155: $i] :
( ( ( ~ ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3488]) ).
thf(3692,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ~ ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3488]) ).
thf(3693,plain,
! [SV370: $i,SV464: $i] :
( ( ( ! [SY1284: $i] :
( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SY1284 )
| ~ ( in @ SY1284 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(3694,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) ) )
= $true )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(3695,plain,
! [SV465: $i,SV371: $i] :
( ( ( ! [SY1285: $i] :
( ! [SY1212: $i] :
( ~ ( in @ SY1285 @ SY1212 )
| ~ ( in @ SY1212 @ SV371 ) )
| ( in @ SY1285 @ SV465 ) ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3491]) ).
thf(3696,plain,
! [SV371: $i,SV465: $i] :
( ( ( ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SV465 )
| ~ ( ~ ( in @ SY1287 @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SY1287 @ SV465 @ SV371 ) @ SV371 ) ) ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3492]) ).
thf(3697,plain,
! [SV564: $i,SV285: $i,SV512: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV512 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) )
= $true )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3698,plain,
! [SV650: $i,SV285: $i,SV156: $i,SV689: $i] :
( ( ~ ( relation @ SV689 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SV689 ) )
| ( in @ SV156 @ SV650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(3699,plain,
! [SV651: $i,SV285: $i,SV156: $i,SV690: $i] :
( ( ~ ( relation @ SV690 )
| ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SV690 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3700,plain,
! [SV372: $i,SV466: $i] :
( ( ( ( ( sK49_C @ SV466 @ SV372 )
!= SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(3701,plain,
! [SV372: $i,SV466: $i] :
( ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
= $true )
| ( ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(3702,plain,
! [SV467: $i,SV373: $i] :
( ( ( ! [SY1288: $i] :
( ( SY1288 != SV373 )
| ( in @ SY1288 @ SV467 ) ) )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3498]) ).
thf(3703,plain,
! [SV373: $i,SV467: $i] :
( ( ( ! [SY1289: $i] :
( ~ ( in @ SY1289 @ SV467 )
| ( SY1289 = SV373 ) ) )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3499]) ).
thf(3704,plain,
! [SV157: $i] :
( ( ( ! [SY903: $i] :
( ~ ( function @ SY903 )
| ~ ( relation @ SY903 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SY903 @ SV157 )
= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SY903 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SY903 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SY903 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SY903 @ SV157 )
!= ( apply @ SY903 @ ( sK72_C @ SY903 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SY903 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SY903 )
!= ( relation_rng @ SV157 ) )
| ( SY903
= ( function_inverse @ SV157 ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3502]) ).
thf(3705,plain,
! [SV157: $i] :
( ( ( ~ ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3706,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
| ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3707,plain,
! [SV567: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV567 ) )
= $true )
| ( ( ordinal_subset @ ( succ @ SV158 ) @ SV567 )
= $true )
| ( ( ordinal @ SV567 )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3708,plain,
! [SV568: $i,SV158: $i] :
( ( ( ~ ( ordinal_subset @ ( succ @ SV158 ) @ SV568 ) )
= $true )
| ( ( in @ SV158 @ SV568 )
= $true )
| ( ( ordinal @ SV568 )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(3709,plain,
! [SV470: $i,SV159: $i,SV513: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 )
| ~ ( in @ SV691 @ SV470 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3710,plain,
! [SV471: $i,SV514: $i,SV159: $i] :
( ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) ) )
= $true )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3509]) ).
thf(3711,plain,
! [SV569: $i,SV160: $i] :
( ( ( ~ ( subset @ SV160 @ SV569 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SV569 ) )
= $true )
| ( ( relation @ SV569 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(3712,plain,
! [SV570: $i,SV160: $i] :
( ( ( ~ ( subset @ SV160 @ SV570 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SV570 ) )
= $true )
| ( ( relation @ SV570 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3713,plain,
! [SV616: $i,SV571: $i] :
( ( ( proper_subset @ SV571 @ SV616 )
= $false )
| ( ( ( SV571 != SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(3714,plain,
! [SV617: $i,SV572: $i] :
( ( ( proper_subset @ SV572 @ SV617 )
= $false )
| ( ( subset @ SV572 @ SV617 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3715,plain,
! [SV692: $i,SV573: $i] :
( ( ( subset @ SV573 @ ( singleton @ SV692 ) )
= $true )
| ( ( SV573 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(3716,plain,
! [SV618: $i,SV574: $i] :
( ( ( SV574
= ( singleton @ SV618 ) )
= $false )
| ( ( subset @ SV574 @ ( singleton @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3515]) ).
thf(3717,plain,
! [SV476: $i,SV515: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV515 ) )
= $true )
| ( ( ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) ) )
= $true )
| ( ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3718,plain,
! [SV619: $i,SV161: $i,SV652: $i] :
( ( ( ~ ( relation @ SV652 ) )
= $true )
| ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV652 @ SV619 ) )
| ( in @ SV161 @ SV652 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3719,plain,
! [SV620: $i,SV161: $i,SV653: $i] :
( ( ( ~ ( relation @ SV653 ) )
= $true )
| ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV653 @ SV620 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3720,plain,
! [SV516: $i,SV477: $i,SV162: $i] :
( ( ( in @ ( ordered_pair @ SV162 @ SV477 ) @ SV516 )
= $false )
| ( ( in @ SV162 @ ( relation_field @ SV516 ) )
= $true )
| ( ( relation @ SV516 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3721,plain,
! [SV517: $i,SV478: $i,SV162: $i] :
( ( ( in @ ( ordered_pair @ SV162 @ SV478 ) @ SV517 )
= $false )
| ( ( in @ SV478 @ ( relation_field @ SV517 ) )
= $true )
| ( ( relation @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3722,plain,
! [SV164: $i,SV481: $i,SV520: $i] :
( ( ( relation @ SV520 )
= $false )
| ( ( function @ SV520 )
= $false )
| ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 )
| ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3723,plain,
! [SV164: $i,SV622: $i,SV654: $i] :
( ( ( ~ ( function @ SV654 )
| ~ ( relation @ SV654 ) )
= $true )
| ( ( ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SV654 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3524]) ).
thf(3724,plain,
! [SV164: $i,SV623: $i,SV655: $i] :
( ( ( ~ ( function @ SV655 )
| ~ ( relation @ SV655 ) )
= $true )
| ( ( ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(3725,plain,
! [SV165: $i,SV287: $i,SV576: $i] :
( ( ( in @ SV576 @ ( sK3_C @ SV287 @ SV165 ) )
= $false )
| ( ( in @ SV576 @ SV287 )
= $false )
| ( ( ~ ( in @ SV165 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3526]) ).
thf(3726,plain,
! [SV521: $i,SV482: $i,SV166: $i] :
( ( ( in @ ( ordered_pair @ SV166 @ SV482 ) @ SV521 )
= $false )
| ( ( in @ SV166 @ ( relation_dom @ SV521 ) )
= $true )
| ( ( relation @ SV521 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3527]) ).
thf(3727,plain,
! [SV522: $i,SV483: $i,SV166: $i] :
( ( ( in @ ( ordered_pair @ SV166 @ SV483 ) @ SV522 )
= $false )
| ( ( in @ SV483 @ ( relation_rng @ SV522 ) )
= $true )
| ( ( relation @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3728,plain,
! [SV167: $i,SV624: $i] :
( ( ( in @ SV624 @ ( sK80_B @ SV167 ) )
= $false )
| ( ( in @ ( powerset @ SV624 ) @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3729,plain,
! [SV167: $i] :
( ( ! [SY952: $i,SY953: $i] :
( ~ ( in @ SY952 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY953 @ SY952 )
| ( in @ SY953 @ ( sK80_B @ SV167 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3530]) ).
thf(3730,plain,
! [SV167: $i] :
( ( in @ SV167 @ ( sK80_B @ SV167 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3731,plain,
! [SV168: $i,SV485: $i,SV523: $i] :
( ( ( relation @ SV523 )
= $false )
| ( ( function @ SV523 )
= $false )
| ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) )
| ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3732,plain,
! [SV625: $i,SV168: $i,SV656: $i] :
( ( ( ~ ( function @ SV656 )
| ~ ( relation @ SV656 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
| ( SV625
= ( apply @ SV656 @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(3733,plain,
! [SV626: $i,SV168: $i,SV657: $i] :
( ( ( ~ ( function @ SV657 )
| ~ ( relation @ SV657 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
| ( in @ SV168 @ ( relation_dom @ SV657 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(3734,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) ) )
| ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3735,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ( SV694
!= ( relation_inverse_image @ SV169 @ SV659 ) )
| ~ ( ~ ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) )
| ~ ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(3736,plain,
! [SV392: $i,SV487: $i,SV578: $i] :
( ( ( in @ SV578 @ SV487 )
= $false )
| ( ( in @ SV578 @ SV392 )
= $false )
| ( ( ~ ( disjoint @ SV392 @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3737,plain,
! [SV170: $i] :
( ( ( ~ ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3738,plain,
! [SV170: $i] :
( ( ( ~ ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3739,plain,
! [SV170: $i] :
( ( ( ~ ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3543]) ).
thf(3740,plain,
! [SV170: $i] :
( ( ( ~ ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3543]) ).
thf(3741,plain,
! [SV524: $i,SV488: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ SV488 ) )
= $true )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ SV524 ) ) )
= $true )
| ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) )
= $true )
| ( ( relation @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3742,plain,
! [SV627: $i,SV171: $i,SV660: $i] :
( ( ( ~ ( relation @ SV660 ) )
= $true )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV660 @ SV627 ) ) )
| ( in @ SV171 @ SV627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(3743,plain,
! [SV628: $i,SV171: $i,SV661: $i] :
( ( ( ~ ( relation @ SV661 ) )
= $true )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV661 @ SV628 ) ) )
| ( in @ SV171 @ ( relation_dom @ SV661 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3546]) ).
thf(3744,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( relation @ SV695 )
| ~ ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
| ( SV695
= ( relation_composition @ SV172 @ SV397 ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3745,plain,
! [SV397: $i,SV172: $i,SV696: $i] :
( ( ( ~ ( relation @ SV696 )
| ( SV696
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(3746,plain,
! [SV173: $i,SV579: $i] :
( ( ( ~ ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) ) )
= $false )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3747,plain,
! [SV173: $i,SV579: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) ) )
= $false )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3748,plain,
! [SV580: $i,SV173: $i] :
( ( ( ~ ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) )
| ~ ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) )
= $false )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3749,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3750,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3751,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) )
| ~ ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3752,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
| ~ ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) ) ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3753,plain,
! [SV584: $i,SV665: $i] :
( ( ( ( SV665
!= ( set_meet @ SV584 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) )
| ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) ) )
= $true )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(3754,plain,
! [SV585: $i,SV697: $i] :
( ( ( ( SV697
!= ( set_meet @ SV585 ) )
| ( SV697 = empty_set ) )
= $true )
| ( ( SV585 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(3755,plain,
! [SV586: $i,SV698: $i] :
( ( ( ( SV698 != empty_set )
| ( SV698
= ( set_meet @ SV586 ) ) )
= $true )
| ( ( SV586 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(3756,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3559]) ).
thf(3757,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3560]) ).
thf(3758,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( ~ ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3759,plain,
! [SV490: $i,SV528: $i,SV175: $i] :
( ( ( ~ ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3760,plain,
! [SV400: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) ) )
= $true )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3562]) ).
thf(3761,plain,
! [SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
= $true )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3563]) ).
thf(3762,plain,
! [SV401: $i,SV699: $i,SV666: $i] :
( ( ( ! [SY1508: $i] :
( ~ ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SV699 @ SY1508 ) @ SV401 )
| ( in @ ( ordered_pair @ SV666 @ SY1508 ) @ SV401 ) ) )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(3763,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( ~ ( function @ SV700 )
| ~ ( relation @ SV700 )
| ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(3764,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) )
| ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3566]) ).
thf(3765,plain,
! [SV629: $i,SV587: $i] :
( ( ( SV587 = SV629 )
= $false )
| ( ( subset @ SV587 @ SV629 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3568]) ).
thf(3766,plain,
! [SV630: $i,SV588: $i] :
( ( ( SV588 = SV630 )
= $false )
| ( ( subset @ SV630 @ SV588 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3569]) ).
thf(3767,plain,
! [SV177: $i,SV529: $i,SV492: $i] :
( ( ( in @ SV492 @ SV529 )
= $false )
| ( ( in @ SV177 @ SV529 )
= $false )
| ( ( subset @ ( unordered_pair @ SV177 @ SV492 ) @ SV529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3768,plain,
! [SV667: $i,SV631: $i,SV177: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV177 @ SV631 ) @ SV667 ) )
= $true )
| ( ( in @ SV177 @ SV667 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(3769,plain,
! [SV668: $i,SV632: $i,SV177: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV177 @ SV632 ) @ SV668 ) )
= $true )
| ( ( in @ SV632 @ SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(3770,plain,
! [SV290: $i,SV178: $i] :
( ( ( subset @ SV178 @ SV290 )
= $false )
| ( ( SV178 = empty_set )
= $true )
| ( ( ordinal @ ( sK77_C @ SV290 @ SV178 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3573]) ).
thf(3771,plain,
! [SV290: $i,SV178: $i] :
( ( ( ~ ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3772,plain,
! [SV178: $i,SV290: $i] :
( ( ( ~ ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 ) )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3773,plain,
! [SV291: $i,SV179: $i,SV633: $i] :
( ( ( element @ SV633 @ ( powerset @ SV179 ) )
= $false )
| ( ( ~ ( disjoint @ SV291 @ SV633 )
| ( subset @ SV291 @ ( subset_complement @ SV179 @ SV633 ) ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3575]) ).
thf(3774,plain,
! [SV291: $i,SV179: $i,SV634: $i] :
( ( ( element @ SV634 @ ( powerset @ SV179 ) )
= $false )
| ( ( ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SV634 ) )
| ( disjoint @ SV291 @ SV634 ) )
= $true )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3775,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) ) )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(3776,plain,
! [SV592: $i,SV181: $i] :
( ( ( ( SV181 != SV592 ) )
= $true )
| ( ( ~ ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3777,plain,
! [SV493: $i,SV408: $i] :
( ( ( function @ SV408 )
= $false )
| ( ( ~ ( relation @ SV408 ) )
= $true )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3581]) ).
thf(3778,plain,
! [SV494: $i,SV409: $i] :
( ( ( function @ SV409 )
= $false )
| ( ( ~ ( relation @ SV409 ) )
= $true )
| ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3779,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ~ ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
| ~ ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) ) ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3780,plain,
! [SV182: $i,SV670: $i] :
( ( ( ( SV670
!= ( relation_rng @ SV182 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) )
| ~ ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(3781,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( function @ SV701 )
| ~ ( relation @ SV701 )
| ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3782,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) )
| ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3783,plain,
! [SV410: $i] :
( ( ( ~ ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3587]) ).
thf(3784,plain,
! [SV410: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3587]) ).
thf(3785,plain,
! [SV411: $i,SV635: $i,SV593: $i] :
( ( ( SV593 = SV635 )
= $true )
| ( ( ~ ( in @ SV593 @ SV411 )
| ~ ( in @ SV635 @ SV411 )
| ( in @ SV593 @ SV635 ) )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3786,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( relation @ SV636 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
| ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3787,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( relation @ SV637 )
= $false )
| ( ( ( SV637
!= ( relation_dom_restriction @ SV185 @ SV595 ) )
| ~ ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) ) )
= $true )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3788,plain,
! [SV596: $i] :
( ( ( ~ ( empty @ SV596 ) )
= $true )
| ( ( ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( function @ SV596 ) )
= $true )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3592]) ).
thf(3789,plain,
! [SV597: $i] :
( ( ( ~ ( empty @ SV597 ) )
= $true )
| ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( function @ SV597 ) )
= $true )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(3790,plain,
! [SV414: $i] :
( ( ( function @ SV414 )
= $false )
| ( ( empty @ SV414 )
= $false )
| ( ( relation @ SV414 )
= $false )
| ( ( one_to_one @ SV414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3791,plain,
! [SV530: $i,SV495: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV495 ) )
= $true )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ SV530 ) ) )
= $true )
| ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) )
= $true )
| ( ( relation @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3792,plain,
! [SV638: $i,SV186: $i,SV671: $i] :
( ( ( ~ ( relation @ SV671 ) )
= $true )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SV671 ) ) )
| ( in @ SV186 @ SV638 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(3793,plain,
! [SV639: $i,SV186: $i,SV672: $i] :
( ( ( ~ ( relation @ SV672 ) )
= $true )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SV672 ) ) )
| ( in @ SV186 @ ( relation_rng @ SV672 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(3794,plain,
! [SV498: $i,SV187: $i,SV531: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 )
| ~ ( in @ SV702 @ SV498 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(3795,plain,
! [SV499: $i,SV532: $i,SV187: $i] :
( ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) ) )
= $true )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3601]) ).
thf(3796,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) ) )
= $true )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(3797,plain,
! [SV599: $i,SV188: $i] :
( ( ( ~ ( subset @ SV188 @ SV599 ) )
= $true )
| ( ( ! [SY1420: $i,SY1421: $i] :
( ~ ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV599 ) ) )
= $true )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3798,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(3799,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3800,plain,
! [SV534: $i,SV501: $i,SV189: $i] :
( ( ( ~ ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3606]) ).
thf(3801,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ~ ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3606]) ).
thf(3802,plain,
! [SV602: $i,SV293: $i,SV535: $i,SV190: $i] :
( ( ( in @ SV190 @ SV535 )
= $false )
| ( ( ~ ( in @ SV293 @ SV602 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3803,plain,
! [SV673: $i,SV293: $i,SV190: $i] :
( ( ( ! [SY1489: $i] :
~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV673 @ SY1489 ) ) )
= $true )
| ( ( in @ SV190 @ SV673 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3610]) ).
thf(3804,plain,
! [SV703: $i,SV674: $i,SV293: $i,SV190: $i] :
( ( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV674 @ SV703 ) )
| ( in @ SV293 @ SV703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(3805,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3806,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) ) )
= $false )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(3807,plain,
! [SV604: $i,SV192: $i,SV641: $i] :
( ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( ~ ( ~ ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) )
| ~ ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3617]) ).
thf(3808,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3618]) ).
thf(3809,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3618]) ).
thf(3810,plain,
! [SV503: $i,SV423: $i] :
( ( ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) )
| ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3811,plain,
! [SV239: $i,SV68: $i,SV536: $i] :
( ( ( relation @ SV536 )
= $false )
| ( ( function @ SV536 )
= $false )
| ( ( ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
| ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) ) )
= $true )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3620]) ).
thf(3812,plain,
! [SV240: $i,SV69: $i,SV537: $i] :
( ( ( relation @ SV537 )
= $false )
| ( ( function @ SV537 )
= $false )
| ( ( ~ ( in @ SV69 @ ( relation_dom @ SV240 ) )
| ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) ) )
= $true )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3813,plain,
! [SV539: $i,SV642: $i] :
( ( ( element @ SV642 @ SV539 )
= $false )
| ( ( in @ SV642 @ SV539 )
= $true )
| ( ( empty @ SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3814,plain,
! [SV540: $i,SV643: $i] :
( ( ( in @ SV643 @ SV540 )
= $false )
| ( ( element @ SV643 @ SV540 )
= $true )
| ( ( empty @ SV540 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3815,plain,
! [SV541: $i,SV677: $i] :
( ( ( ~ ( element @ SV677 @ SV541 ) )
= $true )
| ( ( empty @ SV677 )
= $true )
| ( ( empty @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3816,plain,
! [SV542: $i,SV678: $i] :
( ( ( ~ ( empty @ SV678 ) )
= $true )
| ( ( element @ SV678 @ SV542 )
= $true )
| ( ( empty @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(3817,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3628]) ).
thf(3818,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3629]) ).
thf(3819,plain,
! [SV139: $i,SV544: $i,SV704: $i,SV679: $i] :
( ( ( ( SV679 = SV704 )
| ~ ( in @ SV679 @ SV544 )
| ~ ( in @ SV704 @ SV544 )
| ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
| ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3820,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) ) )
= $false )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3821,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) ) )
= $false )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3822,plain,
! [SV606: $i,SV546: $i,SV140: $i] :
( ( ( ~ ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) )
| ~ ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(3823,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3635]) ).
thf(3824,plain,
! [SV141: $i,SV547: $i] :
( ( ( ( ( sK36_C @ SV547 @ SV141 )
!= ( sK37_SY628 @ SV547 @ SV141 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(3825,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV548 )
| ~ ( in @ SV705 @ SV548 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 )
| ( SV680 = SV705 ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(3826,plain,
! [SV681: $i,SV644: $i,SV336: $i] :
( ( ( ( sK108_B @ SV336 )
= ( ordered_pair @ SV644 @ SV681 ) )
= $false )
| ( ( relation @ SV336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3638]) ).
thf(3827,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(3828,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ( SV608
!= ( relation_rng_restriction @ SV142 @ SV282 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) ) )
= $true )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(3829,plain,
! [SV505: $i,SV143: $i,SV550: $i,SV283: $i] :
( ( ( in @ SV283 @ SV550 )
= $false )
| ( ( in @ SV143 @ SV505 )
= $false )
| ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV505 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(3830,plain,
! [SV706: $i,SV645: $i,SV283: $i,SV143: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV645 @ SV706 ) ) )
= $true )
| ( ( in @ SV143 @ SV645 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(3831,plain,
! [SV682: $i,SV646: $i,SV283: $i,SV143: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV646 @ SV682 ) ) )
= $true )
| ( ( in @ SV283 @ SV682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3832,plain,
! [SV144: $i,SV609: $i] :
( ( ( ~ ! [SY1438: $i] :
( ~ ( subset @ SY1438 @ SV609 )
| ( in @ SY1438 @ ( sK88_SY659 @ SV609 @ SV144 ) ) ) )
= $false )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3644]) ).
thf(3833,plain,
! [SV144: $i,SV609: $i] :
( ( ( ~ ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) ) )
= $false )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3644]) ).
thf(3834,plain,
! [SV144: $i,SV707: $i] :
( ( ! [SY1509: $i] :
( ~ ( in @ SV707 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SY1509 @ SV707 )
| ( in @ SY1509 @ ( sK87_B @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(3835,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
| ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(3836,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $true )
| ( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
| ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(3837,plain,
! [SV437: $i,SV145: $i,SV507: $i] :
( ( ( ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV507 )
| ( in @ SY1324 @ SV145 )
| ( in @ SY1324 @ SV437 ) ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3651]) ).
thf(3838,plain,
! [SV437: $i,SV507: $i,SV145: $i] :
( ( ( ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3652]) ).
thf(3839,plain,
! [SV146: $i,SV551: $i] :
( ( ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 )
| ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(3840,plain,
! [SV146: $i,SV551: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
| ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(3841,plain,
! [SV552: $i,SV146: $i] :
( ( ( ~ ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) ) )
= $false )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3655]) ).
thf(3842,plain,
! [SV146: $i,SV552: $i] :
( ( ( ~ ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) )
= $false )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3655]) ).
thf(3843,plain,
! [SV147: $i,SV553: $i] :
( ( ( in @ ( sK53_C @ SV553 @ SV147 ) @ SV553 )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3656]) ).
thf(3844,plain,
! [SV147: $i,SV553: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 ) )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3657]) ).
thf(3845,plain,
! [SV147: $i,SV554: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV554 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV683 @ SV683 ) @ SV147 )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV554 )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3658]) ).
thf(3846,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3659]) ).
thf(3847,plain,
! [SV555: $i,SV611: $i] :
( ( ( function @ SV611 )
= $false )
| ( ( ~ ( relation @ SV611 ) )
= $true )
| ( ( ( SV611
!= ( identity_relation @ SV555 ) )
| ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3848,plain,
! [SV556: $i,SV612: $i] :
( ( ( function @ SV612 )
= $false )
| ( ( ~ ( relation @ SV612 ) )
= $true )
| ( ( ( SV612
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SV612 )
= SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(3849,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3662]) ).
thf(3850,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3663]) ).
thf(3851,plain,
! [SV149: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ! [SY1510: $i] :
( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 )
| ~ ( in @ SY1510 @ SV558 )
| ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SV708 @ SY1510 ) @ SV149 )
| ( in @ ( ordered_pair @ SV684 @ SY1510 ) @ SV149 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(3852,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
= $false )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3853,plain,
! [SV151: $i,SV560: $i] :
( ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( ~ ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) ) )
= $true )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3666]) ).
thf(3854,plain,
! [SV508: $i,SV449: $i,SV153: $i] :
( ( ( ! [SY1327: $i,SY1328: $i] :
( ~ ( in @ SY1327 @ SV153 )
| ~ ( in @ SY1328 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SY1327 @ SY1328 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3667]) ).
thf(3855,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) ) )
= $true )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3856,plain,
! [SV509: $i,SV450: $i,SV153: $i] :
( ( ( ! [SY1329: $i] :
( ! [SY1274: $i,SY1275: $i] :
( ~ ( in @ SY1274 @ SV153 )
| ~ ( in @ SY1275 @ SV450 )
| ( SY1329
!= ( ordered_pair @ SY1274 @ SY1275 ) ) )
| ( in @ SY1329 @ SV509 ) ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(3857,plain,
! [SV153: $i,SV450: $i,SV509: $i] :
( ( ( ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SY1332
!= ( ordered_pair @ ( sK41_E @ SY1332 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SY1332 @ SV509 @ SV450 @ SV153 ) ) ) ) ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(3858,plain,
! [SV356: $i,SV454: $i] :
( ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
= $false )
| ( ( ~ ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 ) )
= $true )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(3859,plain,
! [SV357: $i,SV455: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV455 )
| ( subset @ SV709 @ SV357 ) )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(3860,plain,
! [SV455: $i,SV357: $i,SV710: $i] :
( ( ( ~ ( subset @ SV710 @ SV357 )
| ( in @ SV710 @ SV455 ) )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(3861,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3677]) ).
thf(3862,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3677]) ).
thf(3863,plain,
! [SV456: $i,SV358: $i] :
( ( ( ordinal_subset @ SV358 @ SV456 )
= $false )
| ( ( subset @ SV358 @ SV456 )
= $true )
| ( ( ordinal @ SV358 )
= $false )
| ( ( ordinal @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3864,plain,
! [SV457: $i,SV359: $i] :
( ( ( subset @ SV359 @ SV457 )
= $false )
| ( ( ordinal_subset @ SV359 @ SV457 )
= $true )
| ( ( ordinal @ SV359 )
= $false )
| ( ( ordinal @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3865,plain,
! [SV458: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( relation_rng @ SV458 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV458 ) )
= $true )
| ( ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) )
= $true )
| ( ( function @ SV458 )
= $false )
| ( ( relation @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3866,plain,
! [SV459: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ ( relation_rng @ SV459 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV459 ) )
= $true )
| ( ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) )
= $true )
| ( ( function @ SV459 )
= $false )
| ( ( relation @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3867,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ~ ( ~ ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) )
| ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) ) ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3868,plain,
! [SV648: $i,SV154: $i,SV687: $i] :
( ( ( ( SV687
!= ( relation_image @ SV154 @ SV648 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) )
| ~ ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3869,plain,
! [SV364: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3684]) ).
thf(3870,plain,
! [SV364: $i] :
( ( ( ~ ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3684]) ).
thf(3871,plain,
! [SV365: $i,SV711: $i] :
( ( ( ! [SY1511: $i] :
( ~ ( in @ SV711 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SY1511 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SY1511 ) )
| ( SV711 = SY1511 ) ) )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(3872,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
| ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(3873,plain,
! [SV368: $i] :
( ( ( ( sK82_B @ SV368 )
= ( sK83_SY653 @ SV368 ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(3874,plain,
! [SV369: $i,SV688: $i,SV649: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV649 @ SV688 ) @ SV369 )
| ~ ( in @ ( ordered_pair @ SV688 @ SV649 ) @ SV369 ) )
= $true )
| ( ( SV649 = SV688 )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3875,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 ) )
= $true )
| ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(3876,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
| ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(3877,plain,
! [SV511: $i,SV463: $i,SV155: $i] :
( ( ( ! [SY1333: $i] :
( ~ ( in @ SY1333 @ SV155 )
| ( in @ SY1333 @ SV463 )
| ( in @ SY1333 @ SV511 ) ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3691]) ).
thf(3878,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ~ ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3692]) ).
thf(3879,plain,
! [SV712: $i,SV370: $i,SV464: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV712 )
| ~ ( in @ SV712 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(3880,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
| ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
= $false )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3881,plain,
! [SV465: $i,SV371: $i,SV713: $i] :
( ( ( ! [SY1512: $i] :
( ~ ( in @ SV713 @ SY1512 )
| ~ ( in @ SY1512 @ SV371 ) )
| ( in @ SV713 @ SV465 ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(3882,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV465 )
| ~ ( ~ ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(3883,plain,
! [SV564: $i,SV285: $i,SV512: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV512 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) )
= $true )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(3884,plain,
! [SV650: $i,SV285: $i,SV156: $i,SV689: $i] :
( ( ( ~ ( relation @ SV689 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SV689 ) )
| ( in @ SV156 @ SV650 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3698]) ).
thf(3885,plain,
! [SV651: $i,SV285: $i,SV156: $i,SV690: $i] :
( ( ( ~ ( relation @ SV690 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SV690 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV690 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(3886,plain,
! [SV372: $i,SV466: $i] :
( ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
= $false )
| ( ( ~ ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 ) )
= $true )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3887,plain,
! [SV467: $i,SV373: $i,SV715: $i] :
( ( ( ( SV715 != SV373 )
| ( in @ SV715 @ SV467 ) )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(3888,plain,
! [SV373: $i,SV467: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ SV467 )
| ( SV716 = SV373 ) )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(3889,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( function @ SV717 )
| ~ ( relation @ SV717 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) )
| ( SV717
= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(3890,plain,
! [SV157: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
| ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3891,plain,
( ( ~ ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3706]) ).
thf(3892,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3706]) ).
thf(3893,plain,
! [SV567: $i,SV158: $i] :
( ( ( in @ SV158 @ SV567 )
= $false )
| ( ( ordinal_subset @ ( succ @ SV158 ) @ SV567 )
= $true )
| ( ( ordinal @ SV567 )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3894,plain,
! [SV568: $i,SV158: $i] :
( ( ( ordinal_subset @ ( succ @ SV158 ) @ SV568 )
= $false )
| ( ( in @ SV158 @ SV568 )
= $true )
| ( ( ordinal @ SV568 )
= $false )
| ( ( ordinal @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3895,plain,
! [SV470: $i,SV159: $i,SV513: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ ( relation_rng @ SV513 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 ) )
= $true )
| ( ( ~ ( in @ SV691 @ SV470 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3896,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
| ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3897,plain,
! [SV569: $i,SV160: $i] :
( ( ( subset @ SV160 @ SV569 )
= $false )
| ( ( subset @ ( relation_dom @ SV160 ) @ ( relation_dom @ SV569 ) )
= $true )
| ( ( relation @ SV569 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3898,plain,
! [SV570: $i,SV160: $i] :
( ( ( subset @ SV160 @ SV570 )
= $false )
| ( ( subset @ ( relation_rng @ SV160 ) @ ( relation_rng @ SV570 ) )
= $true )
| ( ( relation @ SV570 )
= $false )
| ( ( relation @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3899,plain,
! [SV616: $i,SV571: $i] :
( ( ( SV571 = SV616 )
= $false )
| ( ( proper_subset @ SV571 @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3900,plain,
! [SV476: $i,SV515: $i,SV161: $i] :
( ( ( in @ SV161 @ SV515 )
= $false )
| ( ( ~ ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) ) )
= $true )
| ( ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(3901,plain,
! [SV619: $i,SV161: $i,SV652: $i] :
( ( ( relation @ SV652 )
= $false )
| ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV652 @ SV619 ) )
| ( in @ SV161 @ SV652 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3902,plain,
! [SV620: $i,SV161: $i,SV653: $i] :
( ( ( relation @ SV653 )
= $false )
| ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV653 @ SV620 ) )
| ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(3903,plain,
! [SV164: $i,SV520: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) )
| ~ ( in @ SV481 @ SV164 ) )
= $true )
| ( ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(3904,plain,
! [SV164: $i,SV622: $i,SV654: $i] :
( ( ( ~ ( function @ SV654 ) )
= $true )
| ( ( ~ ( relation @ SV654 ) )
= $true )
| ( ( ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SV654 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(3905,plain,
! [SV164: $i,SV623: $i,SV655: $i] :
( ( ( ~ ( function @ SV655 ) )
= $true )
| ( ( ~ ( relation @ SV655 ) )
= $true )
| ( ( ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(3906,plain,
! [SV576: $i,SV287: $i,SV165: $i] :
( ( ( in @ SV165 @ SV287 )
= $false )
| ( ( in @ SV576 @ SV287 )
= $false )
| ( ( in @ SV576 @ ( sK3_C @ SV287 @ SV165 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3907,plain,
! [SV167: $i,SV718: $i] :
( ( ! [SY1513: $i] :
( ~ ( in @ SV718 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SY1513 @ SV718 )
| ( in @ SY1513 @ ( sK80_B @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3908,plain,
! [SV168: $i,SV523: $i,SV485: $i] :
( ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) )
| ~ ( in @ SV168 @ ( relation_dom @ SV523 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(3909,plain,
! [SV625: $i,SV168: $i,SV656: $i] :
( ( ( ~ ( function @ SV656 ) )
= $true )
| ( ( ~ ( relation @ SV656 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
| ( SV625
= ( apply @ SV656 @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(3910,plain,
! [SV626: $i,SV168: $i,SV657: $i] :
( ( ( ~ ( function @ SV657 ) )
= $true )
| ( ( ~ ( relation @ SV657 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
| ( in @ SV168 @ ( relation_dom @ SV657 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(3911,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) ) ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3734]) ).
thf(3912,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ( SV694
!= ( relation_inverse_image @ SV169 @ SV659 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) )
| ~ ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3735]) ).
thf(3913,plain,
! [SV578: $i,SV487: $i,SV392: $i] :
( ( ( disjoint @ SV392 @ SV487 )
= $false )
| ( ( in @ SV578 @ SV392 )
= $false )
| ( ( in @ SV578 @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3914,plain,
! [SV170: $i] :
( ( ( ! [SY967: $i] :
( ~ ( in @ SY967 @ ( relation_dom @ SV170 ) )
| ! [SY968: $i] :
( ( SY968
!= ( apply @ SV170 @ SY967 ) )
| ( in @ ( ordered_pair @ SY967 @ SY968 ) @ SV170 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3737]) ).
thf(3915,plain,
! [SV170: $i] :
( ( ( ! [SY969: $i] :
( ~ ( in @ SY969 @ ( relation_dom @ SV170 ) )
| ! [SY970: $i] :
( ~ ( in @ ( ordered_pair @ SY969 @ SY970 ) @ SV170 )
| ( SY970
= ( apply @ SV170 @ SY969 ) ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3738]) ).
thf(3916,plain,
! [SV170: $i] :
( ( ( ! [SY971: $i] :
( ( in @ SY971 @ ( relation_dom @ SV170 ) )
| ! [SY972: $i] :
( ( SY972
!= ( apply @ SV170 @ SY971 ) )
| ( SY972 = empty_set ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3739]) ).
thf(3917,plain,
! [SV170: $i] :
( ( ( ! [SY973: $i] :
( ( in @ SY973 @ ( relation_dom @ SV170 ) )
| ! [SY974: $i] :
( ( SY974 != empty_set )
| ( SY974
= ( apply @ SV170 @ SY973 ) ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3740]) ).
thf(3918,plain,
! [SV524: $i,SV488: $i,SV171: $i] :
( ( ( in @ SV171 @ SV488 )
= $false )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ SV524 ) ) )
= $true )
| ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) )
= $true )
| ( ( relation @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3919,plain,
! [SV627: $i,SV171: $i,SV660: $i] :
( ( ( relation @ SV660 )
= $false )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV660 @ SV627 ) ) )
| ( in @ SV171 @ SV627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3742]) ).
thf(3920,plain,
! [SV628: $i,SV171: $i,SV661: $i] :
( ( ( relation @ SV661 )
= $false )
| ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV661 @ SV628 ) ) )
| ( in @ SV171 @ ( relation_dom @ SV661 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3921,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( relation @ SV695 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
| ( SV695
= ( relation_composition @ SV172 @ SV397 ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(3922,plain,
! [SV397: $i,SV172: $i,SV696: $i] :
( ( ( ~ ( relation @ SV696 ) )
= $true )
| ( ( ( SV696
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3923,plain,
! [SV173: $i,SV579: $i] :
( ( ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3746]) ).
thf(3924,plain,
! [SV173: $i,SV579: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
| ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(3925,plain,
! [SV580: $i,SV173: $i] :
( ( ( ~ ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) ) )
= $false )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3748]) ).
thf(3926,plain,
! [SV173: $i,SV580: $i] :
( ( ( ~ ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) )
= $false )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3748]) ).
thf(3927,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3928,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3929,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3930,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i] :
( ( ( ~ ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3751]) ).
thf(3931,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
| ~ ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) ) )
= $false )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3932,plain,
! [SV584: $i,SV665: $i] :
( ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( ~ ( ~ ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) )
| ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) ) )
= $true )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3933,plain,
! [SV585: $i,SV697: $i] :
( ( ( ( SV697
!= ( set_meet @ SV585 ) ) )
= $true )
| ( ( SV697 = empty_set )
= $true )
| ( ( SV585 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(3934,plain,
! [SV586: $i,SV698: $i] :
( ( ( ( SV698 != empty_set ) )
= $true )
| ( ( SV698
= ( set_meet @ SV586 ) )
= $true )
| ( ( SV586 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(3935,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
| ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3936,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $true )
| ( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(3937,plain,
! [SV490: $i,SV175: $i,SV528: $i] :
( ( ( ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV528 )
| ( SY1346 = SV175 )
| ( SY1346 = SV490 ) ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3758]) ).
thf(3938,plain,
! [SV490: $i,SV528: $i,SV175: $i] :
( ( ( ~ ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(3939,plain,
! [SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
| ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3760]) ).
thf(3940,plain,
! [SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(3941,plain,
! [SV719: $i,SV401: $i,SV699: $i,SV666: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SV699 @ SV719 ) @ SV401 )
| ( in @ ( ordered_pair @ SV666 @ SV719 ) @ SV401 ) )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3942,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( ~ ( function @ SV700 )
| ~ ( relation @ SV700 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3943,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3764]) ).
thf(3944,plain,
! [SV289: $i,SV176: $i] :
( ( ( ~ ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3764]) ).
thf(3945,plain,
! [SV667: $i,SV631: $i,SV177: $i] :
( ( ( subset @ ( unordered_pair @ SV177 @ SV631 ) @ SV667 )
= $false )
| ( ( in @ SV177 @ SV667 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3946,plain,
! [SV668: $i,SV632: $i,SV177: $i] :
( ( ( subset @ ( unordered_pair @ SV177 @ SV632 ) @ SV668 )
= $false )
| ( ( in @ SV632 @ SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3947,plain,
! [SV290: $i,SV178: $i] :
( ( ( ! [SY1154: $i] :
( ~ ( ordinal @ SY1154 )
| ~ ( in @ SY1154 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SY1154 ) ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3771]) ).
thf(3948,plain,
! [SV178: $i,SV290: $i] :
( ( ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3772]) ).
thf(3949,plain,
! [SV179: $i,SV633: $i,SV291: $i] :
( ( ( ~ ( disjoint @ SV291 @ SV633 ) )
= $true )
| ( ( subset @ SV291 @ ( subset_complement @ SV179 @ SV633 ) )
= $true )
| ( ( element @ SV633 @ ( powerset @ SV179 ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3950,plain,
! [SV634: $i,SV179: $i,SV291: $i] :
( ( ( ~ ( subset @ SV291 @ ( subset_complement @ SV179 @ SV634 ) ) )
= $true )
| ( ( disjoint @ SV291 @ SV634 )
= $true )
| ( ( element @ SV634 @ ( powerset @ SV179 ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3951,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
= $false )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3952,plain,
! [SV592: $i,SV181: $i] :
( ( ( SV181 = SV592 )
= $false )
| ( ( ~ ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) ) )
= $true )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3953,plain,
! [SV493: $i,SV408: $i] :
( ( ( relation @ SV408 )
= $false )
| ( ( function @ SV408 )
= $false )
| ( ( ~ ( relation @ SV493 ) )
= $true )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(3954,plain,
! [SV494: $i,SV409: $i] :
( ( ( relation @ SV409 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( ~ ( relation @ SV494 ) )
= $true )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3955,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
| ~ ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) ) )
= $false )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3956,plain,
! [SV182: $i,SV670: $i] :
( ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( ~ ( ~ ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) )
| ~ ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(3957,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( function @ SV701 )
| ~ ( relation @ SV701 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(3958,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3959,plain,
! [SV184: $i,SV292: $i] :
( ( ( ~ ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3782]) ).
thf(3960,plain,
! [SV410: $i] :
( ( ( ( ( sK39_B @ SV410 )
!= ( sK40_SY629 @ SV410 ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3783]) ).
thf(3961,plain,
! [SV410: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3784]) ).
thf(3962,plain,
! [SV635: $i,SV411: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ SV411 )
| ~ ( in @ SV635 @ SV411 ) )
= $true )
| ( ( in @ SV593 @ SV635 )
= $true )
| ( ( SV593 = SV635 )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(3963,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(3964,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( ( SV637
!= ( relation_dom_restriction @ SV185 @ SV595 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) ) )
= $true )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(3965,plain,
! [SV596: $i] :
( ( ( empty @ SV596 )
= $false )
| ( ( ~ ( relation @ SV596 ) )
= $true )
| ( ( ~ ( function @ SV596 ) )
= $true )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3966,plain,
! [SV597: $i] :
( ( ( empty @ SV597 )
= $false )
| ( ( ~ ( relation @ SV597 ) )
= $true )
| ( ( ~ ( function @ SV597 ) )
= $true )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3967,plain,
! [SV530: $i,SV495: $i,SV186: $i] :
( ( ( in @ SV186 @ SV495 )
= $false )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ SV530 ) ) )
= $true )
| ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) )
= $true )
| ( ( relation @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(3968,plain,
! [SV638: $i,SV186: $i,SV671: $i] :
( ( ( relation @ SV671 )
= $false )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SV671 ) ) )
| ( in @ SV186 @ SV638 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3792]) ).
thf(3969,plain,
! [SV639: $i,SV186: $i,SV672: $i] :
( ( ( relation @ SV672 )
= $false )
| ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SV672 ) ) )
| ( in @ SV186 @ ( relation_rng @ SV672 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3970,plain,
! [SV498: $i,SV187: $i,SV531: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ ( relation_dom @ SV531 ) )
| ~ ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 ) )
= $true )
| ( ( ~ ( in @ SV702 @ SV498 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(3971,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
| ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3972,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
| ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
= $false )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(3973,plain,
! [SV599: $i,SV188: $i] :
( ( ( subset @ SV188 @ SV599 )
= $false )
| ( ( ! [SY1420: $i,SY1421: $i] :
( ~ ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV188 )
| ( in @ ( ordered_pair @ SY1420 @ SY1421 ) @ SV599 ) ) )
= $true )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(3974,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(3975,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
| ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3976,plain,
! [SV534: $i,SV501: $i,SV189: $i] :
( ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV189 )
| ~ ( in @ SY1350 @ SV501 )
| ( in @ SY1350 @ SV534 ) ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3800]) ).
thf(3977,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ~ ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3978,plain,
! [SV535: $i,SV190: $i,SV602: $i,SV293: $i] :
( ( ( in @ SV293 @ SV602 )
= $false )
| ( ( in @ SV190 @ SV535 )
= $false )
| ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV535 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3979,plain,
! [SV720: $i,SV673: $i,SV293: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV673 @ SV720 ) ) )
= $true )
| ( ( in @ SV190 @ SV673 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(3980,plain,
! [SV703: $i,SV674: $i,SV293: $i,SV190: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV674 @ SV703 ) ) )
= $true )
| ( ( in @ SV293 @ SV703 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(3981,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) ) )
= $false )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3982,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) ) )
= $false )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3983,plain,
! [SV641: $i,SV604: $i,SV192: $i] :
( ( ( ~ ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) )
| ~ ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3807]) ).
thf(3984,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3808]) ).
thf(3985,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(3986,plain,
! [SV503: $i,SV423: $i] :
( ( ( ~ ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(3987,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(3988,plain,
! [SV239: $i,SV536: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) )
= $true )
| ( ( function @ SV536 )
= $false )
| ( ( relation @ SV536 )
= $false )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(3989,plain,
! [SV537: $i,SV240: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ ( relation_dom @ SV240 ) ) )
= $true )
| ( ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) )
= $true )
| ( ( function @ SV537 )
= $false )
| ( ( relation @ SV537 )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3812]) ).
thf(3990,plain,
! [SV541: $i,SV677: $i] :
( ( ( element @ SV677 @ SV541 )
= $false )
| ( ( empty @ SV677 )
= $true )
| ( ( empty @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(3991,plain,
! [SV542: $i,SV678: $i] :
( ( ( empty @ SV678 )
= $false )
| ( ( element @ SV678 @ SV542 )
= $true )
| ( ( empty @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(3992,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3817]) ).
thf(3993,plain,
! [SV139: $i,SV543: $i] :
( ( ( in @ ( ordered_pair @ ( sK25_SY621 @ SV543 @ SV139 ) @ ( sK24_C @ SV543 @ SV139 ) ) @ SV139 )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(3994,plain,
! [SV139: $i,SV544: $i,SV704: $i,SV679: $i] :
( ( ( ( SV679 = SV704 )
| ~ ( in @ SV679 @ SV544 )
| ~ ( in @ SV704 @ SV544 )
| ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(3995,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) )
| ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3820]) ).
thf(3996,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
| ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3821]) ).
thf(3997,plain,
! [SV606: $i,SV546: $i,SV140: $i] :
( ( ( ~ ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) ) )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3822]) ).
thf(3998,plain,
! [SV140: $i,SV546: $i,SV606: $i] :
( ( ( ~ ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3822]) ).
thf(3999,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
| ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(4000,plain,
! [SV141: $i,SV547: $i] :
( ( ( ( sK36_C @ SV547 @ SV141 )
= ( sK37_SY628 @ SV547 @ SV141 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3824]) ).
thf(4001,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV548 )
| ~ ( in @ SV705 @ SV548 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 )
| ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(4002,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(4003,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( ~ ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) ) )
= $true )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(4004,plain,
! [SV706: $i,SV645: $i,SV283: $i,SV143: $i] :
( ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV645 @ SV706 ) )
= $false )
| ( ( in @ SV143 @ SV645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(4005,plain,
! [SV682: $i,SV646: $i,SV283: $i,SV143: $i] :
( ( ( in @ ( ordered_pair @ SV143 @ SV283 ) @ ( cartesian_product2 @ SV646 @ SV682 ) )
= $false )
| ( ( in @ SV283 @ SV682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(4006,plain,
! [SV144: $i,SV609: $i] :
( ( ( ! [SY1438: $i] :
( ~ ( subset @ SY1438 @ SV609 )
| ( in @ SY1438 @ ( sK88_SY659 @ SV609 @ SV144 ) ) ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3832]) ).
thf(4007,plain,
! [SV144: $i,SV609: $i] :
( ( ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3833]) ).
thf(4008,plain,
! [SV721: $i,SV144: $i,SV707: $i] :
( ( ~ ( in @ SV707 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SV721 @ SV707 )
| ( in @ SV721 @ ( sK87_B @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4009,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4010,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) ) )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3835]) ).
thf(4011,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 )
= $true )
| ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4012,plain,
! [SV437: $i,SV145: $i,SV507: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV507 )
| ( in @ SV722 @ SV145 )
| ( in @ SV722 @ SV437 ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4013,plain,
! [SV437: $i,SV507: $i,SV145: $i] :
( ( ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) )
| ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(4014,plain,
! [SV146: $i,SV551: $i] :
( ( ( ! [SY1368: $i] :
~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SY1368 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(4015,plain,
! [SV146: $i,SV551: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ ( sK98_SY665 @ SV551 @ SV146 ) ) @ SV146 )
= $true )
| ( ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4016,plain,
! [SV552: $i,SV146: $i] :
( ( ( ! [SY1369: $i] :
( ! [SY850: $i] :
~ ( in @ ( ordered_pair @ SY1369 @ SY850 ) @ SV146 )
| ( in @ SY1369 @ SV552 ) ) )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3841]) ).
thf(4017,plain,
! [SV146: $i,SV552: $i] :
( ( ( ! [SY1371: $i] :
( ~ ( in @ SY1371 @ SV552 )
| ( in @ ( ordered_pair @ SY1371 @ ( sK96_D @ SY1371 @ SV552 @ SV146 ) ) @ SV146 ) ) )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3842]) ).
thf(4018,plain,
! [SV147: $i,SV553: $i] :
( ( ( in @ ( ordered_pair @ ( sK53_C @ SV553 @ SV147 ) @ ( sK53_C @ SV553 @ SV147 ) ) @ SV147 )
= $false )
| ( ( is_reflexive_in @ SV147 @ SV553 )
= $true )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4019,plain,
! [SV147: $i,SV554: $i,SV683: $i] :
( ( ( in @ SV683 @ SV554 )
= $false )
| ( ( in @ ( ordered_pair @ SV683 @ SV683 ) @ SV147 )
= $true )
| ( ( is_reflexive_in @ SV147 @ SV554 )
= $false )
| ( ( relation @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4020,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
| ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(4021,plain,
! [SV555: $i,SV611: $i] :
( ( ( relation @ SV611 )
= $false )
| ( ( function @ SV611 )
= $false )
| ( ( ( SV611
!= ( identity_relation @ SV555 ) )
| ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4022,plain,
! [SV556: $i,SV612: $i] :
( ( ( relation @ SV612 )
= $false )
| ( ( function @ SV612 )
= $false )
| ( ( ( SV612
!= ( identity_relation @ SV556 ) )
| ( ( relation_dom @ SV612 )
= SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3848]) ).
thf(4023,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
| ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(4024,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(4025,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 )
| ~ ( in @ SV723 @ SV558 )
| ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 )
| ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4026,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
= $false )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3852]) ).
thf(4027,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) ) )
= $false )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3852]) ).
thf(4028,plain,
! [SV151: $i,SV560: $i] :
( ( ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) )
| ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) )
= $false )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(4029,plain,
! [SV508: $i,SV449: $i,SV153: $i,SV724: $i] :
( ( ( ! [SY1514: $i] :
( ~ ( in @ SV724 @ SV153 )
| ~ ( in @ SY1514 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SY1514 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4030,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3855]) ).
thf(4031,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV153: $i] :
( ( ( ! [SY1515: $i,SY1516: $i] :
( ~ ( in @ SY1515 @ SV153 )
| ~ ( in @ SY1516 @ SV450 )
| ( SV725
!= ( ordered_pair @ SY1515 @ SY1516 ) ) )
| ( in @ SV725 @ SV509 ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4032,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV509 )
| ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SV726
!= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) ) ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4033,plain,
! [SV356: $i,SV454: $i] :
( ( ( subset @ ( sK105_C @ SV454 @ SV356 ) @ SV356 )
= $false )
| ( ( in @ ( sK105_C @ SV454 @ SV356 ) @ SV454 )
= $false )
| ( ( SV454
= ( powerset @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4034,plain,
! [SV357: $i,SV455: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV455 ) )
= $true )
| ( ( subset @ SV709 @ SV357 )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4035,plain,
! [SV455: $i,SV357: $i,SV710: $i] :
( ( ( ~ ( subset @ SV710 @ SV357 ) )
= $true )
| ( ( in @ SV710 @ SV455 )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4036,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3861]) ).
thf(4037,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3862]) ).
thf(4038,plain,
! [SV458: $i,SV360: $i] :
( ( ( in @ SV360 @ ( relation_rng @ SV458 ) )
= $false )
| ( ( ~ ( one_to_one @ SV458 ) )
= $true )
| ( ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) )
= $true )
| ( ( function @ SV458 )
= $false )
| ( ( relation @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(4039,plain,
! [SV459: $i,SV361: $i] :
( ( ( in @ SV361 @ ( relation_rng @ SV459 ) )
= $false )
| ( ( ~ ( one_to_one @ SV459 ) )
= $true )
| ( ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) )
= $true )
| ( ( function @ SV459 )
= $false )
| ( ( relation @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3866]) ).
thf(4040,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ~ ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) )
| ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) ) )
= $false )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4041,plain,
! [SV648: $i,SV154: $i,SV687: $i] :
( ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( ~ ( ~ ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) )
| ~ ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(4042,plain,
! [SV364: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3869]) ).
thf(4043,plain,
! [SV364: $i] :
( ( ( ( ( sK20_B @ SV364 )
!= ( sK21_SY619 @ SV364 ) ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(4044,plain,
! [SV727: $i,SV365: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SV727 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) )
| ( SV711 = SV727 ) )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(4045,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3872]) ).
thf(4046,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 ) )
= $false )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3872]) ).
thf(4047,plain,
! [SV369: $i,SV688: $i,SV649: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV649 @ SV688 ) @ SV369 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV688 @ SV649 ) @ SV369 ) )
= $true )
| ( ( SV649 = SV688 )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4048,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 ) )
= $true )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
= $true )
| ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4049,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(4050,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) ) )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3876]) ).
thf(4051,plain,
! [SV511: $i,SV463: $i,SV155: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV155 )
| ( in @ SV728 @ SV463 )
| ( in @ SV728 @ SV511 ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4052,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) )
| ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(4053,plain,
! [SV712: $i,SV370: $i,SV464: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV712 ) )
= $true )
| ( ( ~ ( in @ SV712 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4054,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) ) )
= $false )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3880]) ).
thf(4055,plain,
! [SV370: $i,SV464: $i] :
( ( ( ~ ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 ) )
= $false )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3880]) ).
thf(4056,plain,
! [SV465: $i,SV371: $i,SV713: $i] :
( ( ( ! [SY1512: $i] :
( ~ ( in @ SV713 @ SY1512 )
| ~ ( in @ SY1512 @ SV371 ) ) )
= $true )
| ( ( in @ SV713 @ SV465 )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4057,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV465 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4058,plain,
! [SV564: $i,SV285: $i,SV512: $i,SV156: $i] :
( ( ( in @ SV156 @ SV512 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) )
= $true )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(4059,plain,
! [SV650: $i,SV285: $i,SV156: $i,SV689: $i] :
( ( ( relation @ SV689 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SV689 ) )
| ( in @ SV156 @ SV650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(4060,plain,
! [SV651: $i,SV285: $i,SV156: $i,SV690: $i] :
( ( ( relation @ SV690 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SV690 ) )
| ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV690 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4061,plain,
! [SV372: $i,SV466: $i] :
( ( ( in @ ( sK49_C @ SV466 @ SV372 ) @ SV466 )
= $false )
| ( ( ( sK49_C @ SV466 @ SV372 )
= SV372 )
= $false )
| ( ( SV466
= ( singleton @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4062,plain,
! [SV467: $i,SV373: $i,SV715: $i] :
( ( ( ( SV715 != SV373 ) )
= $true )
| ( ( in @ SV715 @ SV467 )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(4063,plain,
! [SV373: $i,SV467: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ SV467 ) )
= $true )
| ( ( SV716 = SV373 )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(4064,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( function @ SV717 )
| ~ ( relation @ SV717 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) )
| ( SV717
= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4065,plain,
! [SV157: $i] :
( ( ( ~ ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(4066,plain,
! [SV157: $i] :
( ( ( ~ ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(4067,plain,
( ( ~ ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3891]) ).
thf(4068,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3892]) ).
thf(4069,plain,
! [SV470: $i,SV159: $i,SV513: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ ( relation_rng @ SV513 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 ) )
= $true )
| ( ( ~ ( in @ SV691 @ SV470 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3895]) ).
thf(4070,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3896]) ).
thf(4071,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3896]) ).
thf(4072,plain,
! [SV515: $i,SV476: $i,SV161: $i] :
( ( ( in @ SV161 @ ( cartesian_product2 @ SV476 @ SV476 ) )
= $false )
| ( ( in @ SV161 @ SV515 )
= $false )
| ( ( in @ SV161 @ ( relation_restriction @ SV515 @ SV476 ) )
= $true )
| ( ( relation @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4073,plain,
! [SV619: $i,SV652: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV652 @ SV619 ) ) )
= $true )
| ( ( in @ SV161 @ SV652 )
= $true )
| ( ( relation @ SV652 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4074,plain,
! [SV620: $i,SV653: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ ( relation_restriction @ SV653 @ SV620 ) ) )
= $true )
| ( ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) )
= $true )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4075,plain,
! [SV164: $i,SV520: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ ( relation_dom @ SV520 ) ) )
= $true )
| ( ( ~ ( in @ SV481 @ SV164 ) )
= $true )
| ( ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4076,plain,
! [SV164: $i,SV622: $i,SV654: $i] :
( ( ( function @ SV654 )
= $false )
| ( ( ~ ( relation @ SV654 ) )
= $true )
| ( ( ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SV654 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3904]) ).
thf(4077,plain,
! [SV164: $i,SV623: $i,SV655: $i] :
( ( ( function @ SV655 )
= $false )
| ( ( ~ ( relation @ SV655 ) )
= $true )
| ( ( ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4078,plain,
! [SV729: $i,SV167: $i,SV718: $i] :
( ( ~ ( in @ SV718 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SV729 @ SV718 )
| ( in @ SV729 @ ( sK80_B @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3907]) ).
thf(4079,plain,
! [SV168: $i,SV523: $i,SV485: $i] :
( ( ( ( SV485
!= ( apply @ SV523 @ SV168 ) ) )
= $true )
| ( ( ~ ( in @ SV168 @ ( relation_dom @ SV523 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3908]) ).
thf(4080,plain,
! [SV625: $i,SV168: $i,SV656: $i] :
( ( ( function @ SV656 )
= $false )
| ( ( ~ ( relation @ SV656 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
| ( SV625
= ( apply @ SV656 @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4081,plain,
! [SV626: $i,SV168: $i,SV657: $i] :
( ( ( function @ SV657 )
= $false )
| ( ( ~ ( relation @ SV657 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
| ( in @ SV168 @ ( relation_dom @ SV657 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3910]) ).
thf(4082,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ~ ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(4083,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( ~ ( ~ ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) )
| ~ ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3912]) ).
thf(4084,plain,
! [SV170: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( relation_dom @ SV170 ) )
| ! [SY1517: $i] :
( ( SY1517
!= ( apply @ SV170 @ SV730 ) )
| ( in @ ( ordered_pair @ SV730 @ SY1517 ) @ SV170 ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4085,plain,
! [SV170: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( relation_dom @ SV170 ) )
| ! [SY1518: $i] :
( ~ ( in @ ( ordered_pair @ SV731 @ SY1518 ) @ SV170 )
| ( SY1518
= ( apply @ SV170 @ SV731 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4086,plain,
! [SV170: $i,SV732: $i] :
( ( ( ( in @ SV732 @ ( relation_dom @ SV170 ) )
| ! [SY1519: $i] :
( ( SY1519
!= ( apply @ SV170 @ SV732 ) )
| ( SY1519 = empty_set ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4087,plain,
! [SV170: $i,SV733: $i] :
( ( ( ( in @ SV733 @ ( relation_dom @ SV170 ) )
| ! [SY1520: $i] :
( ( SY1520 != empty_set )
| ( SY1520
= ( apply @ SV170 @ SV733 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4088,plain,
! [SV488: $i,SV524: $i,SV171: $i] :
( ( ( in @ SV171 @ ( relation_dom @ SV524 ) )
= $false )
| ( ( in @ SV171 @ SV488 )
= $false )
| ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV524 @ SV488 ) ) )
= $true )
| ( ( relation @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(4089,plain,
! [SV627: $i,SV660: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV660 @ SV627 ) ) ) )
= $true )
| ( ( in @ SV171 @ SV627 )
= $true )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3919]) ).
thf(4090,plain,
! [SV628: $i,SV661: $i,SV171: $i] :
( ( ( ~ ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV661 @ SV628 ) ) ) )
= $true )
| ( ( in @ SV171 @ ( relation_dom @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4091,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( relation @ SV695 )
= $false )
| ( ( ~ ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
| ( SV695
= ( relation_composition @ SV172 @ SV397 ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(4092,plain,
! [SV397: $i,SV172: $i,SV696: $i] :
( ( ( relation @ SV696 )
= $false )
| ( ( ( SV696
!= ( relation_composition @ SV172 @ SV397 ) )
| ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) ) )
= $true )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(4093,plain,
! [SV173: $i,SV579: $i] :
( ( ( ! [SY1389: $i] :
~ ( in @ ( ordered_pair @ SY1389 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3923]) ).
thf(4094,plain,
! [SV173: $i,SV579: $i] :
( ( ( in @ ( ordered_pair @ ( sK28_SY623 @ SV579 @ SV173 ) @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
= $true )
| ( ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4095,plain,
! [SV580: $i,SV173: $i] :
( ( ( ! [SY1390: $i] :
( ! [SY994: $i] :
~ ( in @ ( ordered_pair @ SY994 @ SY1390 ) @ SV173 )
| ( in @ SY1390 @ SV580 ) ) )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(4096,plain,
! [SV173: $i,SV580: $i] :
( ( ( ! [SY1392: $i] :
( ~ ( in @ SY1392 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SY1392 @ SV580 @ SV173 ) @ SY1392 ) @ SV173 ) ) )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3926]) ).
thf(4097,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4098,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $true )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4099,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i] :
( ( ( ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV582 )
| ( SY1393 = SV526 )
| ( SY1393 = SV174 )
| ( SY1393 = SV288 ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3929]) ).
thf(4100,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i] :
( ( ( ~ ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3930]) ).
thf(4101,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) ) )
= $false )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4102,plain,
! [SV664: $i,SV583: $i] :
( ( ( ~ ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) ) )
= $false )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4103,plain,
! [SV584: $i,SV665: $i] :
( ( ( ~ ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) )
| ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3932]) ).
thf(4104,plain,
! [SV585: $i,SV697: $i] :
( ( ( SV697
= ( set_meet @ SV585 ) )
= $false )
| ( ( SV697 = empty_set )
= $true )
| ( ( SV585 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3933]) ).
thf(4105,plain,
! [SV586: $i,SV698: $i] :
( ( ( SV698 = empty_set )
= $false )
| ( ( SV698
= ( set_meet @ SV586 ) )
= $true )
| ( ( SV586 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3934]) ).
thf(4106,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4107,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) ) )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4108,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
= $true )
| ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 )
= $true )
| ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3936]) ).
thf(4109,plain,
! [SV490: $i,SV175: $i,SV528: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV528 )
| ( SV734 = SV175 )
| ( SV734 = SV490 ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4110,plain,
! [SV490: $i,SV528: $i,SV175: $i] :
( ( ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) )
| ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4111,plain,
! [SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3939]) ).
thf(4112,plain,
! [SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 ) )
= $false )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3939]) ).
thf(4113,plain,
! [SV719: $i,SV401: $i,SV699: $i,SV666: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 )
| ~ ( in @ ( ordered_pair @ SV699 @ SV719 ) @ SV401 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV666 @ SV719 ) @ SV401 )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4114,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( ~ ( function @ SV700 ) )
= $true )
| ( ( ~ ( relation @ SV700 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3942]) ).
thf(4115,plain,
! [SV289: $i,SV176: $i] :
( ( ( ! [SY1152: $i] :
( ~ ( function @ SY1152 )
| ~ ( relation @ SY1152 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1152 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SY1152 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3943]) ).
thf(4116,plain,
! [SV289: $i,SV176: $i] :
( ( ( ! [SY1153: $i] :
( ~ ( function @ SY1153 )
| ~ ( relation @ SY1153 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SY1153 @ SV289 ) ) )
| ( in @ ( apply @ SY1153 @ SV176 ) @ ( relation_dom @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3944]) ).
thf(4117,plain,
! [SV290: $i,SV178: $i,SV735: $i] :
( ( ( ~ ( ordinal @ SV735 )
| ~ ( in @ SV735 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4118,plain,
! [SV290: $i,SV178: $i] :
( ( ( SV178 = empty_set )
= $true )
| ( ( ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4119,plain,
! [SV179: $i,SV633: $i,SV291: $i] :
( ( ( disjoint @ SV291 @ SV633 )
= $false )
| ( ( subset @ SV291 @ ( subset_complement @ SV179 @ SV633 ) )
= $true )
| ( ( element @ SV633 @ ( powerset @ SV179 ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3949]) ).
thf(4120,plain,
! [SV634: $i,SV179: $i,SV291: $i] :
( ( ( subset @ SV291 @ ( subset_complement @ SV179 @ SV634 ) )
= $false )
| ( ( disjoint @ SV291 @ SV634 )
= $true )
| ( ( element @ SV634 @ ( powerset @ SV179 ) )
= $false )
| ( ( element @ SV291 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4121,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
= $false )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3951]) ).
thf(4122,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) ) )
= $false )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3951]) ).
thf(4123,plain,
! [SV592: $i,SV181: $i] :
( ( ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) )
| ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) )
= $false )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4124,plain,
! [SV408: $i,SV493: $i] :
( ( ( relation @ SV493 )
= $false )
| ( ( function @ SV408 )
= $false )
| ( ( relation @ SV408 )
= $false )
| ( ( ~ ( function @ SV493 ) )
= $true )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4125,plain,
! [SV409: $i,SV494: $i] :
( ( ( relation @ SV494 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( ~ ( function @ SV494 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4126,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) ) )
= $false )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3955]) ).
thf(4127,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) ) )
= $false )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3955]) ).
thf(4128,plain,
! [SV670: $i,SV182: $i] :
( ( ( ~ ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) )
| ~ ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4129,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( function @ SV701 ) )
= $true )
| ( ( ~ ( relation @ SV701 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4130,plain,
! [SV184: $i,SV292: $i] :
( ( ( ! [SY1158: $i] :
( ~ ( function @ SY1158 )
| ~ ( relation @ SY1158 )
| ( SV292
!= ( relation_dom_restriction @ SY1158 @ SV184 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1159 )
= ( apply @ SY1158 @ SY1159 ) ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3958]) ).
thf(4131,plain,
! [SV184: $i,SV292: $i] :
( ( ( ! [SY1160: $i] :
( ~ ( function @ SY1160 )
| ~ ( relation @ SY1160 )
| ( SV292
!= ( relation_dom_restriction @ SY1160 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SY1160 ) @ SV184 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3959]) ).
thf(4132,plain,
! [SV410: $i] :
( ( ( ( sK39_B @ SV410 )
= ( sK40_SY629 @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4133,plain,
! [SV410: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
| ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4134,plain,
! [SV635: $i,SV411: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ SV411 ) )
= $true )
| ( ( ~ ( in @ SV635 @ SV411 ) )
= $true )
| ( ( in @ SV593 @ SV635 )
= $true )
| ( ( SV593 = SV635 )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4135,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3963]) ).
thf(4136,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( ~ ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) ) )
= $true )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4137,plain,
! [SV596: $i] :
( ( ( relation @ SV596 )
= $false )
| ( ( empty @ SV596 )
= $false )
| ( ( ~ ( function @ SV596 ) )
= $true )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4138,plain,
! [SV597: $i] :
( ( ( relation @ SV597 )
= $false )
| ( ( empty @ SV597 )
= $false )
| ( ( ~ ( function @ SV597 ) )
= $true )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4139,plain,
! [SV495: $i,SV530: $i,SV186: $i] :
( ( ( in @ SV186 @ ( relation_rng @ SV530 ) )
= $false )
| ( ( in @ SV186 @ SV495 )
= $false )
| ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV495 @ SV530 ) ) )
= $true )
| ( ( relation @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4140,plain,
! [SV671: $i,SV638: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SV671 ) ) ) )
= $true )
| ( ( in @ SV186 @ SV638 )
= $true )
| ( ( relation @ SV671 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4141,plain,
! [SV672: $i,SV639: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SV672 ) ) ) )
= $true )
| ( ( in @ SV186 @ ( relation_rng @ SV672 ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4142,plain,
! [SV498: $i,SV187: $i,SV531: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ ( relation_dom @ SV531 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 ) )
= $true )
| ( ( ~ ( in @ SV702 @ SV498 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4143,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4144,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4145,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 ) )
= $false )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3972]) ).
thf(4146,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
= $false )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3972]) ).
thf(4147,plain,
! [SV599: $i,SV188: $i,SV736: $i] :
( ( ( ! [SY1521: $i] :
( ~ ( in @ ( ordered_pair @ SV736 @ SY1521 ) @ SV188 )
| ( in @ ( ordered_pair @ SV736 @ SY1521 ) @ SV599 ) ) )
= $true )
| ( ( subset @ SV188 @ SV599 )
= $false )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3973]) ).
thf(4148,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3974]) ).
thf(4149,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3975]) ).
thf(4150,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ~ ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) ) )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3975]) ).
thf(4151,plain,
! [SV534: $i,SV501: $i,SV189: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV189 )
| ~ ( in @ SV737 @ SV501 )
| ( in @ SV737 @ SV534 ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4152,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) )
| ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4153,plain,
! [SV720: $i,SV673: $i,SV293: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV673 @ SV720 ) )
= $false )
| ( ( in @ SV190 @ SV673 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4154,plain,
! [SV703: $i,SV674: $i,SV293: $i,SV190: $i] :
( ( ( in @ ( ordered_pair @ SV190 @ SV293 ) @ ( cartesian_product2 @ SV674 @ SV703 ) )
= $false )
| ( ( in @ SV293 @ SV703 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4155,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) )
| ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3981]) ).
thf(4156,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
| ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3982]) ).
thf(4157,plain,
! [SV641: $i,SV604: $i,SV192: $i] :
( ( ( ~ ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) ) )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4158,plain,
! [SV192: $i,SV604: $i,SV641: $i] :
( ( ( ~ ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3983]) ).
thf(4159,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) )
| ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4160,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
| ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3985]) ).
thf(4161,plain,
! [SV503: $i,SV423: $i] :
( ( ( ! [SY1317: $i,SY1318: $i] :
( ( SY1317 != SY1318 )
| ~ ( in @ SY1317 @ SV423 )
| ( in @ ( ordered_pair @ SY1317 @ SY1318 ) @ SV503 ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4162,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4163,plain,
! [SV239: $i,SV536: $i,SV68: $i] :
( ( ( in @ SV68 @ ( relation_dom @ ( relation_composition @ SV536 @ SV239 ) ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV536 @ SV239 ) @ SV68 )
= ( apply @ SV239 @ ( apply @ SV536 @ SV68 ) ) )
= $true )
| ( ( function @ SV536 )
= $false )
| ( ( relation @ SV536 )
= $false )
| ( ( function @ SV239 )
= $false )
| ( ( relation @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3988]) ).
thf(4164,plain,
! [SV537: $i,SV240: $i,SV69: $i] :
( ( ( in @ SV69 @ ( relation_dom @ SV240 ) )
= $false )
| ( ( ( apply @ ( relation_composition @ SV240 @ SV537 ) @ SV69 )
= ( apply @ SV537 @ ( apply @ SV240 @ SV69 ) ) )
= $true )
| ( ( function @ SV537 )
= $false )
| ( ( relation @ SV537 )
= $false )
| ( ( function @ SV240 )
= $false )
| ( ( relation @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4165,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4166,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4167,plain,
! [SV139: $i,SV544: $i,SV704: $i,SV679: $i] :
( ( ( ( SV679 = SV704 )
| ~ ( in @ SV679 @ SV544 )
| ~ ( in @ SV704 @ SV544 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4168,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ! [SY1428: $i] :
( ~ ( in @ ( ordered_pair @ SY1428 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SY1428 @ SV545 ) ) )
= $true )
| ( ( ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4169,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) ) )
= $true )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4170,plain,
! [SV606: $i,SV546: $i,SV140: $i] :
( ( ( ! [SY1429: $i] :
( ! [SY1364: $i] :
( ~ ( in @ ( ordered_pair @ SY1364 @ SY1429 ) @ SV140 )
| ~ ( in @ SY1364 @ SV546 ) )
| ( in @ SY1429 @ SV606 ) ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3997]) ).
thf(4171,plain,
! [SV140: $i,SV546: $i,SV606: $i] :
( ( ( ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SY1431 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SY1431 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3998]) ).
thf(4172,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4173,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3999]) ).
thf(4174,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV548 )
| ~ ( in @ SV705 @ SV548 )
| ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4001]) ).
thf(4175,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4002]) ).
thf(4176,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4002]) ).
thf(4177,plain,
! [SV608: $i,SV282: $i,SV142: $i] :
( ( ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) )
| ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4178,plain,
! [SV144: $i,SV609: $i,SV738: $i] :
( ( ( ~ ( subset @ SV738 @ SV609 )
| ( in @ SV738 @ ( sK88_SY659 @ SV609 @ SV144 ) ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4179,plain,
! [SV144: $i,SV609: $i] :
( ( ( in @ SV609 @ ( sK87_B @ SV144 ) )
= $false )
| ( ( in @ ( sK88_SY659 @ SV609 @ SV144 ) @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4007]) ).
thf(4180,plain,
! [SV721: $i,SV144: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ ( sK87_B @ SV144 ) )
| ~ ( subset @ SV721 @ SV707 ) )
= $true )
| ( ( in @ SV721 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4181,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4009]) ).
thf(4182,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
| ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4010]) ).
thf(4183,plain,
! [SV437: $i,SV145: $i,SV507: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV507 ) )
= $true )
| ( ( ( in @ SV722 @ SV145 )
| ( in @ SV722 @ SV437 ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4184,plain,
! [SV437: $i,SV507: $i,SV145: $i] :
( ( ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4013]) ).
thf(4185,plain,
! [SV145: $i,SV507: $i,SV437: $i] :
( ( ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4013]) ).
thf(4186,plain,
! [SV739: $i,SV146: $i,SV551: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SV739 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4187,plain,
! [SV552: $i,SV146: $i,SV740: $i] :
( ( ( ! [SY1522: $i] :
~ ( in @ ( ordered_pair @ SV740 @ SY1522 ) @ SV146 )
| ( in @ SV740 @ SV552 ) )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4188,plain,
! [SV146: $i,SV552: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV552 )
| ( in @ ( ordered_pair @ SV741 @ ( sK96_D @ SV741 @ SV552 @ SV146 ) ) @ SV146 ) )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4189,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 ) )
= $false )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4020]) ).
thf(4190,plain,
! [SV342: $i,SV438: $i] :
( ( ( ~ ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4020]) ).
thf(4191,plain,
! [SV555: $i,SV611: $i] :
( ( ( ( SV611
!= ( identity_relation @ SV555 ) ) )
= $true )
| ( ( ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true )
| ( ( function @ SV611 )
= $false )
| ( ( relation @ SV611 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4021]) ).
thf(4192,plain,
! [SV556: $i,SV612: $i] :
( ( ( ( SV612
!= ( identity_relation @ SV556 ) ) )
= $true )
| ( ( ( relation_dom @ SV612 )
= SV556 )
= $true )
| ( ( function @ SV612 )
= $false )
| ( ( relation @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4022]) ).
thf(4193,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4023]) ).
thf(4194,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4023]) ).
thf(4195,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 )
| ~ ( in @ SV723 @ SV558 )
| ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 )
| ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4025]) ).
thf(4196,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4026]) ).
thf(4197,plain,
! [SV151: $i,SV559: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
| ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4027]) ).
thf(4198,plain,
! [SV151: $i,SV560: $i] :
( ( ( ~ ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) ) )
= $false )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4028]) ).
thf(4199,plain,
! [SV560: $i,SV151: $i] :
( ( ( ~ ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) )
= $false )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4028]) ).
thf(4200,plain,
! [SV508: $i,SV449: $i,SV742: $i,SV153: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV153 )
| ~ ( in @ SV742 @ SV449 )
| ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SV742 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4029]) ).
thf(4201,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4202,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4030]) ).
thf(4203,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV153: $i] :
( ( ( ! [SY1515: $i,SY1516: $i] :
( ~ ( in @ SY1515 @ SV153 )
| ~ ( in @ SY1516 @ SV450 )
| ( SV725
!= ( ordered_pair @ SY1515 @ SY1516 ) ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4204,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV509 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SV726
!= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) ) ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4205,plain,
! [SV357: $i,SV455: $i,SV709: $i] :
( ( ( in @ SV709 @ SV455 )
= $false )
| ( ( subset @ SV709 @ SV357 )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4206,plain,
! [SV455: $i,SV357: $i,SV710: $i] :
( ( ( subset @ SV710 @ SV357 )
= $false )
| ( ( in @ SV710 @ SV455 )
= $true )
| ( ( SV455
= ( powerset @ SV357 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4207,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
| ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4208,plain,
! [SV360: $i,SV458: $i] :
( ( ( one_to_one @ SV458 )
= $false )
| ( ( in @ SV360 @ ( relation_rng @ SV458 ) )
= $false )
| ( ( SV360
= ( apply @ SV458 @ ( apply @ ( function_inverse @ SV458 ) @ SV360 ) ) )
= $true )
| ( ( function @ SV458 )
= $false )
| ( ( relation @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4209,plain,
! [SV361: $i,SV459: $i] :
( ( ( one_to_one @ SV459 )
= $false )
| ( ( in @ SV361 @ ( relation_rng @ SV459 ) )
= $false )
| ( ( SV361
= ( apply @ ( relation_composition @ ( function_inverse @ SV459 ) @ SV459 ) @ SV361 ) )
= $true )
| ( ( function @ SV459 )
= $false )
| ( ( relation @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4210,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ~ ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) )
| ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) ) )
= $false )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4040]) ).
thf(4211,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) ) )
= $false )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4040]) ).
thf(4212,plain,
! [SV687: $i,SV648: $i,SV154: $i] :
( ( ( ~ ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) )
| ~ ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4213,plain,
! [SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
| ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4214,plain,
! [SV364: $i] :
( ( ( ( sK20_B @ SV364 )
= ( sK21_SY619 @ SV364 ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4215,plain,
! [SV727: $i,SV365: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SV727 @ ( relation_dom @ SV365 ) )
| ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) ) )
= $true )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4044]) ).
thf(4216,plain,
! [SV368: $i] :
( ( ( in @ ( ordered_pair @ ( sK82_B @ SV368 ) @ ( sK83_SY653 @ SV368 ) ) @ SV368 )
= $true )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4045]) ).
thf(4217,plain,
! [SV368: $i] :
( ( ( in @ ( ordered_pair @ ( sK83_SY653 @ SV368 ) @ ( sK82_B @ SV368 ) ) @ SV368 )
= $true )
| ( ( antisymmetric @ SV368 )
= $true )
| ( ( relation @ SV368 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4046]) ).
thf(4218,plain,
! [SV369: $i,SV688: $i,SV649: $i] :
( ( ( in @ ( ordered_pair @ SV649 @ SV688 ) @ SV369 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV688 @ SV649 ) @ SV369 ) )
= $true )
| ( ( SV649 = SV688 )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4219,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
= $false )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
= $true )
| ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4220,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4049]) ).
thf(4221,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
| ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 ) )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4050]) ).
thf(4222,plain,
! [SV511: $i,SV463: $i,SV155: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV155 )
| ( in @ SV728 @ SV463 ) )
= $true )
| ( ( in @ SV728 @ SV511 )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4051]) ).
thf(4223,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ~ ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4052]) ).
thf(4224,plain,
! [SV155: $i,SV463: $i,SV511: $i] :
( ( ( ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4052]) ).
thf(4225,plain,
! [SV712: $i,SV370: $i,SV464: $i] :
( ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV712 )
= $false )
| ( ( ~ ( in @ SV712 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4226,plain,
! [SV370: $i,SV464: $i] :
( ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ ( sK35_SY627 @ SV464 @ SV370 ) )
= $true )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4054]) ).
thf(4227,plain,
! [SV370: $i,SV464: $i] :
( ( ( in @ ( sK35_SY627 @ SV464 @ SV370 ) @ SV370 )
= $true )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4055]) ).
thf(4228,plain,
! [SV465: $i,SV371: $i,SV743: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ SV743 )
| ~ ( in @ SV743 @ SV371 ) )
= $true )
| ( ( in @ SV713 @ SV465 )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4056]) ).
thf(4229,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( in @ SV714 @ SV465 )
= $false )
| ( ( ~ ( ~ ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4230,plain,
! [SV512: $i,SV564: $i,SV285: $i,SV156: $i] :
( ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV564 )
= $false )
| ( ( in @ SV156 @ SV512 )
= $false )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV512 ) @ SV564 ) )
= $true )
| ( ( relation @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4231,plain,
! [SV689: $i,SV650: $i,SV285: $i,SV156: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SV689 ) ) )
= $true )
| ( ( in @ SV156 @ SV650 )
= $true )
| ( ( relation @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4232,plain,
! [SV690: $i,SV651: $i,SV285: $i,SV156: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SV690 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV690 )
= $true )
| ( ( relation @ SV690 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4233,plain,
! [SV467: $i,SV373: $i,SV715: $i] :
( ( ( SV715 = SV373 )
= $false )
| ( ( in @ SV715 @ SV467 )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4234,plain,
! [SV373: $i,SV467: $i,SV716: $i] :
( ( ( in @ SV716 @ SV467 )
= $false )
| ( ( SV716 = SV373 )
= $true )
| ( ( SV467
= ( singleton @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4063]) ).
thf(4235,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( function @ SV717 ) )
= $true )
| ( ( ~ ( relation @ SV717 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) )
| ( SV717
= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4236,plain,
! [SV157: $i] :
( ( ( ! [SY904: $i] :
( ~ ( function @ SY904 )
| ~ ( relation @ SY904 )
| ( SY904
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY905: $i,SY906: $i] :
( ( SY906
!= ( apply @ SY904 @ SY905 ) )
| ~ ( in @ SY905 @ ( relation_rng @ SV157 ) )
| ( SY905
= ( apply @ SV157 @ SY906 ) ) )
| ~ ! [SY907: $i,SY908: $i] :
( ( SY908
!= ( apply @ SY904 @ SY907 ) )
| ~ ( in @ SY907 @ ( relation_rng @ SV157 ) )
| ( in @ SY908 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY909: $i,SY910: $i] :
( ( SY909
!= ( apply @ SV157 @ SY910 ) )
| ~ ( in @ SY910 @ ( relation_dom @ SV157 ) )
| ( SY910
= ( apply @ SY904 @ SY909 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4065]) ).
thf(4237,plain,
! [SV157: $i] :
( ( ( ! [SY913: $i] :
( ~ ( function @ SY913 )
| ~ ( relation @ SY913 )
| ( SY913
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SY913 )
= ( relation_rng @ SV157 ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4066]) ).
thf(4238,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
| ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4239,plain,
! [SV470: $i,SV159: $i,SV513: $i,SV691: $i] :
( ( ( in @ SV691 @ ( relation_rng @ SV513 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 ) )
= $true )
| ( ( ~ ( in @ SV691 @ SV470 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4069]) ).
thf(4240,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4070]) ).
thf(4241,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ SV471 )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4071]) ).
thf(4242,plain,
! [SV619: $i,SV652: $i,SV161: $i] :
( ( ( in @ SV161 @ ( relation_restriction @ SV652 @ SV619 ) )
= $false )
| ( ( in @ SV161 @ SV652 )
= $true )
| ( ( relation @ SV652 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4243,plain,
! [SV620: $i,SV653: $i,SV161: $i] :
( ( ( in @ SV161 @ ( relation_restriction @ SV653 @ SV620 ) )
= $false )
| ( ( in @ SV161 @ ( cartesian_product2 @ SV620 @ SV620 ) )
= $true )
| ( ( relation @ SV653 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4244,plain,
! [SV164: $i,SV520: $i,SV481: $i] :
( ( ( in @ SV481 @ ( relation_dom @ SV520 ) )
= $false )
| ( ( ~ ( in @ SV481 @ SV164 ) )
= $true )
| ( ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4075]) ).
thf(4245,plain,
! [SV164: $i,SV622: $i,SV654: $i] :
( ( ( relation @ SV654 )
= $false )
| ( ( function @ SV654 )
= $false )
| ( ( ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
| ( in @ SV622 @ ( relation_dom @ SV654 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4246,plain,
! [SV164: $i,SV623: $i,SV655: $i] :
( ( ( relation @ SV655 )
= $false )
| ( ( function @ SV655 )
= $false )
| ( ( ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
| ( in @ SV623 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4247,plain,
! [SV729: $i,SV167: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ ( sK80_B @ SV167 ) )
| ~ ( subset @ SV729 @ SV718 ) )
= $true )
| ( ( in @ SV729 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4078]) ).
thf(4248,plain,
! [SV168: $i,SV523: $i,SV485: $i] :
( ( ( SV485
= ( apply @ SV523 @ SV168 ) )
= $false )
| ( ( ~ ( in @ SV168 @ ( relation_dom @ SV523 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4249,plain,
! [SV625: $i,SV168: $i,SV656: $i] :
( ( ( relation @ SV656 )
= $false )
| ( ( function @ SV656 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
| ( SV625
= ( apply @ SV656 @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4250,plain,
! [SV626: $i,SV168: $i,SV657: $i] :
( ( ( relation @ SV657 )
= $false )
| ( ( function @ SV657 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
| ( in @ SV168 @ ( relation_dom @ SV657 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4251,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4252,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4082]) ).
thf(4253,plain,
! [SV694: $i,SV659: $i,SV169: $i] :
( ( ( ~ ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) )
| ~ ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4254,plain,
! [SV170: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( relation_dom @ SV170 ) ) )
= $true )
| ( ( ! [SY1517: $i] :
( ( SY1517
!= ( apply @ SV170 @ SV730 ) )
| ( in @ ( ordered_pair @ SV730 @ SY1517 ) @ SV170 ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4255,plain,
! [SV170: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( relation_dom @ SV170 ) ) )
= $true )
| ( ( ! [SY1518: $i] :
( ~ ( in @ ( ordered_pair @ SV731 @ SY1518 ) @ SV170 )
| ( SY1518
= ( apply @ SV170 @ SV731 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4256,plain,
! [SV170: $i,SV732: $i] :
( ( ( in @ SV732 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( ! [SY1519: $i] :
( ( SY1519
!= ( apply @ SV170 @ SV732 ) )
| ( SY1519 = empty_set ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4257,plain,
! [SV170: $i,SV733: $i] :
( ( ( in @ SV733 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( ! [SY1520: $i] :
( ( SY1520 != empty_set )
| ( SY1520
= ( apply @ SV170 @ SV733 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4087]) ).
thf(4258,plain,
! [SV627: $i,SV660: $i,SV171: $i] :
( ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV660 @ SV627 ) ) )
= $false )
| ( ( in @ SV171 @ SV627 )
= $true )
| ( ( relation @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4259,plain,
! [SV628: $i,SV661: $i,SV171: $i] :
( ( ( in @ SV171 @ ( relation_dom @ ( relation_dom_restriction @ SV661 @ SV628 ) ) )
= $false )
| ( ( in @ SV171 @ ( relation_dom @ SV661 ) )
= $true )
| ( ( relation @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4260,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4261,plain,
! [SV397: $i,SV172: $i,SV696: $i] :
( ( ( ( SV696
!= ( relation_composition @ SV172 @ SV397 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) ) )
= $true )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4092]) ).
thf(4262,plain,
! [SV173: $i,SV579: $i,SV744: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV744 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 ) )
= $true )
| ( ( ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4263,plain,
! [SV580: $i,SV173: $i,SV745: $i] :
( ( ( ! [SY1523: $i] :
~ ( in @ ( ordered_pair @ SY1523 @ SV745 ) @ SV173 )
| ( in @ SV745 @ SV580 ) )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4264,plain,
! [SV173: $i,SV580: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV580 )
| ( in @ ( ordered_pair @ ( sK26_D @ SV746 @ SV580 @ SV173 ) @ SV746 ) @ SV173 ) )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4265,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4097]) ).
thf(4266,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4097]) ).
thf(4267,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
= $true )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 ) )
= $true )
| ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4098]) ).
thf(4268,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ SV582 )
| ( SV747 = SV526 )
| ( SV747 = SV174 )
| ( SV747 = SV288 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4269,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i] :
( ( ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) )
| ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4270,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
| ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4101]) ).
thf(4271,plain,
! [SV664: $i,SV583: $i] :
( ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4102]) ).
thf(4272,plain,
! [SV584: $i,SV665: $i] :
( ( ( ~ ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) ) )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4273,plain,
! [SV584: $i,SV665: $i] :
( ( ( ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4103]) ).
thf(4274,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4106]) ).
thf(4275,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
| ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4107]) ).
thf(4276,plain,
! [SV490: $i,SV175: $i,SV528: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV528 ) )
= $true )
| ( ( ( SV734 = SV175 )
| ( SV734 = SV490 ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4109]) ).
thf(4277,plain,
! [SV490: $i,SV528: $i,SV175: $i] :
( ( ( ~ ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4110]) ).
thf(4278,plain,
! [SV175: $i,SV528: $i,SV490: $i] :
( ( ( ~ ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4110]) ).
thf(4279,plain,
! [SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK84_B @ SV400 ) @ ( sK85_SY654 @ SV400 ) ) @ SV400 )
= $true )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4111]) ).
thf(4280,plain,
! [SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK85_SY654 @ SV400 ) @ ( sK86_SY656 @ SV400 ) ) @ SV400 )
= $true )
| ( ( transitive @ SV400 )
= $true )
| ( ( relation @ SV400 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4112]) ).
thf(4281,plain,
! [SV719: $i,SV401: $i,SV699: $i,SV666: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV699 @ SV719 ) @ SV401 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV666 @ SV719 ) @ SV401 )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4282,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( function @ SV700 )
= $false )
| ( ( ~ ( relation @ SV700 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4283,plain,
! [SV289: $i,SV176: $i,SV748: $i] :
( ( ( ~ ( function @ SV748 )
| ~ ( relation @ SV748 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SV748 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4115]) ).
thf(4284,plain,
! [SV289: $i,SV176: $i,SV749: $i] :
( ( ( ~ ( function @ SV749 )
| ~ ( relation @ SV749 )
| ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
| ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4285,plain,
! [SV290: $i,SV178: $i,SV735: $i] :
( ( ( ~ ( ordinal @ SV735 ) )
= $true )
| ( ( ~ ( in @ SV735 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4117]) ).
thf(4286,plain,
! [SV290: $i,SV178: $i] :
( ( ( subset @ SV178 @ SV290 )
= $false )
| ( ( SV178 = empty_set )
= $true )
| ( ( in @ ( sK77_C @ SV290 @ SV178 ) @ SV178 )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4118]) ).
thf(4287,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4121]) ).
thf(4288,plain,
! [SV181: $i,SV591: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
| ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4122]) ).
thf(4289,plain,
! [SV592: $i,SV181: $i] :
( ( ( ~ ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) ) )
= $false )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4123]) ).
thf(4290,plain,
! [SV181: $i,SV592: $i] :
( ( ( ~ ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) )
= $false )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4123]) ).
thf(4291,plain,
! [SV408: $i,SV493: $i] :
( ( ( function @ SV493 )
= $false )
| ( ( relation @ SV408 )
= $false )
| ( ( function @ SV408 )
= $false )
| ( ( relation @ SV493 )
= $false )
| ( ( function @ ( relation_composition @ SV408 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4124]) ).
thf(4292,plain,
! [SV409: $i,SV494: $i] :
( ( ( function @ SV494 )
= $false )
| ( ( relation @ SV409 )
= $false )
| ( ( function @ SV409 )
= $false )
| ( ( relation @ SV494 )
= $false )
| ( ( relation @ ( relation_composition @ SV409 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4293,plain,
! [SV182: $i,SV669: $i] :
( ( ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) )
| ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4126]) ).
thf(4294,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
| ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4127]) ).
thf(4295,plain,
! [SV670: $i,SV182: $i] :
( ( ( ~ ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) ) )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4128]) ).
thf(4296,plain,
! [SV182: $i,SV670: $i] :
( ( ( ~ ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4128]) ).
thf(4297,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( function @ SV701 )
= $false )
| ( ( ~ ( relation @ SV701 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4129]) ).
thf(4298,plain,
! [SV184: $i,SV292: $i,SV750: $i] :
( ( ( ~ ( function @ SV750 )
| ~ ( relation @ SV750 )
| ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4299,plain,
! [SV184: $i,SV292: $i,SV751: $i] :
( ( ( ~ ( function @ SV751 )
| ~ ( relation @ SV751 )
| ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4300,plain,
! [SV410: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4133]) ).
thf(4301,plain,
! [SV410: $i] :
( ( ( ~ ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4133]) ).
thf(4302,plain,
! [SV635: $i,SV411: $i,SV593: $i] :
( ( ( in @ SV593 @ SV411 )
= $false )
| ( ( ~ ( in @ SV635 @ SV411 ) )
= $true )
| ( ( in @ SV593 @ SV635 )
= $true )
| ( ( SV593 = SV635 )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4303,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4135]) ).
thf(4304,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4135]) ).
thf(4305,plain,
! [SV637: $i,SV185: $i,SV595: $i] :
( ( ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) )
| ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4136]) ).
thf(4306,plain,
! [SV596: $i] :
( ( ( function @ SV596 )
= $false )
| ( ( empty @ SV596 )
= $false )
| ( ( relation @ SV596 )
= $false )
| ( ( function @ SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4307,plain,
! [SV597: $i] :
( ( ( function @ SV597 )
= $false )
| ( ( empty @ SV597 )
= $false )
| ( ( relation @ SV597 )
= $false )
| ( ( relation @ SV597 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4308,plain,
! [SV671: $i,SV638: $i,SV186: $i] :
( ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV638 @ SV671 ) ) )
= $false )
| ( ( in @ SV186 @ SV638 )
= $true )
| ( ( relation @ SV671 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4309,plain,
! [SV672: $i,SV639: $i,SV186: $i] :
( ( ( in @ SV186 @ ( relation_rng @ ( relation_rng_restriction @ SV639 @ SV672 ) ) )
= $false )
| ( ( in @ SV186 @ ( relation_rng @ SV672 ) )
= $true )
| ( ( relation @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4141]) ).
thf(4310,plain,
! [SV498: $i,SV187: $i,SV531: $i,SV702: $i] :
( ( ( in @ SV702 @ ( relation_dom @ SV531 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 ) )
= $true )
| ( ( ~ ( in @ SV702 @ SV498 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4311,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4143]) ).
thf(4312,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV499 )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4144]) ).
thf(4313,plain,
! [SV188: $i,SV598: $i] :
( ( ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV188 )
= $true )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4145]) ).
thf(4314,plain,
! [SV188: $i,SV598: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 ) )
= $true )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4146]) ).
thf(4315,plain,
! [SV599: $i,SV188: $i,SV752: $i,SV736: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV188 )
| ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV599 ) )
= $true )
| ( ( subset @ SV188 @ SV599 )
= $false )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4316,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
= $false )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 ) )
= $true )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4317,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4149]) ).
thf(4318,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
| ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4150]) ).
thf(4319,plain,
! [SV534: $i,SV501: $i,SV189: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV189 )
| ~ ( in @ SV737 @ SV501 ) )
= $true )
| ( ( in @ SV737 @ SV534 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4320,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ~ ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4321,plain,
! [SV189: $i,SV501: $i,SV534: $i] :
( ( ( ~ ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) )
= $false )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4152]) ).
thf(4322,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ! [SY1458: $i] :
( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SY1458 ) @ SV192 )
| ~ ( in @ SY1458 @ SV603 ) ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4323,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) ) )
= $true )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4324,plain,
! [SV641: $i,SV604: $i,SV192: $i] :
( ( ( ! [SY1459: $i] :
( ! [SY1426: $i] :
( ~ ( in @ ( ordered_pair @ SY1459 @ SY1426 ) @ SV192 )
| ~ ( in @ SY1426 @ SV604 ) )
| ( in @ SY1459 @ SV641 ) ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4157]) ).
thf(4325,plain,
! [SV192: $i,SV604: $i,SV641: $i] :
( ( ( ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1461 @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SY1461 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4158]) ).
thf(4326,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( ( sK67_C @ SV502 @ SV422 )
!= ( sK68_SY645 @ SV502 @ SV422 ) ) )
= $true )
| ( ( ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4327,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4328,plain,
! [SV422: $i,SV502: $i] :
( ( ( ~ ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) ) )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4329,plain,
! [SV503: $i,SV423: $i,SV753: $i] :
( ( ( ! [SY1525: $i] :
( ( SV753 != SY1525 )
| ~ ( in @ SV753 @ SV423 )
| ( in @ ( ordered_pair @ SV753 @ SY1525 ) @ SV503 ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4161]) ).
thf(4330,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) )
| ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4162]) ).
thf(4331,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4165]) ).
thf(4332,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4333,plain,
! [SV139: $i,SV544: $i,SV704: $i,SV679: $i] :
( ( ( SV679 = SV704 )
= $true )
| ( ( ~ ( in @ SV679 @ SV544 )
| ~ ( in @ SV704 @ SV544 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4334,plain,
! [SV140: $i,SV545: $i,SV605: $i,SV754: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV754 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ SV754 @ SV545 ) )
= $true )
| ( ( ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4335,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
| ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
= $false )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4336,plain,
! [SV606: $i,SV546: $i,SV140: $i,SV755: $i] :
( ( ( ! [SY1526: $i] :
( ~ ( in @ ( ordered_pair @ SY1526 @ SV755 ) @ SV140 )
| ~ ( in @ SY1526 @ SV546 ) )
| ( in @ SV755 @ SV606 ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4337,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV606 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4338,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4172]) ).
thf(4339,plain,
! [SV141: $i,SV547: $i] :
( ( ( in @ ( ordered_pair @ ( sK37_SY628 @ SV547 @ SV141 ) @ ( sK36_C @ SV547 @ SV141 ) ) @ SV141 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4173]) ).
thf(4340,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV548 )
| ~ ( in @ SV705 @ SV548 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4174]) ).
thf(4341,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4175]) ).
thf(4342,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4176]) ).
thf(4343,plain,
! [SV608: $i,SV282: $i,SV142: $i] :
( ( ( ~ ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4344,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4177]) ).
thf(4345,plain,
! [SV144: $i,SV609: $i,SV738: $i] :
( ( ( ~ ( subset @ SV738 @ SV609 ) )
= $true )
| ( ( in @ SV738 @ ( sK88_SY659 @ SV609 @ SV144 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4178]) ).
thf(4346,plain,
! [SV721: $i,SV144: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ ( sK87_B @ SV144 ) ) )
= $true )
| ( ( ~ ( subset @ SV721 @ SV707 ) )
= $true )
| ( ( in @ SV721 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4347,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4181]) ).
thf(4348,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4182]) ).
thf(4349,plain,
! [SV437: $i,SV145: $i,SV507: $i,SV722: $i] :
( ( ( in @ SV722 @ SV507 )
= $false )
| ( ( ( in @ SV722 @ SV145 )
| ( in @ SV722 @ SV437 ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4350,plain,
! [SV437: $i,SV507: $i,SV145: $i] :
( ( ( ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV145 )
| ( in @ SY1325 @ SV507 ) ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4184]) ).
thf(4351,plain,
! [SV145: $i,SV507: $i,SV437: $i] :
( ( ( ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV437 )
| ( in @ SY1326 @ SV507 ) ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4185]) ).
thf(4352,plain,
! [SV739: $i,SV146: $i,SV551: $i] :
( ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SV739 ) @ SV146 )
= $false )
| ( ( ~ ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 ) )
= $true )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4186]) ).
thf(4353,plain,
! [SV552: $i,SV146: $i,SV740: $i] :
( ( ( ! [SY1522: $i] :
~ ( in @ ( ordered_pair @ SV740 @ SY1522 ) @ SV146 ) )
= $true )
| ( ( in @ SV740 @ SV552 )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4354,plain,
! [SV146: $i,SV552: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV552 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV741 @ ( sK96_D @ SV741 @ SV552 @ SV146 ) ) @ SV146 )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4355,plain,
! [SV342: $i,SV438: $i] :
( ( ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
= $true )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4189]) ).
thf(4356,plain,
! [SV342: $i,SV438: $i] :
( ( ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
!= ( sK76_C @ SV438 @ SV342 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4190]) ).
thf(4357,plain,
! [SV555: $i,SV611: $i] :
( ( ( SV611
= ( identity_relation @ SV555 ) )
= $false )
| ( ( ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV555 )
| ( ( apply @ SV611 @ SY1439 )
= SY1439 ) ) )
= $true )
| ( ( function @ SV611 )
= $false )
| ( ( relation @ SV611 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4191]) ).
thf(4358,plain,
! [SV556: $i,SV612: $i] :
( ( ( SV612
= ( identity_relation @ SV556 ) )
= $false )
| ( ( ( relation_dom @ SV612 )
= SV556 )
= $true )
| ( ( function @ SV612 )
= $false )
| ( ( relation @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4359,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4193]) ).
thf(4360,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_SY611 @ SV557 @ SV149 ) @ ( sK15_SY613 @ SV557 @ SV149 ) ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4194]) ).
thf(4361,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 )
| ~ ( in @ SV723 @ SV558 )
| ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4362,plain,
! [SV151: $i,SV559: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4196]) ).
thf(4363,plain,
! [SV151: $i,SV559: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4364,plain,
! [SV151: $i,SV560: $i] :
( ( ( ! [SY1379: $i,SY1380: $i] :
( ~ ( in @ ( ordered_pair @ SY1379 @ SY1380 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1380 @ SY1379 ) @ SV151 ) ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4198]) ).
thf(4365,plain,
! [SV560: $i,SV151: $i] :
( ( ( ! [SY1381: $i,SY1382: $i] :
( ~ ( in @ ( ordered_pair @ SY1382 @ SY1381 ) @ SV151 )
| ( in @ ( ordered_pair @ SY1381 @ SY1382 ) @ SV560 ) ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4199]) ).
thf(4366,plain,
! [SV508: $i,SV449: $i,SV742: $i,SV153: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV153 )
| ~ ( in @ SV742 @ SV449 ) )
= $true )
| ( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SV742 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4367,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) ) )
= $true )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4201]) ).
thf(4368,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
= ( ordered_pair @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) ) )
= $true )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4202]) ).
thf(4369,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV153: $i,SV757: $i] :
( ( ( ! [SY1527: $i] :
( ~ ( in @ SV757 @ SV153 )
| ~ ( in @ SY1527 @ SV450 )
| ( SV725
!= ( ordered_pair @ SV757 @ SY1527 ) ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4370,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( in @ SV726 @ SV509 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SV726
!= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) ) ) )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4371,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4372,plain,
( ( ~ ( one_to_one @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4207]) ).
thf(4373,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) )
| ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4210]) ).
thf(4374,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
| ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4211]) ).
thf(4375,plain,
! [SV687: $i,SV648: $i,SV154: $i] :
( ( ( ~ ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) ) )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4212]) ).
thf(4376,plain,
! [SV154: $i,SV648: $i,SV687: $i] :
( ( ( ~ ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4212]) ).
thf(4377,plain,
! [SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4213]) ).
thf(4378,plain,
! [SV364: $i] :
( ( ( ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
!= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4213]) ).
thf(4379,plain,
! [SV727: $i,SV365: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( relation_dom @ SV365 ) )
| ~ ( in @ SV727 @ ( relation_dom @ SV365 ) ) )
= $true )
| ( ( ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) ) )
= $true )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4215]) ).
thf(4380,plain,
! [SV369: $i,SV649: $i,SV688: $i] :
( ( ( in @ ( ordered_pair @ SV688 @ SV649 ) @ SV369 )
= $false )
| ( ( in @ ( ordered_pair @ SV649 @ SV688 ) @ SV369 )
= $false )
| ( ( SV649 = SV688 )
= $true )
| ( ( antisymmetric @ SV369 )
= $false )
| ( ( relation @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4381,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 )
= $false )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
= $true )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
= $false )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4382,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4383,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( ~ ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 ) )
= $true )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4384,plain,
! [SV511: $i,SV463: $i,SV155: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV155 ) )
= $true )
| ( ( in @ SV728 @ SV463 )
= $true )
| ( ( in @ SV728 @ SV511 )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(4385,plain,
! [SV463: $i,SV155: $i,SV511: $i] :
( ( ( ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV511 )
| ( in @ SY1334 @ SV155 ) ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4223]) ).
thf(4386,plain,
! [SV155: $i,SV463: $i,SV511: $i] :
( ( ( ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SV511 )
| ~ ( in @ SY1335 @ SV463 ) ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4224]) ).
thf(4387,plain,
! [SV464: $i,SV370: $i,SV712: $i] :
( ( ( in @ SV712 @ SV370 )
= $false )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV712 )
= $false )
| ( ( ~ ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 ) )
= $true )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4388,plain,
! [SV465: $i,SV371: $i,SV743: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ SV743 ) )
= $true )
| ( ( ~ ( in @ SV743 @ SV371 ) )
= $true )
| ( ( in @ SV713 @ SV465 )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4228]) ).
thf(4389,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) )
| ~ ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 ) )
= $false )
| ( ( in @ SV714 @ SV465 )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4390,plain,
! [SV689: $i,SV650: $i,SV285: $i,SV156: $i] :
( ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV650 ) @ SV689 ) )
= $false )
| ( ( in @ SV156 @ SV650 )
= $true )
| ( ( relation @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4391,plain,
! [SV690: $i,SV651: $i,SV285: $i,SV156: $i] :
( ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ ( relation_composition @ ( identity_relation @ SV651 ) @ SV690 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV156 @ SV285 ) @ SV690 )
= $true )
| ( ( relation @ SV690 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4392,plain,
! [SV157: $i,SV717: $i] :
( ( ( function @ SV717 )
= $false )
| ( ( ~ ( relation @ SV717 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) )
| ( SV717
= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4393,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ( function @ SV758 )
| ~ ( relation @ SV758 )
| ( SV758
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4394,plain,
! [SV157: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 )
| ~ ( relation @ SV759 )
| ( SV759
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4395,plain,
( ( ~ ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4396,plain,
( ( ~ ( one_to_one @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4397,plain,
! [SV470: $i,SV513: $i,SV691: $i,SV159: $i] :
( ( ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 )
= $false )
| ( ( in @ SV691 @ ( relation_rng @ SV513 ) )
= $false )
| ( ( ~ ( in @ SV691 @ SV470 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4398,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
| ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4399,plain,
! [SV520: $i,SV164: $i,SV481: $i] :
( ( ( in @ SV481 @ SV164 )
= $false )
| ( ( in @ SV481 @ ( relation_dom @ SV520 ) )
= $false )
| ( ( in @ SV481 @ ( relation_dom @ ( relation_dom_restriction @ SV520 @ SV164 ) ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4400,plain,
! [SV164: $i,SV654: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) ) )
= $true )
| ( ( in @ SV622 @ ( relation_dom @ SV654 ) )
= $true )
| ( ( function @ SV654 )
= $false )
| ( ( relation @ SV654 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4401,plain,
! [SV164: $i,SV655: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) ) )
= $true )
| ( ( in @ SV623 @ SV164 )
= $true )
| ( ( function @ SV655 )
= $false )
| ( ( relation @ SV655 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4246]) ).
thf(4402,plain,
! [SV729: $i,SV167: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ ( sK80_B @ SV167 ) ) )
= $true )
| ( ( ~ ( subset @ SV729 @ SV718 ) )
= $true )
| ( ( in @ SV729 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4403,plain,
! [SV485: $i,SV523: $i,SV168: $i] :
( ( ( in @ SV168 @ ( relation_dom @ SV523 ) )
= $false )
| ( ( SV485
= ( apply @ SV523 @ SV168 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV168 @ SV485 ) @ SV523 )
= $true )
| ( ( function @ SV523 )
= $false )
| ( ( relation @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4404,plain,
! [SV656: $i,SV625: $i,SV168: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 ) )
= $true )
| ( ( SV625
= ( apply @ SV656 @ SV168 ) )
= $true )
| ( ( function @ SV656 )
= $false )
| ( ( relation @ SV656 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4249]) ).
thf(4405,plain,
! [SV657: $i,SV626: $i,SV168: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 ) )
= $true )
| ( ( in @ SV168 @ ( relation_dom @ SV657 ) )
= $true )
| ( ( function @ SV657 )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4406,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4251]) ).
thf(4407,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4252]) ).
thf(4408,plain,
! [SV694: $i,SV659: $i,SV169: $i] :
( ( ( ~ ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4409,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ~ ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4410,plain,
! [SV170: $i,SV730: $i] :
( ( ( in @ SV730 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( ! [SY1517: $i] :
( ( SY1517
!= ( apply @ SV170 @ SV730 ) )
| ( in @ ( ordered_pair @ SV730 @ SY1517 ) @ SV170 ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4411,plain,
! [SV170: $i,SV731: $i] :
( ( ( in @ SV731 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( ! [SY1518: $i] :
( ~ ( in @ ( ordered_pair @ SV731 @ SY1518 ) @ SV170 )
| ( SY1518
= ( apply @ SV170 @ SV731 ) ) ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4412,plain,
! [SV732: $i,SV170: $i,SV760: $i] :
( ( ( ( SV760
!= ( apply @ SV170 @ SV732 ) )
| ( SV760 = empty_set ) )
= $true )
| ( ( in @ SV732 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4413,plain,
! [SV733: $i,SV170: $i,SV761: $i] :
( ( ( ( SV761 != empty_set )
| ( SV761
= ( apply @ SV170 @ SV733 ) ) )
= $true )
| ( ( in @ SV733 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(4414,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
= $false )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4415,plain,
! [SV397: $i,SV172: $i,SV696: $i] :
( ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( ~ ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) ) )
= $true )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4261]) ).
thf(4416,plain,
! [SV173: $i,SV579: $i,SV744: $i] :
( ( ( in @ ( ordered_pair @ SV744 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
= $false )
| ( ( ~ ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 ) )
= $true )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4417,plain,
! [SV580: $i,SV173: $i,SV745: $i] :
( ( ( ! [SY1523: $i] :
~ ( in @ ( ordered_pair @ SY1523 @ SV745 ) @ SV173 ) )
= $true )
| ( ( in @ SV745 @ SV580 )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4418,plain,
! [SV173: $i,SV580: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ SV580 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK26_D @ SV746 @ SV580 @ SV173 ) @ SV746 ) @ SV173 )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4419,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4265]) ).
thf(4420,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4266]) ).
thf(4421,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
= $true )
| ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 )
= $true )
| ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
= $true )
| ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4422,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ SV582 ) )
= $true )
| ( ( ( SV747 = SV526 )
| ( SV747 = SV174 )
| ( SV747 = SV288 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4268]) ).
thf(4423,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i] :
( ( ( ~ ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4269]) ).
thf(4424,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4269]) ).
thf(4425,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4426,plain,
! [SV664: $i,SV583: $i] :
( ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SY1479 ) ) )
= $true )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4427,plain,
! [SV584: $i,SV665: $i] :
( ( ( ! [SY1480: $i] :
( ~ ( ~ ( in @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SY1480 @ ( sK50_D @ SY1480 @ SV665 @ SV584 ) ) )
| ( in @ SY1480 @ SV665 ) ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4272]) ).
thf(4428,plain,
! [SV584: $i,SV665: $i] :
( ( ( ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV665 )
| ! [SY1402: $i] :
( ~ ( in @ SY1402 @ SV584 )
| ( in @ SY1481 @ SY1402 ) ) ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4273]) ).
thf(4429,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 ) )
= $true )
| ( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4430,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 ) )
= $true )
| ( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4431,plain,
! [SV490: $i,SV175: $i,SV528: $i,SV734: $i] :
( ( ( in @ SV734 @ SV528 )
= $false )
| ( ( ( SV734 = SV175 )
| ( SV734 = SV490 ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4432,plain,
! [SV490: $i,SV528: $i,SV175: $i] :
( ( ( ! [SY1347: $i] :
( ( SY1347 != SV175 )
| ( in @ SY1347 @ SV528 ) ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4433,plain,
! [SV175: $i,SV528: $i,SV490: $i] :
( ( ( ! [SY1348: $i] :
( ( SY1348 != SV490 )
| ( in @ SY1348 @ SV528 ) ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4278]) ).
thf(4434,plain,
! [SV719: $i,SV401: $i,SV699: $i,SV666: $i] :
( ( ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV699 @ SV719 ) @ SV401 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV666 @ SV719 ) @ SV401 )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4281]) ).
thf(4435,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( relation @ SV700 )
= $false )
| ( ( function @ SV700 )
= $false )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
| ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4282]) ).
thf(4436,plain,
! [SV289: $i,SV176: $i,SV748: $i] :
( ( ( ~ ( function @ SV748 )
| ~ ( relation @ SV748 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SV748 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4437,plain,
! [SV289: $i,SV176: $i,SV749: $i] :
( ( ( ~ ( function @ SV749 )
| ~ ( relation @ SV749 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
| ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(4438,plain,
! [SV290: $i,SV178: $i,SV735: $i] :
( ( ( ordinal @ SV735 )
= $false )
| ( ( ~ ( in @ SV735 @ SV178 )
| ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 ) )
= $true )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4439,plain,
! [SV181: $i,SV591: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4287]) ).
thf(4440,plain,
! [SV181: $i,SV591: $i] :
( ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4441,plain,
! [SV592: $i,SV181: $i] :
( ( ( ! [SY1407: $i,SY1408: $i] :
( ~ ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV181 )
| ( in @ ( ordered_pair @ SY1407 @ SY1408 ) @ SV592 ) ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4289]) ).
thf(4442,plain,
! [SV181: $i,SV592: $i] :
( ( ( ! [SY1409: $i,SY1410: $i] :
( ~ ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV592 )
| ( in @ ( ordered_pair @ SY1409 @ SY1410 ) @ SV181 ) ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4290]) ).
thf(4443,plain,
! [SV182: $i,SV669: $i] :
( ( ( ! [SY1485: $i] :
( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SY1485 ) )
| ~ ( in @ SY1485 @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4444,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4294]) ).
thf(4445,plain,
! [SV670: $i,SV182: $i] :
( ( ( ! [SY1486: $i] :
( ! [SY1037: $i] :
( ( SY1486
!= ( apply @ SV182 @ SY1037 ) )
| ~ ( in @ SY1037 @ ( relation_dom @ SV182 ) ) )
| ( in @ SY1486 @ SV670 ) ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4295]) ).
thf(4446,plain,
! [SV182: $i,SV670: $i] :
( ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV670 )
| ~ ( ( SY1488
!= ( apply @ SV182 @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SY1488 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4296]) ).
thf(4447,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( relation @ SV701 )
= $false )
| ( ( function @ SV701 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
| ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4448,plain,
! [SV184: $i,SV292: $i,SV750: $i] :
( ( ( ~ ( function @ SV750 )
| ~ ( relation @ SV750 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4298]) ).
thf(4449,plain,
! [SV184: $i,SV292: $i,SV751: $i] :
( ( ( ~ ( function @ SV751 )
| ~ ( relation @ SV751 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4450,plain,
! [SV410: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4300]) ).
thf(4451,plain,
! [SV410: $i] :
( ( ( ~ ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) ) )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4301]) ).
thf(4452,plain,
! [SV593: $i,SV411: $i,SV635: $i] :
( ( ( in @ SV635 @ SV411 )
= $false )
| ( ( in @ SV593 @ SV411 )
= $false )
| ( ( in @ SV593 @ SV635 )
= $true )
| ( ( SV593 = SV635 )
= $true )
| ( ( in @ SV635 @ SV593 )
= $true )
| ( ( epsilon_connected @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4453,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4303]) ).
thf(4454,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4304]) ).
thf(4455,plain,
! [SV637: $i,SV185: $i,SV595: $i] :
( ( ( ~ ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4305]) ).
thf(4456,plain,
! [SV185: $i,SV595: $i,SV637: $i] :
( ( ( ~ ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4305]) ).
thf(4457,plain,
! [SV498: $i,SV531: $i,SV187: $i,SV702: $i] :
( ( ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 )
= $false )
| ( ( in @ SV702 @ ( relation_dom @ SV531 ) )
= $false )
| ( ( ~ ( in @ SV702 @ SV498 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4458,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
| ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4459,plain,
! [SV188: $i,SV598: $i] :
( ( ( in @ ( ordered_pair @ ( sK100_C @ SV598 @ SV188 ) @ ( sK101_SY666 @ SV598 @ SV188 ) ) @ SV598 )
= $false )
| ( ( subset @ SV188 @ SV598 )
= $true )
| ( ( relation @ SV598 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4314]) ).
thf(4460,plain,
! [SV599: $i,SV188: $i,SV752: $i,SV736: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV188 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV599 )
= $true )
| ( ( subset @ SV188 @ SV599 )
= $false )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4461,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
= $false )
| ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
= $false )
| ( ( ~ ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 ) )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4462,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
= $true )
| ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4463,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
= $true )
| ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 )
= $true )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(4464,plain,
! [SV534: $i,SV501: $i,SV189: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV189 ) )
= $true )
| ( ( ~ ( in @ SV737 @ SV501 ) )
= $true )
| ( ( in @ SV737 @ SV534 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4465,plain,
! [SV501: $i,SV189: $i,SV534: $i] :
( ( ( ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV534 )
| ( in @ SY1351 @ SV189 ) ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4320]) ).
thf(4466,plain,
! [SV189: $i,SV501: $i,SV534: $i] :
( ( ( ! [SY1352: $i] :
( ~ ( in @ SY1352 @ SV534 )
| ( in @ SY1352 @ SV501 ) ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4321]) ).
thf(4467,plain,
! [SV762: $i,SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV762 ) @ SV192 )
| ~ ( in @ SV762 @ SV603 ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4468,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
= $false )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4469,plain,
! [SV641: $i,SV604: $i,SV192: $i,SV763: $i] :
( ( ( ! [SY1536: $i] :
( ~ ( in @ ( ordered_pair @ SV763 @ SY1536 ) @ SV192 )
| ~ ( in @ SY1536 @ SV604 ) )
| ( in @ SV763 @ SV641 ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4470,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV641 )
| ~ ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4471,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
= $false )
| ( ( ~ ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4472,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4327]) ).
thf(4473,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
| ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4328]) ).
thf(4474,plain,
! [SV503: $i,SV423: $i,SV765: $i,SV753: $i] :
( ( ( ( SV753 != SV765 )
| ~ ( in @ SV753 @ SV423 )
| ( in @ ( ordered_pair @ SV753 @ SV765 ) @ SV503 ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(4475,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4476,plain,
! [SV423: $i,SV503: $i] :
( ( ( ~ ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) )
= $false )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4330]) ).
thf(4477,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
| ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4478,plain,
! [SV139: $i,SV543: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV543 @ SV139 ) @ ( sK25_SY621 @ SV543 @ SV139 ) ) @ SV139 )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4479,plain,
! [SV139: $i,SV704: $i,SV544: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV544 ) )
= $true )
| ( ( ~ ( in @ SV704 @ SV544 ) )
= $true )
| ( ( SV679 = SV704 )
= $true )
| ( ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(4480,plain,
! [SV140: $i,SV545: $i,SV605: $i,SV754: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV754 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 ) )
= $true )
| ( ( ~ ( in @ SV754 @ SV545 ) )
= $true )
| ( ( ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4334]) ).
thf(4481,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 ) )
= $false )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4335]) ).
thf(4482,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( ~ ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 ) )
= $false )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4335]) ).
thf(4483,plain,
! [SV606: $i,SV546: $i,SV140: $i,SV755: $i] :
( ( ( ! [SY1526: $i] :
( ~ ( in @ ( ordered_pair @ SY1526 @ SV755 ) @ SV140 )
| ~ ( in @ SY1526 @ SV546 ) ) )
= $true )
| ( ( in @ SV755 @ SV606 )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4484,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV606 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4337]) ).
thf(4485,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
| ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4486,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV548 ) )
= $true )
| ( ( ~ ( in @ SV705 @ SV548 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4340]) ).
thf(4487,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4341]) ).
thf(4488,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4489,plain,
! [SV608: $i,SV282: $i,SV142: $i] :
( ( ( ! [SY1432: $i,SY1433: $i] :
( ~ ( in @ SY1433 @ SV142 )
| ~ ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV282 )
| ( in @ ( ordered_pair @ SY1432 @ SY1433 ) @ SV608 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4343]) ).
thf(4490,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4344]) ).
thf(4491,plain,
! [SV144: $i,SV609: $i,SV738: $i] :
( ( ( subset @ SV738 @ SV609 )
= $false )
| ( ( in @ SV738 @ ( sK88_SY659 @ SV609 @ SV144 ) )
= $true )
| ( ( ~ ( in @ SV609 @ ( sK87_B @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4492,plain,
! [SV721: $i,SV144: $i,SV707: $i] :
( ( ( in @ SV707 @ ( sK87_B @ SV144 ) )
= $false )
| ( ( ~ ( subset @ SV721 @ SV707 ) )
= $true )
| ( ( in @ SV721 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4493,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $false )
| ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4494,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $false )
| ( ( ~ ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 ) )
= $true )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4348]) ).
thf(4495,plain,
! [SV507: $i,SV437: $i,SV145: $i,SV722: $i] :
( ( ( in @ SV722 @ SV145 )
= $true )
| ( ( in @ SV722 @ SV437 )
= $true )
| ( ( in @ SV722 @ SV507 )
= $false )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4496,plain,
! [SV437: $i,SV507: $i,SV145: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV145 )
| ( in @ SV766 @ SV507 ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(4497,plain,
! [SV145: $i,SV507: $i,SV437: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV437 )
| ( in @ SV767 @ SV507 ) )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(4498,plain,
! [SV739: $i,SV146: $i,SV551: $i] :
( ( ( in @ ( sK97_C @ SV551 @ SV146 ) @ SV551 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK97_C @ SV551 @ SV146 ) @ SV739 ) @ SV146 )
= $false )
| ( ( SV551
= ( relation_dom @ SV146 ) )
= $true )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4352]) ).
thf(4499,plain,
! [SV552: $i,SV146: $i,SV768: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV740 @ SV768 ) @ SV146 ) )
= $true )
| ( ( in @ SV740 @ SV552 )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(4500,plain,
! [SV146: $i,SV552: $i,SV741: $i] :
( ( ( in @ SV741 @ SV552 )
= $false )
| ( ( in @ ( ordered_pair @ SV741 @ ( sK96_D @ SV741 @ SV552 @ SV146 ) ) @ SV146 )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4501,plain,
! [SV342: $i,SV438: $i] :
( ( ( ( relation_dom @ SV438 )
= SV342 )
= $false )
| ( ( in @ ( sK76_C @ SV438 @ SV342 ) @ SV342 )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4502,plain,
! [SV342: $i,SV438: $i] :
( ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
= ( sK76_C @ SV438 @ SV342 ) )
= $false )
| ( ( ( ( relation_dom @ SV438 )
!= SV342 ) )
= $true )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4503,plain,
! [SV611: $i,SV555: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV555 )
| ( ( apply @ SV611 @ SV769 )
= SV769 ) )
= $true )
| ( ( SV611
= ( identity_relation @ SV555 ) )
= $false )
| ( ( function @ SV611 )
= $false )
| ( ( relation @ SV611 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4504,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4505,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 )
| ~ ( in @ SV723 @ SV558 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4361]) ).
thf(4506,plain,
! [SV151: $i,SV559: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 ) )
= $true )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4362]) ).
thf(4507,plain,
! [SV151: $i,SV560: $i,SV770: $i] :
( ( ( ! [SY1537: $i] :
( ~ ( in @ ( ordered_pair @ SV770 @ SY1537 ) @ SV560 )
| ( in @ ( ordered_pair @ SY1537 @ SV770 ) @ SV151 ) ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(4508,plain,
! [SV560: $i,SV151: $i,SV771: $i] :
( ( ( ! [SY1538: $i] :
( ~ ( in @ ( ordered_pair @ SY1538 @ SV771 ) @ SV151 )
| ( in @ ( ordered_pair @ SV771 @ SY1538 ) @ SV560 ) ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4509,plain,
! [SV508: $i,SV449: $i,SV742: $i,SV153: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV742 @ SV449 ) )
= $true )
| ( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SV742 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4510,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4367]) ).
thf(4511,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV772: $i,SV153: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV153 )
| ~ ( in @ SV772 @ SV450 )
| ( SV725
!= ( ordered_pair @ SV757 @ SV772 ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4512,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
| ( SV726
!= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4370]) ).
thf(4513,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4371]) ).
thf(4514,plain,
( ( one_to_one @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4515,plain,
! [SV686: $i,SV647: $i,SV154: $i] :
( ( ( ! [SY1495: $i] :
( ~ ( in @ SY1495 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1495 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SY1495 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4516,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) ) )
= $true )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4374]) ).
thf(4517,plain,
! [SV687: $i,SV648: $i,SV154: $i] :
( ( ( ! [SY1496: $i] :
( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1469 @ SV648 )
| ( SY1496
!= ( apply @ SV154 @ SY1469 ) ) )
| ( in @ SY1496 @ SV687 ) ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4375]) ).
thf(4518,plain,
! [SV154: $i,SV648: $i,SV687: $i] :
( ( ( ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SY1498
!= ( apply @ SV154 @ ( sK62_E @ SY1498 @ SV687 @ SV648 @ SV154 ) ) ) ) ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4376]) ).
thf(4519,plain,
! [SV364: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4377]) ).
thf(4520,plain,
! [SV364: $i] :
( ( ( ( apply @ SV364 @ ( sK20_B @ SV364 ) )
= ( apply @ SV364 @ ( sK21_SY619 @ SV364 ) ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4378]) ).
thf(4521,plain,
! [SV727: $i,SV365: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ ( relation_dom @ SV365 ) ) )
= $true )
| ( ( ~ ( in @ SV727 @ ( relation_dom @ SV365 ) ) )
= $true )
| ( ( ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) ) )
= $true )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4379]) ).
thf(4522,plain,
! [SV155: $i,SV462: $i,SV510: $i] :
( ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV462 )
= $false )
| ( ( in @ ( sK32_D @ SV510 @ SV462 @ SV155 ) @ SV510 )
= $true )
| ( ( SV510
= ( set_difference @ SV155 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4523,plain,
! [SV511: $i,SV463: $i,SV155: $i,SV728: $i] :
( ( ( in @ SV728 @ SV155 )
= $false )
| ( ( in @ SV728 @ SV463 )
= $true )
| ( ( in @ SV728 @ SV511 )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4524,plain,
! [SV463: $i,SV155: $i,SV511: $i,SV773: $i] :
( ( ( ~ ( in @ SV773 @ SV511 )
| ( in @ SV773 @ SV155 ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4525,plain,
! [SV155: $i,SV463: $i,SV511: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV511 )
| ~ ( in @ SV774 @ SV463 ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(4526,plain,
! [SV712: $i,SV370: $i,SV464: $i] :
( ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV464 )
= $false )
| ( ( in @ ( sK34_C @ SV464 @ SV370 ) @ SV712 )
= $false )
| ( ( in @ SV712 @ SV370 )
= $false )
| ( ( SV464
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4527,plain,
! [SV465: $i,SV371: $i,SV743: $i,SV713: $i] :
( ( ( in @ SV713 @ SV743 )
= $false )
| ( ( ~ ( in @ SV743 @ SV371 ) )
= $true )
| ( ( in @ SV713 @ SV465 )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4528,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) ) )
= $false )
| ( ( in @ SV714 @ SV465 )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4389]) ).
thf(4529,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( ~ ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 ) )
= $false )
| ( ( in @ SV714 @ SV465 )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4389]) ).
thf(4530,plain,
! [SV157: $i,SV717: $i] :
( ( ( relation @ SV717 )
= $false )
| ( ( function @ SV717 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) )
| ( SV717
= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4531,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ( function @ SV758 )
| ~ ( relation @ SV758 ) )
= $true )
| ( ( ( SV758
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4532,plain,
! [SV157: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 )
| ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV759
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4394]) ).
thf(4533,plain,
( ( ~ ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4395]) ).
thf(4534,plain,
( ( one_to_one @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4396]) ).
thf(4535,plain,
! [SV159: $i,SV513: $i,SV470: $i,SV691: $i] :
( ( ( in @ SV691 @ SV470 )
= $false )
| ( ( in @ SV691 @ ( relation_rng @ SV513 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV691 ) @ SV513 )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV513 @ SV470 ) )
= $true )
| ( ( relation @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4536,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( ~ ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4537,plain,
! [SV471: $i,SV514: $i,SV159: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 ) )
= $false )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4538,plain,
! [SV164: $i,SV654: $i,SV622: $i] :
( ( ( in @ SV622 @ ( relation_dom @ ( relation_dom_restriction @ SV654 @ SV164 ) ) )
= $false )
| ( ( in @ SV622 @ ( relation_dom @ SV654 ) )
= $true )
| ( ( function @ SV654 )
= $false )
| ( ( relation @ SV654 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4539,plain,
! [SV164: $i,SV655: $i,SV623: $i] :
( ( ( in @ SV623 @ ( relation_dom @ ( relation_dom_restriction @ SV655 @ SV164 ) ) )
= $false )
| ( ( in @ SV623 @ SV164 )
= $true )
| ( ( function @ SV655 )
= $false )
| ( ( relation @ SV655 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4540,plain,
! [SV729: $i,SV167: $i,SV718: $i] :
( ( ( in @ SV718 @ ( sK80_B @ SV167 ) )
= $false )
| ( ( ~ ( subset @ SV729 @ SV718 ) )
= $true )
| ( ( in @ SV729 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4541,plain,
! [SV656: $i,SV625: $i,SV168: $i] :
( ( ( in @ ( ordered_pair @ SV168 @ SV625 ) @ SV656 )
= $false )
| ( ( SV625
= ( apply @ SV656 @ SV168 ) )
= $true )
| ( ( function @ SV656 )
= $false )
| ( ( relation @ SV656 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4404]) ).
thf(4542,plain,
! [SV657: $i,SV626: $i,SV168: $i] :
( ( ( in @ ( ordered_pair @ SV168 @ SV626 ) @ SV657 )
= $false )
| ( ( in @ SV168 @ ( relation_dom @ SV657 ) )
= $true )
| ( ( function @ SV657 )
= $false )
| ( ( relation @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4405]) ).
thf(4543,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4544,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
| ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4545,plain,
! [SV694: $i,SV659: $i,SV169: $i] :
( ( ( ! [SY1499: $i] :
( ~ ( in @ SY1499 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SY1499 ) @ SV659 )
| ( in @ SY1499 @ SV694 ) ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4408]) ).
thf(4546,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ~ ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4409]) ).
thf(4547,plain,
! [SV730: $i,SV170: $i,SV775: $i] :
( ( ( ( SV775
!= ( apply @ SV170 @ SV730 ) )
| ( in @ ( ordered_pair @ SV730 @ SV775 ) @ SV170 ) )
= $true )
| ( ( in @ SV730 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(4548,plain,
! [SV170: $i,SV776: $i,SV731: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV731 @ SV776 ) @ SV170 )
| ( SV776
= ( apply @ SV170 @ SV731 ) ) )
= $true )
| ( ( in @ SV731 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4411]) ).
thf(4549,plain,
! [SV732: $i,SV170: $i,SV760: $i] :
( ( ( ( SV760
!= ( apply @ SV170 @ SV732 ) ) )
= $true )
| ( ( SV760 = empty_set )
= $true )
| ( ( in @ SV732 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(4550,plain,
! [SV733: $i,SV170: $i,SV761: $i] :
( ( ( ( SV761 != empty_set ) )
= $true )
| ( ( SV761
= ( apply @ SV170 @ SV733 ) )
= $true )
| ( ( in @ SV733 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(4551,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
= $false )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4414]) ).
thf(4552,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) ) )
= $false )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4414]) ).
thf(4553,plain,
! [SV696: $i,SV397: $i,SV172: $i] :
( ( ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) )
| ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(4554,plain,
! [SV744: $i,SV173: $i,SV579: $i] :
( ( ( in @ ( sK27_C @ SV579 @ SV173 ) @ SV579 )
= $false )
| ( ( in @ ( ordered_pair @ SV744 @ ( sK27_C @ SV579 @ SV173 ) ) @ SV173 )
= $false )
| ( ( SV579
= ( relation_rng @ SV173 ) )
= $true )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4416]) ).
thf(4555,plain,
! [SV580: $i,SV173: $i,SV745: $i,SV777: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV777 @ SV745 ) @ SV173 ) )
= $true )
| ( ( in @ SV745 @ SV580 )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(4556,plain,
! [SV173: $i,SV580: $i,SV746: $i] :
( ( ( in @ SV746 @ SV580 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK26_D @ SV746 @ SV580 @ SV173 ) @ SV746 ) @ SV173 )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4557,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 ) )
= $true )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(4558,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
| ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4420]) ).
thf(4559,plain,
! [SV288: $i,SV174: $i,SV526: $i,SV582: $i,SV747: $i] :
( ( ( in @ SV747 @ SV582 )
= $false )
| ( ( ( SV747 = SV526 )
| ( SV747 = SV174 )
| ( SV747 = SV288 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4560,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i] :
( ( ( ! [SY1394: $i] :
( ( SY1394 != SV526 )
| ( in @ SY1394 @ SV582 ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4423]) ).
thf(4561,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i] :
( ( ( ~ ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4424]) ).
thf(4562,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
| ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
= $false )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4425]) ).
thf(4563,plain,
! [SV664: $i,SV583: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV583 )
| ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV778 ) )
= $true )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(4564,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV779 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) ) )
| ( in @ SV779 @ SV665 ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(4565,plain,
! [SV584: $i,SV665: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV665 )
| ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV584 )
| ( in @ SV780 @ SY1539 ) ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4428]) ).
thf(4566,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $false )
| ( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV175 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(4567,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $false )
| ( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
!= SV489 ) )
= $true )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4568,plain,
! [SV528: $i,SV490: $i,SV175: $i,SV734: $i] :
( ( ( SV734 = SV175 )
= $true )
| ( ( SV734 = SV490 )
= $true )
| ( ( in @ SV734 @ SV528 )
= $false )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4431]) ).
thf(4569,plain,
! [SV490: $i,SV528: $i,SV175: $i,SV781: $i] :
( ( ( ( SV781 != SV175 )
| ( in @ SV781 @ SV528 ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(4570,plain,
! [SV175: $i,SV528: $i,SV490: $i,SV782: $i] :
( ( ( ( SV782 != SV490 )
| ( in @ SV782 @ SV528 ) )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(4571,plain,
! [SV666: $i,SV401: $i,SV719: $i,SV699: $i] :
( ( ( in @ ( ordered_pair @ SV699 @ SV719 ) @ SV401 )
= $false )
| ( ( in @ ( ordered_pair @ SV666 @ SV699 ) @ SV401 )
= $false )
| ( ( in @ ( ordered_pair @ SV666 @ SV719 ) @ SV401 )
= $true )
| ( ( transitive @ SV401 )
= $false )
| ( ( relation @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4434]) ).
thf(4572,plain,
! [SV289: $i,SV700: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) )
| ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) )
= $true )
| ( ( function @ SV700 )
= $false )
| ( ( relation @ SV700 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4573,plain,
! [SV289: $i,SV176: $i,SV748: $i] :
( ( ( ~ ( function @ SV748 ) )
= $true )
| ( ( ~ ( relation @ SV748 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SV748 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4436]) ).
thf(4574,plain,
! [SV289: $i,SV176: $i,SV749: $i] :
( ( ( ~ ( function @ SV749 ) )
= $true )
| ( ( ~ ( relation @ SV749 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
| ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4575,plain,
! [SV290: $i,SV178: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV178 ) )
= $true )
| ( ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 )
= $true )
| ( ( ordinal @ SV735 )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(4576,plain,
! [SV181: $i,SV591: $i] :
( ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 ) )
= $true )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4439]) ).
thf(4577,plain,
! [SV592: $i,SV181: $i,SV783: $i] :
( ( ( ! [SY1540: $i] :
( ~ ( in @ ( ordered_pair @ SV783 @ SY1540 ) @ SV181 )
| ( in @ ( ordered_pair @ SV783 @ SY1540 ) @ SV592 ) ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(4578,plain,
! [SV181: $i,SV592: $i,SV784: $i] :
( ( ( ! [SY1541: $i] :
( ~ ( in @ ( ordered_pair @ SV784 @ SY1541 ) @ SV592 )
| ( in @ ( ordered_pair @ SV784 @ SY1541 ) @ SV181 ) ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(4579,plain,
! [SV785: $i,SV182: $i,SV669: $i] :
( ( ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SV785 ) )
| ~ ( in @ SV785 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4580,plain,
! [SV182: $i,SV669: $i] :
( ( ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
| ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
= $false )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4581,plain,
! [SV670: $i,SV182: $i,SV786: $i] :
( ( ( ! [SY1542: $i] :
( ( SV786
!= ( apply @ SV182 @ SY1542 ) )
| ~ ( in @ SY1542 @ ( relation_dom @ SV182 ) ) )
| ( in @ SV786 @ SV670 ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(4582,plain,
! [SV182: $i,SV670: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV670 )
| ~ ( ( SV787
!= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4446]) ).
thf(4583,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
| ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4584,plain,
! [SV184: $i,SV292: $i,SV750: $i] :
( ( ( ~ ( function @ SV750 ) )
= $true )
| ( ( ~ ( relation @ SV750 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4448]) ).
thf(4585,plain,
! [SV184: $i,SV292: $i,SV751: $i] :
( ( ( ~ ( function @ SV751 ) )
= $true )
| ( ( ~ ( relation @ SV751 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4586,plain,
! [SV410: $i] :
( ( ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 )
| ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4450]) ).
thf(4587,plain,
! [SV410: $i] :
( ( ( in @ ( sK39_B @ SV410 ) @ ( sK40_SY629 @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4588,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(4589,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4454]) ).
thf(4590,plain,
! [SV637: $i,SV185: $i,SV595: $i] :
( ( ( ! [SY1450: $i,SY1451: $i] :
( ~ ( in @ SY1450 @ SV595 )
| ~ ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV185 )
| ( in @ ( ordered_pair @ SY1450 @ SY1451 ) @ SV637 ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4455]) ).
thf(4591,plain,
! [SV185: $i,SV595: $i,SV637: $i] :
( ( ( ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4456]) ).
thf(4592,plain,
! [SV187: $i,SV531: $i,SV498: $i,SV702: $i] :
( ( ( in @ SV702 @ SV498 )
= $false )
| ( ( in @ SV702 @ ( relation_dom @ SV531 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV702 @ SV187 ) @ SV531 )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV531 @ SV498 ) )
= $true )
| ( ( relation @ SV531 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(4593,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4458]) ).
thf(4594,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 ) )
= $false )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4458]) ).
thf(4595,plain,
! [SV599: $i,SV188: $i,SV752: $i,SV736: $i] :
( ( ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV188 )
= $false )
| ( ( in @ ( ordered_pair @ SV736 @ SV752 ) @ SV599 )
= $true )
| ( ( subset @ SV188 @ SV599 )
= $false )
| ( ( relation @ SV599 )
= $false )
| ( ( relation @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4460]) ).
thf(4596,plain,
! [SV189: $i,SV500: $i,SV533: $i] :
( ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV533 )
= $false )
| ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV189 )
= $false )
| ( ( in @ ( sK38_D @ SV533 @ SV500 @ SV189 ) @ SV500 )
= $false )
| ( ( SV533
= ( set_intersection2 @ SV189 @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(4597,plain,
! [SV534: $i,SV501: $i,SV189: $i,SV737: $i] :
( ( ( in @ SV737 @ SV189 )
= $false )
| ( ( ~ ( in @ SV737 @ SV501 ) )
= $true )
| ( ( in @ SV737 @ SV534 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4598,plain,
! [SV501: $i,SV189: $i,SV534: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV534 )
| ( in @ SV788 @ SV189 ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4465]) ).
thf(4599,plain,
! [SV189: $i,SV501: $i,SV534: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV534 )
| ( in @ SV789 @ SV501 ) )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4466]) ).
thf(4600,plain,
! [SV762: $i,SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV762 ) @ SV192 ) )
= $true )
| ( ( ~ ( in @ SV762 @ SV603 ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4601,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 ) )
= $false )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4602,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( ~ ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 ) )
= $false )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4603,plain,
! [SV641: $i,SV604: $i,SV192: $i,SV763: $i] :
( ( ( ! [SY1536: $i] :
( ~ ( in @ ( ordered_pair @ SV763 @ SY1536 ) @ SV192 )
| ~ ( in @ SY1536 @ SV604 ) ) )
= $true )
| ( ( in @ SV763 @ SV641 )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(4604,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV641 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4470]) ).
thf(4605,plain,
! [SV422: $i,SV502: $i] :
( ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
= $false )
| ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 ) )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4606,plain,
! [SV422: $i,SV502: $i] :
( ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4472]) ).
thf(4607,plain,
! [SV422: $i,SV502: $i] :
( ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 )
= $true )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(4608,plain,
! [SV503: $i,SV423: $i,SV765: $i,SV753: $i] :
( ( ( ( SV753 != SV765 )
| ~ ( in @ SV753 @ SV423 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV753 @ SV765 ) @ SV503 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(4609,plain,
! [SV423: $i,SV503: $i] :
( ( ( ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ ( ordered_pair @ SY1319 @ SY1320 ) @ SV503 )
| ( SY1319 = SY1320 ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4475]) ).
thf(4610,plain,
! [SV423: $i,SV503: $i] :
( ( ( ! [SY1321: $i] :
( ! [SY1322: $i] :
~ ( in @ ( ordered_pair @ SY1321 @ SY1322 ) @ SV503 )
| ( in @ SY1321 @ SV423 ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4476]) ).
thf(4611,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4477]) ).
thf(4612,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4477]) ).
thf(4613,plain,
! [SV139: $i,SV704: $i,SV544: $i,SV679: $i] :
( ( ( in @ SV679 @ SV544 )
= $false )
| ( ( ~ ( in @ SV704 @ SV544 ) )
= $true )
| ( ( SV679 = SV704 )
= $true )
| ( ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4614,plain,
! [SV140: $i,SV545: $i,SV605: $i,SV754: $i] :
( ( ( in @ ( ordered_pair @ SV754 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
= $false )
| ( ( ~ ( in @ SV754 @ SV545 ) )
= $true )
| ( ( ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4480]) ).
thf(4615,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( in @ ( ordered_pair @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
= $true )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4481]) ).
thf(4616,plain,
! [SV140: $i,SV545: $i,SV605: $i] :
( ( ( in @ ( sK60_SY641 @ SV605 @ SV545 @ SV140 ) @ SV545 )
= $true )
| ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4482]) ).
thf(4617,plain,
! [SV606: $i,SV546: $i,SV140: $i,SV755: $i,SV790: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV790 @ SV755 ) @ SV140 )
| ~ ( in @ SV790 @ SV546 ) )
= $true )
| ( ( in @ SV755 @ SV606 )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4618,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( in @ SV756 @ SV606 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 ) ) )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4619,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4485]) ).
thf(4620,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4485]) ).
thf(4621,plain,
! [SV141: $i,SV705: $i,SV548: $i,SV680: $i] :
( ( ( in @ SV680 @ SV548 )
= $false )
| ( ( ~ ( in @ SV705 @ SV548 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4622,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(4623,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4488]) ).
thf(4624,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) ) )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4488]) ).
thf(4625,plain,
! [SV608: $i,SV282: $i,SV791: $i,SV142: $i] :
( ( ( ! [SY1543: $i] :
( ~ ( in @ SY1543 @ SV142 )
| ~ ( in @ ( ordered_pair @ SV791 @ SY1543 ) @ SV282 )
| ( in @ ( ordered_pair @ SV791 @ SY1543 ) @ SV608 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4489]) ).
thf(4626,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) )
| ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(4627,plain,
! [SV738: $i,SV144: $i,SV609: $i] :
( ( ( in @ SV609 @ ( sK87_B @ SV144 ) )
= $false )
| ( ( in @ SV738 @ ( sK88_SY659 @ SV609 @ SV144 ) )
= $true )
| ( ( subset @ SV738 @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4628,plain,
! [SV144: $i,SV707: $i,SV721: $i] :
( ( ( subset @ SV721 @ SV707 )
= $false )
| ( ( in @ SV707 @ ( sK87_B @ SV144 ) )
= $false )
| ( ( in @ SV721 @ ( sK87_B @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4492]) ).
thf(4629,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV145 )
= $false )
| ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4493]) ).
thf(4630,plain,
! [SV145: $i,SV436: $i,SV506: $i] :
( ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV436 )
= $false )
| ( ( in @ ( sK46_D @ SV506 @ SV436 @ SV145 ) @ SV506 )
= $false )
| ( ( SV506
= ( set_union2 @ SV145 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4631,plain,
! [SV437: $i,SV507: $i,SV145: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV145 ) )
= $true )
| ( ( in @ SV766 @ SV507 )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(4632,plain,
! [SV145: $i,SV507: $i,SV437: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV437 ) )
= $true )
| ( ( in @ SV767 @ SV507 )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(4633,plain,
! [SV552: $i,SV146: $i,SV768: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ SV740 @ SV768 ) @ SV146 )
= $false )
| ( ( in @ SV740 @ SV552 )
= $true )
| ( ( SV552
= ( relation_dom @ SV146 ) )
= $false )
| ( ( relation @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4634,plain,
! [SV342: $i,SV438: $i] :
( ( ( ( relation_dom @ SV438 )
= SV342 )
= $false )
| ( ( ( apply @ SV438 @ ( sK76_C @ SV438 @ SV342 ) )
= ( sK76_C @ SV438 @ SV342 ) )
= $false )
| ( ( SV438
= ( identity_relation @ SV342 ) )
= $true )
| ( ( function @ SV438 )
= $false )
| ( ( relation @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4635,plain,
! [SV611: $i,SV555: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV555 ) )
= $true )
| ( ( ( apply @ SV611 @ SV769 )
= SV769 )
= $true )
| ( ( SV611
= ( identity_relation @ SV555 ) )
= $false )
| ( ( function @ SV611 )
= $false )
| ( ( relation @ SV611 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(4636,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4504]) ).
thf(4637,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4504]) ).
thf(4638,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 )
| ~ ( in @ SV708 @ SV558 ) )
= $true )
| ( ( ~ ( in @ SV723 @ SV558 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4639,plain,
! [SV151: $i,SV559: $i] :
( ( ( in @ ( ordered_pair @ ( sK23_SY620 @ SV559 @ SV151 ) @ ( sK22_C @ SV559 @ SV151 ) ) @ SV151 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_C @ SV559 @ SV151 ) @ ( sK23_SY620 @ SV559 @ SV151 ) ) @ SV559 )
= $false )
| ( ( SV559
= ( relation_inverse @ SV151 ) )
= $true )
| ( ( relation @ SV559 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4506]) ).
thf(4640,plain,
! [SV151: $i,SV560: $i,SV792: $i,SV770: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV770 @ SV792 ) @ SV560 )
| ( in @ ( ordered_pair @ SV792 @ SV770 ) @ SV151 ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4507]) ).
thf(4641,plain,
! [SV560: $i,SV151: $i,SV771: $i,SV793: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV793 @ SV771 ) @ SV151 )
| ( in @ ( ordered_pair @ SV771 @ SV793 ) @ SV560 ) )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4508]) ).
thf(4642,plain,
! [SV508: $i,SV449: $i,SV742: $i,SV153: $i,SV724: $i] :
( ( ( in @ SV724 @ SV153 )
= $false )
| ( ( ~ ( in @ SV742 @ SV449 ) )
= $true )
| ( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SV742 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4509]) ).
thf(4643,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4644,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( ~ ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 ) )
= $false )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4510]) ).
thf(4645,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV772: $i,SV153: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV153 )
| ~ ( in @ SV772 @ SV450 ) )
= $true )
| ( ( ( SV725
!= ( ordered_pair @ SV757 @ SV772 ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4511]) ).
thf(4646,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4647,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ( SV726
!= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4648,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
| ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(4649,plain,
! [SV686: $i,SV647: $i,SV154: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV794 @ SV647 )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SV794 ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4515]) ).
thf(4650,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
| ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4516]) ).
thf(4651,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i] :
( ( ( ! [SY1544: $i] :
( ~ ( in @ SY1544 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1544 @ SV648 )
| ( SV795
!= ( apply @ SV154 @ SY1544 ) ) )
| ( in @ SV795 @ SV687 ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4517]) ).
thf(4652,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ SV687 )
| ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SV796
!= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) ) ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(4653,plain,
! [SV364: $i] :
( ( ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
| ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4654,plain,
! [SV727: $i,SV365: $i,SV711: $i] :
( ( ( in @ SV711 @ ( relation_dom @ SV365 ) )
= $false )
| ( ( ~ ( in @ SV727 @ ( relation_dom @ SV365 ) ) )
= $true )
| ( ( ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) ) )
= $true )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4655,plain,
! [SV463: $i,SV155: $i,SV511: $i,SV773: $i] :
( ( ( ~ ( in @ SV773 @ SV511 ) )
= $true )
| ( ( in @ SV773 @ SV155 )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4656,plain,
! [SV155: $i,SV463: $i,SV511: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV511 ) )
= $true )
| ( ( ~ ( in @ SV774 @ SV463 ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4657,plain,
! [SV465: $i,SV713: $i,SV371: $i,SV743: $i] :
( ( ( in @ SV743 @ SV371 )
= $false )
| ( ( in @ SV713 @ SV743 )
= $false )
| ( ( in @ SV713 @ SV465 )
= $true )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(4658,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( in @ SV714 @ ( sK33_D @ SV714 @ SV465 @ SV371 ) )
= $true )
| ( ( in @ SV714 @ SV465 )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4528]) ).
thf(4659,plain,
! [SV371: $i,SV465: $i,SV714: $i] :
( ( ( in @ ( sK33_D @ SV714 @ SV465 @ SV371 ) @ SV371 )
= $true )
| ( ( in @ SV714 @ SV465 )
= $false )
| ( ( SV465
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4529]) ).
thf(4660,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4661,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ( function @ SV758 ) )
= $true )
| ( ( ~ ( relation @ SV758 ) )
= $true )
| ( ( ( SV758
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(4662,plain,
! [SV157: $i,SV759: $i] :
( ( ( ~ ( function @ SV759 ) )
= $true )
| ( ( ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV759
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(4663,plain,
( ( ~ ( function @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4664,plain,
! [SV159: $i,SV471: $i,SV514: $i] :
( ( ( in @ ( sK78_D @ SV514 @ SV471 @ SV159 ) @ ( relation_rng @ SV514 ) )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4536]) ).
thf(4665,plain,
! [SV471: $i,SV514: $i,SV159: $i] :
( ( ( in @ ( ordered_pair @ SV159 @ ( sK78_D @ SV514 @ SV471 @ SV159 ) ) @ SV514 )
= $true )
| ( ( in @ SV159 @ ( relation_inverse_image @ SV514 @ SV471 ) )
= $false )
| ( ( relation @ SV514 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4537]) ).
thf(4666,plain,
! [SV167: $i,SV718: $i,SV729: $i] :
( ( ( subset @ SV729 @ SV718 )
= $false )
| ( ( in @ SV718 @ ( sK80_B @ SV167 ) )
= $false )
| ( ( in @ SV729 @ ( sK80_B @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4667,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(4668,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ~ ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4544]) ).
thf(4669,plain,
! [SV658: $i,SV693: $i,SV169: $i] :
( ( ( ~ ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) ) )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4544]) ).
thf(4670,plain,
! [SV694: $i,SV659: $i,SV169: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SV797 ) @ SV659 )
| ( in @ SV797 @ SV694 ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4545]) ).
thf(4671,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) )
| ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4672,plain,
! [SV730: $i,SV170: $i,SV775: $i] :
( ( ( ( SV775
!= ( apply @ SV170 @ SV730 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV730 @ SV775 ) @ SV170 )
= $true )
| ( ( in @ SV730 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4673,plain,
! [SV170: $i,SV776: $i,SV731: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV731 @ SV776 ) @ SV170 ) )
= $true )
| ( ( SV776
= ( apply @ SV170 @ SV731 ) )
= $true )
| ( ( in @ SV731 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(4674,plain,
! [SV732: $i,SV170: $i,SV760: $i] :
( ( ( SV760
= ( apply @ SV170 @ SV732 ) )
= $false )
| ( ( SV760 = empty_set )
= $true )
| ( ( in @ SV732 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4549]) ).
thf(4675,plain,
! [SV733: $i,SV170: $i,SV761: $i] :
( ( ( SV761 = empty_set )
= $false )
| ( ( SV761
= ( apply @ SV170 @ SV733 ) )
= $true )
| ( ( in @ SV733 @ ( relation_dom @ SV170 ) )
= $true )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4676,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4551]) ).
thf(4677,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
| ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4552]) ).
thf(4678,plain,
! [SV696: $i,SV397: $i,SV172: $i] :
( ( ( ~ ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) ) )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4679,plain,
! [SV172: $i,SV397: $i,SV696: $i] :
( ( ( ~ ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4680,plain,
! [SV580: $i,SV173: $i,SV745: $i,SV777: $i] :
( ( ( in @ ( ordered_pair @ SV777 @ SV745 ) @ SV173 )
= $false )
| ( ( in @ SV745 @ SV580 )
= $true )
| ( ( SV580
= ( relation_rng @ SV173 ) )
= $false )
| ( ( relation @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4555]) ).
thf(4681,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV525 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4682,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4683,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) ) )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4684,plain,
! [SV582: $i,SV288: $i,SV174: $i,SV526: $i,SV747: $i] :
( ( ( SV747 = SV526 )
= $true )
| ( ( ( SV747 = SV174 )
| ( SV747 = SV288 ) )
= $true )
| ( ( in @ SV747 @ SV582 )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4685,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i,SV798: $i] :
( ( ( ( SV798 != SV526 )
| ( in @ SV798 @ SV582 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4560]) ).
thf(4686,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i] :
( ( ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) )
| ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4687,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 ) )
= $false )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4688,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
= $false )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4562]) ).
thf(4689,plain,
! [SV664: $i,SV583: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ SV583 ) )
= $true )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV778 )
= $true )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(4690,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV779 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) ) ) )
= $true )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(4691,plain,
! [SV584: $i,SV665: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV665 ) )
= $true )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV584 )
| ( in @ SV780 @ SY1539 ) ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(4692,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV175 )
= $false )
| ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4693,plain,
! [SV175: $i,SV489: $i,SV527: $i] :
( ( ( ( sK47_D @ SV527 @ SV489 @ SV175 )
= SV489 )
= $false )
| ( ( in @ ( sK47_D @ SV527 @ SV489 @ SV175 ) @ SV527 )
= $false )
| ( ( SV527
= ( unordered_pair @ SV175 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(4694,plain,
! [SV490: $i,SV528: $i,SV175: $i,SV781: $i] :
( ( ( ( SV781 != SV175 ) )
= $true )
| ( ( in @ SV781 @ SV528 )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4695,plain,
! [SV175: $i,SV528: $i,SV490: $i,SV782: $i] :
( ( ( ( SV782 != SV490 ) )
= $true )
| ( ( in @ SV782 @ SV528 )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(4696,plain,
! [SV289: $i,SV700: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ ( relation_dom @ SV700 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) )
= $true )
| ( ( function @ SV700 )
= $false )
| ( ( relation @ SV700 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(4697,plain,
! [SV289: $i,SV176: $i,SV748: $i] :
( ( ( function @ SV748 )
= $false )
| ( ( ~ ( relation @ SV748 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SV748 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4698,plain,
! [SV289: $i,SV176: $i,SV749: $i] :
( ( ( function @ SV749 )
= $false )
| ( ( ~ ( relation @ SV749 ) )
= $true )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
| ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4699,plain,
! [SV290: $i,SV178: $i,SV735: $i] :
( ( ( in @ SV735 @ SV178 )
= $false )
| ( ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 )
= $true )
| ( ( ordinal @ SV735 )
= $false )
| ( ( ( SV178 = empty_set )
| ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4700,plain,
! [SV181: $i,SV591: $i] :
( ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV591 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK102_C @ SV591 @ SV181 ) @ ( sK103_SY667 @ SV591 @ SV181 ) ) @ SV181 )
= $false )
| ( ( SV181 = SV591 )
= $true )
| ( ( relation @ SV591 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(4701,plain,
! [SV592: $i,SV181: $i,SV799: $i,SV783: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV181 )
| ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV592 ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4577]) ).
thf(4702,plain,
! [SV181: $i,SV592: $i,SV800: $i,SV784: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV592 )
| ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV181 ) )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(4703,plain,
! [SV785: $i,SV182: $i,SV669: $i] :
( ( ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ SV785 ) ) )
= $true )
| ( ( ~ ( in @ SV785 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(4704,plain,
! [SV182: $i,SV669: $i] :
( ( ( ( ( sK30_C @ SV669 @ SV182 )
!= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) ) )
= $false )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4580]) ).
thf(4705,plain,
! [SV182: $i,SV669: $i] :
( ( ( ~ ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
= $false )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4580]) ).
thf(4706,plain,
! [SV670: $i,SV182: $i,SV786: $i] :
( ( ( ! [SY1542: $i] :
( ( SV786
!= ( apply @ SV182 @ SY1542 ) )
| ~ ( in @ SY1542 @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( in @ SV786 @ SV670 )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(4707,plain,
! [SV182: $i,SV670: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV670 ) )
= $true )
| ( ( ~ ( ( SV787
!= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(4708,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(4709,plain,
! [SV184: $i,SV292: $i,SV750: $i] :
( ( ( function @ SV750 )
= $false )
| ( ( ~ ( relation @ SV750 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4710,plain,
! [SV184: $i,SV292: $i,SV751: $i] :
( ( ( function @ SV751 )
= $false )
| ( ( ~ ( relation @ SV751 ) )
= $true )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4711,plain,
! [SV410: $i] :
( ( ( ~ ( in @ ( sK39_B @ SV410 ) @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4586]) ).
thf(4712,plain,
! [SV410: $i] :
( ( ( ~ ( in @ ( sK40_SY629 @ SV410 ) @ SV410 ) )
= $false )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4586]) ).
thf(4713,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(4714,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4589]) ).
thf(4715,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) ) )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4589]) ).
thf(4716,plain,
! [SV637: $i,SV185: $i,SV595: $i,SV801: $i] :
( ( ( ! [SY1545: $i] :
( ~ ( in @ SV801 @ SV595 )
| ~ ( in @ ( ordered_pair @ SV801 @ SY1545 ) @ SV185 )
| ( in @ ( ordered_pair @ SV801 @ SY1545 ) @ SV637 ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4590]) ).
thf(4717,plain,
! [SV185: $i,SV595: $i,SV637: $i] :
( ( ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) )
| ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4718,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( in @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ ( relation_dom @ SV532 ) )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4593]) ).
thf(4719,plain,
! [SV187: $i,SV499: $i,SV532: $i] :
( ( ( in @ ( ordered_pair @ ( sK79_D @ SV532 @ SV499 @ SV187 ) @ SV187 ) @ SV532 )
= $true )
| ( ( in @ SV187 @ ( relation_image @ SV532 @ SV499 ) )
= $false )
| ( ( relation @ SV532 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4594]) ).
thf(4720,plain,
! [SV534: $i,SV189: $i,SV501: $i,SV737: $i] :
( ( ( in @ SV737 @ SV501 )
= $false )
| ( ( in @ SV737 @ SV189 )
= $false )
| ( ( in @ SV737 @ SV534 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4597]) ).
thf(4721,plain,
! [SV501: $i,SV189: $i,SV534: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV534 ) )
= $true )
| ( ( in @ SV788 @ SV189 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(4722,plain,
! [SV189: $i,SV501: $i,SV534: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV534 ) )
= $true )
| ( ( in @ SV789 @ SV501 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4599]) ).
thf(4723,plain,
! [SV762: $i,SV192: $i,SV603: $i,SV640: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV762 ) @ SV192 )
= $false )
| ( ( ~ ( in @ SV762 @ SV603 ) )
= $true )
| ( ( ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4600]) ).
thf(4724,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) ) @ SV192 )
= $true )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4601]) ).
thf(4725,plain,
! [SV192: $i,SV603: $i,SV640: $i] :
( ( ( in @ ( sK57_SY639 @ SV640 @ SV603 @ SV192 ) @ SV603 )
= $true )
| ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4602]) ).
thf(4726,plain,
! [SV641: $i,SV604: $i,SV192: $i,SV802: $i,SV763: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV763 @ SV802 ) @ SV192 )
| ~ ( in @ SV802 @ SV604 ) )
= $true )
| ( ( in @ SV763 @ SV641 )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4603]) ).
thf(4727,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( in @ SV764 @ SV641 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 ) ) )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(4728,plain,
! [SV422: $i,SV502: $i] :
( ( ( in @ ( ordered_pair @ ( sK67_C @ SV502 @ SV422 ) @ ( sK68_SY645 @ SV502 @ SV422 ) ) @ SV502 )
= $false )
| ( ( ( sK67_C @ SV502 @ SV422 )
= ( sK68_SY645 @ SV502 @ SV422 ) )
= $false )
| ( ( in @ ( sK67_C @ SV502 @ SV422 ) @ SV422 )
= $false )
| ( ( SV502
= ( identity_relation @ SV422 ) )
= $true )
| ( ( relation @ SV502 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4605]) ).
thf(4729,plain,
! [SV503: $i,SV423: $i,SV765: $i,SV753: $i] :
( ( ( ( SV753 != SV765 ) )
= $true )
| ( ( ~ ( in @ SV753 @ SV423 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV753 @ SV765 ) @ SV503 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4608]) ).
thf(4730,plain,
! [SV423: $i,SV503: $i,SV803: $i] :
( ( ( ! [SY1546: $i] :
( ~ ( in @ ( ordered_pair @ SV803 @ SY1546 ) @ SV503 )
| ( SV803 = SY1546 ) ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4609]) ).
thf(4731,plain,
! [SV423: $i,SV503: $i,SV804: $i] :
( ( ( ! [SY1547: $i] :
~ ( in @ ( ordered_pair @ SV804 @ SY1547 ) @ SV503 )
| ( in @ SV804 @ SV423 ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4610]) ).
thf(4732,plain,
! [SV139: $i,SV543: $i] :
( ( ( ( ( sK24_C @ SV543 @ SV139 )
!= ( sK25_SY621 @ SV543 @ SV139 ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4611]) ).
thf(4733,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) ) )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4612]) ).
thf(4734,plain,
! [SV139: $i,SV679: $i,SV544: $i,SV704: $i] :
( ( ( in @ SV704 @ SV544 )
= $false )
| ( ( in @ SV679 @ SV544 )
= $false )
| ( ( SV679 = SV704 )
= $true )
| ( ( in @ ( ordered_pair @ SV679 @ SV704 ) @ SV139 )
= $true )
| ( ( in @ ( ordered_pair @ SV704 @ SV679 ) @ SV139 )
= $true )
| ( ( is_connected_in @ SV139 @ SV544 )
= $false )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(4735,plain,
! [SV140: $i,SV605: $i,SV545: $i,SV754: $i] :
( ( ( in @ SV754 @ SV545 )
= $false )
| ( ( in @ ( ordered_pair @ SV754 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
= $false )
| ( ( ~ ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4614]) ).
thf(4736,plain,
! [SV606: $i,SV546: $i,SV140: $i,SV755: $i,SV790: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV790 @ SV755 ) @ SV140 ) )
= $true )
| ( ( ~ ( in @ SV790 @ SV546 ) )
= $true )
| ( ( in @ SV755 @ SV606 )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(4737,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 )
| ~ ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 ) )
= $false )
| ( ( in @ SV756 @ SV606 )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(4738,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4619]) ).
thf(4739,plain,
! [SV141: $i,SV547: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV547 @ SV141 ) @ ( sK37_SY628 @ SV547 @ SV141 ) ) @ SV141 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4620]) ).
thf(4740,plain,
! [SV141: $i,SV680: $i,SV548: $i,SV705: $i] :
( ( ( in @ SV705 @ SV548 )
= $false )
| ( ( in @ SV680 @ SV548 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(4741,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4622]) ).
thf(4742,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4623]) ).
thf(4743,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
| ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4624]) ).
thf(4744,plain,
! [SV608: $i,SV282: $i,SV791: $i,SV142: $i,SV805: $i] :
( ( ( ~ ( in @ SV805 @ SV142 )
| ~ ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV282 )
| ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV608 ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4625]) ).
thf(4745,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ~ ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4626]) ).
thf(4746,plain,
! [SV142: $i,SV282: $i,SV608: $i] :
( ( ( ~ ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) )
= $false )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4626]) ).
thf(4747,plain,
! [SV437: $i,SV507: $i,SV145: $i,SV766: $i] :
( ( ( in @ SV766 @ SV145 )
= $false )
| ( ( in @ SV766 @ SV507 )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4631]) ).
thf(4748,plain,
! [SV145: $i,SV507: $i,SV437: $i,SV767: $i] :
( ( ( in @ SV767 @ SV437 )
= $false )
| ( ( in @ SV767 @ SV507 )
= $true )
| ( ( SV507
= ( set_union2 @ SV145 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4632]) ).
thf(4749,plain,
! [SV611: $i,SV555: $i,SV769: $i] :
( ( ( in @ SV769 @ SV555 )
= $false )
| ( ( ( apply @ SV611 @ SV769 )
= SV769 )
= $true )
| ( ( SV611
= ( identity_relation @ SV555 ) )
= $false )
| ( ( function @ SV611 )
= $false )
| ( ( relation @ SV611 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4635]) ).
thf(4750,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4636]) ).
thf(4751,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_C @ SV557 @ SV149 ) @ ( sK14_SY611 @ SV557 @ SV149 ) ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4637]) ).
thf(4752,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV558 ) )
= $true )
| ( ( ~ ( in @ SV708 @ SV558 ) )
= $true )
| ( ( ~ ( in @ SV723 @ SV558 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(4753,plain,
! [SV151: $i,SV560: $i,SV792: $i,SV770: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV770 @ SV792 ) @ SV560 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV792 @ SV770 ) @ SV151 )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(4754,plain,
! [SV560: $i,SV151: $i,SV771: $i,SV793: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV793 @ SV771 ) @ SV151 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV771 @ SV793 ) @ SV560 )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(4755,plain,
! [SV508: $i,SV153: $i,SV724: $i,SV449: $i,SV742: $i] :
( ( ( in @ SV742 @ SV449 )
= $false )
| ( ( in @ SV724 @ SV153 )
= $false )
| ( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
!= ( ordered_pair @ SV724 @ SV742 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4642]) ).
thf(4756,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( in @ ( sK44_SY633 @ SV508 @ SV449 @ SV153 ) @ SV153 )
= $true )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4643]) ).
thf(4757,plain,
! [SV153: $i,SV449: $i,SV508: $i] :
( ( ( in @ ( sK45_SY635 @ SV508 @ SV449 @ SV153 ) @ SV449 )
= $true )
| ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4644]) ).
thf(4758,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV772: $i,SV153: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV153 ) )
= $true )
| ( ( ~ ( in @ SV772 @ SV450 ) )
= $true )
| ( ( ( SV725
!= ( ordered_pair @ SV757 @ SV772 ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(4759,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) ) )
= $true )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4646]) ).
thf(4760,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( SV726
= ( ordered_pair @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) ) )
= $true )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4647]) ).
thf(4761,plain,
( ( ~ ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4648]) ).
thf(4762,plain,
( ( ~ ( function @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4648]) ).
thf(4763,plain,
! [SV686: $i,SV647: $i,SV154: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV794 @ SV647 ) )
= $true )
| ( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SV794 ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(4764,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4650]) ).
thf(4765,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4650]) ).
thf(4766,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i] :
( ( ( ! [SY1544: $i] :
( ~ ( in @ SY1544 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SY1544 @ SV648 )
| ( SV795
!= ( apply @ SV154 @ SY1544 ) ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(4767,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( in @ SV796 @ SV687 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SV796
!= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) ) ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(4768,plain,
! [SV364: $i] :
( ( ( ~ ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4653]) ).
thf(4769,plain,
! [SV364: $i] :
( ( ( ~ ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) ) )
= $false )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4653]) ).
thf(4770,plain,
! [SV711: $i,SV365: $i,SV727: $i] :
( ( ( in @ SV727 @ ( relation_dom @ SV365 ) )
= $false )
| ( ( in @ SV711 @ ( relation_dom @ SV365 ) )
= $false )
| ( ( ( ( apply @ SV365 @ SV711 )
!= ( apply @ SV365 @ SV727 ) ) )
= $true )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4771,plain,
! [SV463: $i,SV155: $i,SV511: $i,SV773: $i] :
( ( ( in @ SV773 @ SV511 )
= $false )
| ( ( in @ SV773 @ SV155 )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4772,plain,
! [SV155: $i,SV463: $i,SV511: $i,SV774: $i] :
( ( ( in @ SV774 @ SV511 )
= $false )
| ( ( ~ ( in @ SV774 @ SV463 ) )
= $true )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4656]) ).
thf(4773,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(4774,plain,
! [SV157: $i,SV758: $i] :
( ( ( function @ SV758 )
= $false )
| ( ( ~ ( relation @ SV758 ) )
= $true )
| ( ( ( SV758
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4775,plain,
! [SV157: $i,SV759: $i] :
( ( ( function @ SV759 )
= $false )
| ( ( ~ ( relation @ SV759 ) )
= $true )
| ( ( ( SV759
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4662]) ).
thf(4776,plain,
( ( ~ ( function @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4663]) ).
thf(4777,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4663]) ).
thf(4778,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 ) )
= $true )
| ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4667]) ).
thf(4779,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4668]) ).
thf(4780,plain,
! [SV658: $i,SV693: $i,SV169: $i] :
( ( ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
| ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4669]) ).
thf(4781,plain,
! [SV694: $i,SV659: $i,SV169: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( relation_dom @ SV169 ) )
| ~ ( in @ ( apply @ SV169 @ SV797 ) @ SV659 ) )
= $true )
| ( ( in @ SV797 @ SV694 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(4782,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ~ ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4783,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ~ ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) )
= $false )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4784,plain,
! [SV730: $i,SV170: $i,SV775: $i] :
( ( ( SV775
= ( apply @ SV170 @ SV730 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV730 @ SV775 ) @ SV170 )
= $true )
| ( ( in @ SV730 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4672]) ).
thf(4785,plain,
! [SV170: $i,SV776: $i,SV731: $i] :
( ( ( in @ ( ordered_pair @ SV731 @ SV776 ) @ SV170 )
= $false )
| ( ( SV776
= ( apply @ SV170 @ SV731 ) )
= $true )
| ( ( in @ SV731 @ ( relation_dom @ SV170 ) )
= $false )
| ( ( function @ SV170 )
= $false )
| ( ( relation @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4786,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ! [SY1502: $i] :
( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SY1502 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1502 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(4787,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(4788,plain,
! [SV696: $i,SV397: $i,SV172: $i] :
( ( ( ! [SY1503: $i,SY1504: $i] :
( ! [SY1235: $i] :
( ~ ( in @ ( ordered_pair @ SY1503 @ SY1235 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1235 @ SY1504 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SY1503 @ SY1504 ) @ SV696 ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4678]) ).
thf(4789,plain,
! [SV172: $i,SV397: $i,SV696: $i] :
( ( ( ! [SY1506: $i,SY1507: $i] :
( ~ ( in @ ( ordered_pair @ SY1506 @ SY1507 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SY1506 @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1507 @ SY1506 @ SV696 @ SV397 @ SV172 ) @ SY1507 ) @ SV397 ) ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4679]) ).
thf(4790,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV525 )
= $false )
| ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4791,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4682]) ).
thf(4792,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
| ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4683]) ).
thf(4793,plain,
! [SV582: $i,SV526: $i,SV288: $i,SV174: $i,SV747: $i] :
( ( ( SV747 = SV174 )
= $true )
| ( ( SV747 = SV288 )
= $true )
| ( ( SV747 = SV526 )
= $true )
| ( ( in @ SV747 @ SV582 )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(4794,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i,SV798: $i] :
( ( ( ( SV798 != SV526 ) )
= $true )
| ( ( in @ SV798 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(4795,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i] :
( ( ( ~ ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4686]) ).
thf(4796,plain,
! [SV526: $i,SV174: $i,SV582: $i,SV288: $i] :
( ( ( ~ ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) )
= $false )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4686]) ).
thf(4797,plain,
! [SV583: $i,SV664: $i] :
( ( ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
= $true )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4687]) ).
thf(4798,plain,
! [SV583: $i,SV664: $i] :
( ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) ) )
= $true )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4688]) ).
thf(4799,plain,
! [SV664: $i,SV583: $i,SV778: $i] :
( ( ( in @ SV778 @ SV583 )
= $false )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV778 )
= $true )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(4800,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV779 @ SV665 @ SV584 ) @ SV584 )
| ~ ~ ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) ) )
= $false )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(4801,plain,
! [SV584: $i,SV665: $i,SV780: $i] :
( ( ( in @ SV780 @ SV665 )
= $false )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV584 )
| ( in @ SV780 @ SY1539 ) ) )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(4802,plain,
! [SV490: $i,SV528: $i,SV175: $i,SV781: $i] :
( ( ( SV781 = SV175 )
= $false )
| ( ( in @ SV781 @ SV528 )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(4803,plain,
! [SV175: $i,SV528: $i,SV490: $i,SV782: $i] :
( ( ( SV782 = SV490 )
= $false )
| ( ( in @ SV782 @ SV528 )
= $true )
| ( ( SV528
= ( unordered_pair @ SV175 @ SV490 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(4804,plain,
! [SV289: $i,SV700: $i,SV176: $i] :
( ( ( in @ SV176 @ ( relation_dom @ SV700 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) )
= $true )
| ( ( function @ SV700 )
= $false )
| ( ( relation @ SV700 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4805,plain,
! [SV289: $i,SV176: $i,SV748: $i] :
( ( ( relation @ SV748 )
= $false )
| ( ( function @ SV748 )
= $false )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
| ( in @ SV176 @ ( relation_dom @ SV748 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(4806,plain,
! [SV289: $i,SV176: $i,SV749: $i] :
( ( ( relation @ SV749 )
= $false )
| ( ( function @ SV749 )
= $false )
| ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
| ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) ) )
= $true )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4698]) ).
thf(4807,plain,
! [SV735: $i,SV290: $i,SV178: $i] :
( ( ( SV178 = empty_set )
= $true )
| ( ( ~ ( subset @ SV178 @ SV290 ) )
= $true )
| ( ( ordinal @ SV735 )
= $false )
| ( ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 )
= $true )
| ( ( in @ SV735 @ SV178 )
= $false )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(4808,plain,
! [SV592: $i,SV181: $i,SV799: $i,SV783: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV181 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV592 )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(4809,plain,
! [SV181: $i,SV592: $i,SV800: $i,SV784: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV592 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV181 )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(4810,plain,
! [SV785: $i,SV182: $i,SV669: $i] :
( ( ( ( sK30_C @ SV669 @ SV182 )
= ( apply @ SV182 @ SV785 ) )
= $false )
| ( ( ~ ( in @ SV785 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(4811,plain,
! [SV182: $i,SV669: $i] :
( ( ( ( sK30_C @ SV669 @ SV182 )
= ( apply @ SV182 @ ( sK31_SY625 @ SV669 @ SV182 ) ) )
= $true )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4704]) ).
thf(4812,plain,
! [SV182: $i,SV669: $i] :
( ( ( in @ ( sK31_SY625 @ SV669 @ SV182 ) @ ( relation_dom @ SV182 ) )
= $true )
| ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4705]) ).
thf(4813,plain,
! [SV670: $i,SV806: $i,SV182: $i,SV786: $i] :
( ( ( ( SV786
!= ( apply @ SV182 @ SV806 ) )
| ~ ( in @ SV806 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( in @ SV786 @ SV670 )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(4814,plain,
! [SV182: $i,SV670: $i,SV787: $i] :
( ( ( in @ SV787 @ SV670 )
= $false )
| ( ( ~ ( ( SV787
!= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) ) )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(4815,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
| ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4708]) ).
thf(4816,plain,
! [SV184: $i,SV292: $i,SV750: $i] :
( ( ( relation @ SV750 )
= $false )
| ( ( function @ SV750 )
= $false )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(4817,plain,
! [SV184: $i,SV292: $i,SV751: $i] :
( ( ( relation @ SV751 )
= $false )
| ( ( function @ SV751 )
= $false )
| ( ( ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) )
| ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) ) )
= $true )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(4818,plain,
! [SV410: $i] :
( ( ( in @ ( sK39_B @ SV410 ) @ SV410 )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4711]) ).
thf(4819,plain,
! [SV410: $i] :
( ( ( in @ ( sK40_SY629 @ SV410 ) @ SV410 )
= $true )
| ( ( epsilon_connected @ SV410 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4712]) ).
thf(4820,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4821,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4714]) ).
thf(4822,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
| ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4715]) ).
thf(4823,plain,
! [SV637: $i,SV185: $i,SV807: $i,SV595: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV595 )
| ~ ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV185 )
| ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV637 ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4716]) ).
thf(4824,plain,
! [SV185: $i,SV595: $i,SV637: $i] :
( ( ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4717]) ).
thf(4825,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( ~ ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) )
= $false )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4717]) ).
thf(4826,plain,
! [SV501: $i,SV189: $i,SV534: $i,SV788: $i] :
( ( ( in @ SV788 @ SV534 )
= $false )
| ( ( in @ SV788 @ SV189 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(4827,plain,
! [SV189: $i,SV501: $i,SV534: $i,SV789: $i] :
( ( ( in @ SV789 @ SV534 )
= $false )
| ( ( in @ SV789 @ SV501 )
= $true )
| ( ( SV534
= ( set_intersection2 @ SV189 @ SV501 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(4828,plain,
! [SV192: $i,SV640: $i,SV603: $i,SV762: $i] :
( ( ( in @ SV762 @ SV603 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV762 ) @ SV192 )
= $false )
| ( ( ~ ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 ) )
= $true )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(4829,plain,
! [SV641: $i,SV604: $i,SV192: $i,SV802: $i,SV763: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV763 @ SV802 ) @ SV192 ) )
= $true )
| ( ( ~ ( in @ SV802 @ SV604 ) )
= $true )
| ( ( in @ SV763 @ SV641 )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(4830,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
| ~ ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 ) )
= $false )
| ( ( in @ SV764 @ SV641 )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(4831,plain,
! [SV503: $i,SV423: $i,SV765: $i,SV753: $i] :
( ( ( SV753 = SV765 )
= $false )
| ( ( ~ ( in @ SV753 @ SV423 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV753 @ SV765 ) @ SV503 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(4832,plain,
! [SV423: $i,SV503: $i,SV808: $i,SV803: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV803 @ SV808 ) @ SV503 )
| ( SV803 = SV808 ) )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4730]) ).
thf(4833,plain,
! [SV423: $i,SV503: $i,SV804: $i] :
( ( ( ! [SY1547: $i] :
~ ( in @ ( ordered_pair @ SV804 @ SY1547 ) @ SV503 ) )
= $true )
| ( ( in @ SV804 @ SV423 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(4834,plain,
! [SV139: $i,SV543: $i] :
( ( ( ( sK24_C @ SV543 @ SV139 )
= ( sK25_SY621 @ SV543 @ SV139 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4732]) ).
thf(4835,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
| ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4733]) ).
thf(4836,plain,
! [SV754: $i,SV140: $i,SV545: $i,SV605: $i] :
( ( ( in @ ( sK59_D @ SV605 @ SV545 @ SV140 ) @ SV605 )
= $false )
| ( ( in @ ( ordered_pair @ SV754 @ ( sK59_D @ SV605 @ SV545 @ SV140 ) ) @ SV140 )
= $false )
| ( ( in @ SV754 @ SV545 )
= $false )
| ( ( SV605
= ( relation_image @ SV140 @ SV545 ) )
= $true )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4735]) ).
thf(4837,plain,
! [SV606: $i,SV546: $i,SV140: $i,SV755: $i,SV790: $i] :
( ( ( in @ ( ordered_pair @ SV790 @ SV755 ) @ SV140 )
= $false )
| ( ( ~ ( in @ SV790 @ SV546 ) )
= $true )
| ( ( in @ SV755 @ SV606 )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4736]) ).
thf(4838,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 ) )
= $false )
| ( ( in @ SV756 @ SV606 )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4737]) ).
thf(4839,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( ~ ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 ) )
= $false )
| ( ( in @ SV756 @ SV606 )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4737]) ).
thf(4840,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
| ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4738]) ).
thf(4841,plain,
! [SV548: $i,SV141: $i,SV705: $i,SV680: $i] :
( ( ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 )
= $false )
| ( ( in @ SV680 @ SV548 )
= $false )
| ( ( in @ SV705 @ SV548 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 ) )
= $true )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4740]) ).
thf(4842,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
= $false )
| ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 ) )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(4843,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(4844,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 )
= $true )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4743]) ).
thf(4845,plain,
! [SV608: $i,SV282: $i,SV791: $i,SV142: $i,SV805: $i] :
( ( ( ~ ( in @ SV805 @ SV142 )
| ~ ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV282 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV608 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(4846,plain,
! [SV282: $i,SV142: $i,SV608: $i] :
( ( ( ! [SY1434: $i,SY1435: $i] :
( ~ ( in @ ( ordered_pair @ SY1434 @ SY1435 ) @ SV608 )
| ( in @ SY1435 @ SV142 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4745]) ).
thf(4847,plain,
! [SV142: $i,SV282: $i,SV608: $i] :
( ( ( ! [SY1436: $i,SY1437: $i] :
( ~ ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV608 )
| ( in @ ( ordered_pair @ SY1436 @ SY1437 ) @ SV282 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4746]) ).
thf(4848,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
| ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4750]) ).
thf(4849,plain,
! [SV149: $i,SV723: $i,SV708: $i,SV558: $i,SV684: $i] :
( ( ( in @ SV684 @ SV558 )
= $false )
| ( ( ~ ( in @ SV708 @ SV558 ) )
= $true )
| ( ( ~ ( in @ SV723 @ SV558 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(4850,plain,
! [SV151: $i,SV560: $i,SV792: $i,SV770: $i] :
( ( ( in @ ( ordered_pair @ SV770 @ SV792 ) @ SV560 )
= $false )
| ( ( in @ ( ordered_pair @ SV792 @ SV770 ) @ SV151 )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4753]) ).
thf(4851,plain,
! [SV560: $i,SV151: $i,SV771: $i,SV793: $i] :
( ( ( in @ ( ordered_pair @ SV793 @ SV771 ) @ SV151 )
= $false )
| ( ( in @ ( ordered_pair @ SV771 @ SV793 ) @ SV560 )
= $true )
| ( ( SV560
= ( relation_inverse @ SV151 ) )
= $false )
| ( ( relation @ SV560 )
= $false )
| ( ( relation @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4754]) ).
thf(4852,plain,
! [SV742: $i,SV724: $i,SV153: $i,SV449: $i,SV508: $i] :
( ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
= ( ordered_pair @ SV724 @ SV742 ) )
= $false )
| ( ( in @ SV724 @ SV153 )
= $false )
| ( ( in @ SV742 @ SV449 )
= $false )
| ( ( ~ ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 ) )
= $true )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(4853,plain,
! [SV509: $i,SV725: $i,SV450: $i,SV772: $i,SV153: $i,SV757: $i] :
( ( ( in @ SV757 @ SV153 )
= $false )
| ( ( ~ ( in @ SV772 @ SV450 ) )
= $true )
| ( ( ( SV725
!= ( ordered_pair @ SV757 @ SV772 ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(4854,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
| ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(4855,plain,
( ( ~ ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4761]) ).
thf(4856,plain,
( ( function @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4762]) ).
thf(4857,plain,
! [SV686: $i,SV647: $i,SV154: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ~ ( in @ SV794 @ SV647 ) )
= $true )
| ( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SV794 ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4763]) ).
thf(4858,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) ) )
= $true )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4764]) ).
thf(4859,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
= ( apply @ SV154 @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) ) )
= $true )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4765]) ).
thf(4860,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV809 @ SV648 )
| ( SV795
!= ( apply @ SV154 @ SV809 ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4766]) ).
thf(4861,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( in @ SV796 @ SV687 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SV796
!= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) ) ) )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(4862,plain,
! [SV364: $i] :
( ( ( in @ ( sK20_B @ SV364 ) @ ( relation_dom @ SV364 ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4768]) ).
thf(4863,plain,
! [SV364: $i] :
( ( ( in @ ( sK21_SY619 @ SV364 ) @ ( relation_dom @ SV364 ) )
= $true )
| ( ( one_to_one @ SV364 )
= $true )
| ( ( function @ SV364 )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4769]) ).
thf(4864,plain,
! [SV727: $i,SV711: $i,SV365: $i] :
( ( ( ( apply @ SV365 @ SV711 )
= ( apply @ SV365 @ SV727 ) )
= $false )
| ( ( in @ SV711 @ ( relation_dom @ SV365 ) )
= $false )
| ( ( in @ SV727 @ ( relation_dom @ SV365 ) )
= $false )
| ( ( SV711 = SV727 )
= $true )
| ( ( one_to_one @ SV365 )
= $false )
| ( ( function @ SV365 )
= $false )
| ( ( relation @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(4865,plain,
! [SV155: $i,SV511: $i,SV463: $i,SV774: $i] :
( ( ( in @ SV774 @ SV463 )
= $false )
| ( ( in @ SV774 @ SV511 )
= $false )
| ( ( SV511
= ( set_difference @ SV155 @ SV463 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4866,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(4867,plain,
! [SV157: $i,SV758: $i] :
( ( ( relation @ SV758 )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( ( SV758
!= ( function_inverse @ SV157 ) )
| ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4868,plain,
! [SV157: $i,SV759: $i] :
( ( ( relation @ SV759 )
= $false )
| ( ( function @ SV759 )
= $false )
| ( ( ( SV759
!= ( function_inverse @ SV157 ) )
| ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4869,plain,
( ( function @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4776]) ).
thf(4870,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4777]) ).
thf(4871,plain,
! [SV658: $i,SV693: $i,SV169: $i] :
( ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
= $false )
| ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
= $false )
| ( ( ~ ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 ) )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(4872,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
= $true )
| ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(4873,plain,
! [SV658: $i,SV693: $i,SV169: $i] :
( ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
= $true )
| ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 )
= $true )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(4874,plain,
! [SV694: $i,SV659: $i,SV169: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( relation_dom @ SV169 ) ) )
= $true )
| ( ( ~ ( in @ ( apply @ SV169 @ SV797 ) @ SV659 ) )
= $true )
| ( ( in @ SV797 @ SV694 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(4875,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ! [SY1500: $i] :
( ~ ( in @ SY1500 @ SV694 )
| ( in @ SY1500 @ ( relation_dom @ SV169 ) ) ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4782]) ).
thf(4876,plain,
! [SV659: $i,SV169: $i,SV694: $i] :
( ( ( ! [SY1501: $i] :
( ~ ( in @ SY1501 @ SV694 )
| ( in @ ( apply @ SV169 @ SY1501 ) @ SV659 ) ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4783]) ).
thf(4877,plain,
! [SV810: $i,SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SV810 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SV810 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4786]) ).
thf(4878,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(4879,plain,
! [SV696: $i,SV397: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1548: $i] :
( ! [SY1549: $i] :
( ~ ( in @ ( ordered_pair @ SV811 @ SY1549 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1549 @ SY1548 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SV811 @ SY1548 ) @ SV696 ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4788]) ).
thf(4880,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV812: $i] :
( ( ( ! [SY1550: $i] :
( ~ ( in @ ( ordered_pair @ SV812 @ SY1550 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SY1550 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SY1550 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SY1550 ) @ SV397 ) ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4789]) ).
thf(4881,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 ) )
= $true )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(4882,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ~ ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 ) )
= $true )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(4883,plain,
! [SV288: $i,SV174: $i,SV582: $i,SV526: $i,SV798: $i] :
( ( ( SV798 = SV526 )
= $false )
| ( ( in @ SV798 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4794]) ).
thf(4884,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i] :
( ( ( ! [SY1395: $i] :
( ( SY1395 != SV174 )
| ( in @ SY1395 @ SV582 ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4795]) ).
thf(4885,plain,
! [SV526: $i,SV174: $i,SV582: $i,SV288: $i] :
( ( ( ! [SY1396: $i] :
( ( SY1396 != SV288 )
| ( in @ SY1396 @ SV582 ) ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4796]) ).
thf(4886,plain,
! [SV583: $i,SV664: $i] :
( ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $false )
| ( ( in @ ( sK52_SY636 @ SV664 @ SV583 ) @ SV583 )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4887,plain,
! [SV583: $i,SV664: $i] :
( ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) )
= $false )
| ( ( ~ ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 ) )
= $true )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(4888,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV779 @ SV665 @ SV584 ) @ SV584 ) )
= $false )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4800]) ).
thf(4889,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ~ ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) ) )
= $false )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4800]) ).
thf(4890,plain,
! [SV665: $i,SV780: $i,SV584: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV584 )
| ( in @ SV780 @ SV813 ) )
= $true )
| ( ( in @ SV780 @ SV665 )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(4891,plain,
! [SV289: $i,SV176: $i,SV700: $i] :
( ( ( in @ ( apply @ SV700 @ SV176 ) @ ( relation_dom @ SV289 ) )
= $false )
| ( ( in @ SV176 @ ( relation_dom @ SV700 ) )
= $false )
| ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV700 @ SV289 ) ) )
= $true )
| ( ( function @ SV700 )
= $false )
| ( ( relation @ SV700 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(4892,plain,
! [SV289: $i,SV748: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) ) )
= $true )
| ( ( in @ SV176 @ ( relation_dom @ SV748 ) )
= $true )
| ( ( function @ SV748 )
= $false )
| ( ( relation @ SV748 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(4893,plain,
! [SV289: $i,SV749: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) ) )
= $true )
| ( ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) )
= $true )
| ( ( function @ SV749 )
= $false )
| ( ( relation @ SV749 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(4894,plain,
! [SV735: $i,SV290: $i,SV178: $i] :
( ( ( subset @ SV178 @ SV290 )
= $false )
| ( ( SV178 = empty_set )
= $true )
| ( ( ordinal @ SV735 )
= $false )
| ( ( ordinal_subset @ ( sK77_C @ SV290 @ SV178 ) @ SV735 )
= $true )
| ( ( in @ SV735 @ SV178 )
= $false )
| ( ( ordinal @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4895,plain,
! [SV592: $i,SV181: $i,SV799: $i,SV783: $i] :
( ( ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV181 )
= $false )
| ( ( in @ ( ordered_pair @ SV783 @ SV799 ) @ SV592 )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4808]) ).
thf(4896,plain,
! [SV181: $i,SV592: $i,SV800: $i,SV784: $i] :
( ( ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV592 )
= $false )
| ( ( in @ ( ordered_pair @ SV784 @ SV800 ) @ SV181 )
= $true )
| ( ( SV181 = SV592 )
= $false )
| ( ( relation @ SV592 )
= $false )
| ( ( relation @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4809]) ).
thf(4897,plain,
! [SV669: $i,SV182: $i,SV785: $i] :
( ( ( in @ SV785 @ ( relation_dom @ SV182 ) )
= $false )
| ( ( ( sK30_C @ SV669 @ SV182 )
= ( apply @ SV182 @ SV785 ) )
= $false )
| ( ( ~ ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 ) )
= $true )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4810]) ).
thf(4898,plain,
! [SV670: $i,SV806: $i,SV182: $i,SV786: $i] :
( ( ( ( SV786
!= ( apply @ SV182 @ SV806 ) ) )
= $true )
| ( ( ~ ( in @ SV806 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( in @ SV786 @ SV670 )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(4899,plain,
! [SV670: $i,SV182: $i,SV787: $i] :
( ( ( ( SV787
!= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) )
| ~ ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
= $false )
| ( ( in @ SV787 @ SV670 )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4900,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( ~ ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4815]) ).
thf(4901,plain,
! [SV184: $i,SV701: $i,SV292: $i] :
( ( ( ~ ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4815]) ).
thf(4902,plain,
! [SV184: $i,SV750: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_dom_restriction @ SV750 @ SV184 ) ) )
= $true )
| ( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV750 )
= $false )
| ( ( relation @ SV750 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(4903,plain,
! [SV184: $i,SV751: $i,SV292: $i] :
( ( ( ( SV292
!= ( relation_dom_restriction @ SV751 @ SV184 ) ) )
= $true )
| ( ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) )
= $true )
| ( ( function @ SV751 )
= $false )
| ( ( relation @ SV751 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4817]) ).
thf(4904,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
= $false )
| ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 ) )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(4905,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(4906,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 )
= $true )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4822]) ).
thf(4907,plain,
! [SV637: $i,SV185: $i,SV807: $i,SV595: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV595 )
| ~ ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV185 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV637 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4823]) ).
thf(4908,plain,
! [SV185: $i,SV595: $i,SV637: $i] :
( ( ( ! [SY1452: $i] :
( ! [SY1453: $i] :
~ ( in @ ( ordered_pair @ SY1452 @ SY1453 ) @ SV637 )
| ( in @ SY1452 @ SV595 ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4824]) ).
thf(4909,plain,
! [SV595: $i,SV185: $i,SV637: $i] :
( ( ( ! [SY1454: $i,SY1455: $i] :
( ~ ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV637 )
| ( in @ ( ordered_pair @ SY1454 @ SY1455 ) @ SV185 ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4825]) ).
thf(4910,plain,
! [SV762: $i,SV192: $i,SV603: $i,SV640: $i] :
( ( ( in @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV640 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK56_D @ SV640 @ SV603 @ SV192 ) @ SV762 ) @ SV192 )
= $false )
| ( ( in @ SV762 @ SV603 )
= $false )
| ( ( SV640
= ( relation_inverse_image @ SV192 @ SV603 ) )
= $true )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4828]) ).
thf(4911,plain,
! [SV641: $i,SV604: $i,SV192: $i,SV802: $i,SV763: $i] :
( ( ( in @ ( ordered_pair @ SV763 @ SV802 ) @ SV192 )
= $false )
| ( ( ~ ( in @ SV802 @ SV604 ) )
= $true )
| ( ( in @ SV763 @ SV641 )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(4912,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 ) )
= $false )
| ( ( in @ SV764 @ SV641 )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4830]) ).
thf(4913,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( ~ ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 ) )
= $false )
| ( ( in @ SV764 @ SV641 )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4830]) ).
thf(4914,plain,
! [SV503: $i,SV765: $i,SV423: $i,SV753: $i] :
( ( ( in @ SV753 @ SV423 )
= $false )
| ( ( SV753 = SV765 )
= $false )
| ( ( in @ ( ordered_pair @ SV753 @ SV765 ) @ SV503 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(4915,plain,
! [SV423: $i,SV503: $i,SV808: $i,SV803: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV803 @ SV808 ) @ SV503 ) )
= $true )
| ( ( SV803 = SV808 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(4916,plain,
! [SV423: $i,SV503: $i,SV814: $i,SV804: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV804 @ SV814 ) @ SV503 ) )
= $true )
| ( ( in @ SV804 @ SV423 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4833]) ).
thf(4917,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4918,plain,
! [SV139: $i,SV543: $i] :
( ( ( ~ ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 ) )
= $false )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4835]) ).
thf(4919,plain,
! [SV606: $i,SV140: $i,SV755: $i,SV546: $i,SV790: $i] :
( ( ( in @ SV790 @ SV546 )
= $false )
| ( ( in @ ( ordered_pair @ SV790 @ SV755 ) @ SV140 )
= $false )
| ( ( in @ SV755 @ SV606 )
= $true )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(4920,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( in @ ( ordered_pair @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV756 ) @ SV140 )
= $true )
| ( ( in @ SV756 @ SV606 )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4838]) ).
thf(4921,plain,
! [SV140: $i,SV546: $i,SV606: $i,SV756: $i] :
( ( ( in @ ( sK58_E @ SV756 @ SV606 @ SV546 @ SV140 ) @ SV546 )
= $true )
| ( ( in @ SV756 @ SV606 )
= $false )
| ( ( SV606
= ( relation_image @ SV140 @ SV546 ) )
= $false )
| ( ( relation @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4839]) ).
thf(4922,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4923,plain,
! [SV141: $i,SV547: $i] :
( ( ( ~ ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 ) )
= $false )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4840]) ).
thf(4924,plain,
! [SV548: $i,SV141: $i,SV680: $i,SV705: $i] :
( ( ( in @ ( ordered_pair @ SV705 @ SV680 ) @ SV141 )
= $false )
| ( ( in @ SV705 @ SV548 )
= $false )
| ( ( in @ SV680 @ SV548 )
= $false )
| ( ( in @ ( ordered_pair @ SV680 @ SV705 ) @ SV141 )
= $false )
| ( ( SV680 = SV705 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV548 )
= $false )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4925,plain,
! [SV142: $i,SV282: $i,SV607: $i] :
( ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV607 )
= $false )
| ( ( in @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) @ SV142 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK109_D @ SV607 @ SV282 @ SV142 ) @ ( sK110_SY671 @ SV607 @ SV282 @ SV142 ) ) @ SV282 )
= $false )
| ( ( SV607
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $true )
| ( ( relation @ SV607 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4842]) ).
thf(4926,plain,
! [SV608: $i,SV282: $i,SV791: $i,SV142: $i,SV805: $i] :
( ( ( ~ ( in @ SV805 @ SV142 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV282 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV608 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(4927,plain,
! [SV282: $i,SV142: $i,SV608: $i,SV815: $i] :
( ( ( ! [SY1551: $i] :
( ~ ( in @ ( ordered_pair @ SV815 @ SY1551 ) @ SV608 )
| ( in @ SY1551 @ SV142 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4846]) ).
thf(4928,plain,
! [SV142: $i,SV282: $i,SV608: $i,SV816: $i] :
( ( ( ! [SY1552: $i] :
( ~ ( in @ ( ordered_pair @ SV816 @ SY1552 ) @ SV608 )
| ( in @ ( ordered_pair @ SV816 @ SY1552 ) @ SV282 ) ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4847]) ).
thf(4929,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4848]) ).
thf(4930,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4848]) ).
thf(4931,plain,
! [SV149: $i,SV723: $i,SV684: $i,SV558: $i,SV708: $i] :
( ( ( in @ SV708 @ SV558 )
= $false )
| ( ( in @ SV684 @ SV558 )
= $false )
| ( ( ~ ( in @ SV723 @ SV558 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(4932,plain,
! [SV724: $i,SV742: $i,SV153: $i,SV449: $i,SV508: $i] :
( ( ( in @ ( sK43_D @ SV508 @ SV449 @ SV153 ) @ SV508 )
= $false )
| ( ( in @ SV742 @ SV449 )
= $false )
| ( ( in @ SV724 @ SV153 )
= $false )
| ( ( ( sK43_D @ SV508 @ SV449 @ SV153 )
= ( ordered_pair @ SV724 @ SV742 ) )
= $false )
| ( ( SV508
= ( cartesian_product2 @ SV153 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4933,plain,
! [SV509: $i,SV725: $i,SV153: $i,SV757: $i,SV450: $i,SV772: $i] :
( ( ( in @ SV772 @ SV450 )
= $false )
| ( ( in @ SV757 @ SV153 )
= $false )
| ( ( ( SV725
!= ( ordered_pair @ SV757 @ SV772 ) ) )
= $true )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4934,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4854]) ).
thf(4935,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( ~ ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 ) )
= $false )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4854]) ).
thf(4936,plain,
( ( ~ ( relation @ empty_set )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(4937,plain,
! [SV686: $i,SV647: $i,SV154: $i,SV794: $i] :
( ( ( in @ SV794 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ~ ( in @ SV794 @ SV647 ) )
= $true )
| ( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SV794 ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(4938,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(4939,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ ( relation_dom @ SV154 ) )
| ~ ( in @ SV809 @ SV648 ) )
= $true )
| ( ( ( SV795
!= ( apply @ SV154 @ SV809 ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4860]) ).
thf(4940,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
| ( SV796
!= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4861]) ).
thf(4941,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4866]) ).
thf(4942,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4866]) ).
thf(4943,plain,
! [SV157: $i,SV758: $i] :
( ( ( ( SV758
!= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(4944,plain,
! [SV157: $i,SV759: $i] :
( ( ( ( SV759
!= ( function_inverse @ SV157 ) ) )
= $true )
| ( ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) )
= $true )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(4945,plain,
! [SV169: $i,SV658: $i,SV693: $i] :
( ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ SV693 )
= $false )
| ( ( in @ ( sK61_D @ SV693 @ SV658 @ SV169 ) @ ( relation_dom @ SV169 ) )
= $false )
| ( ( in @ ( apply @ SV169 @ ( sK61_D @ SV693 @ SV658 @ SV169 ) ) @ SV658 )
= $false )
| ( ( SV693
= ( relation_inverse_image @ SV169 @ SV658 ) )
= $true )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4871]) ).
thf(4946,plain,
! [SV694: $i,SV659: $i,SV169: $i,SV797: $i] :
( ( ( in @ SV797 @ ( relation_dom @ SV169 ) )
= $false )
| ( ( ~ ( in @ ( apply @ SV169 @ SV797 ) @ SV659 ) )
= $true )
| ( ( in @ SV797 @ SV694 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4874]) ).
thf(4947,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV694 )
| ( in @ SV817 @ ( relation_dom @ SV169 ) ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4875]) ).
thf(4948,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV694 )
| ( in @ ( apply @ SV169 @ SV818 ) @ SV659 ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4876]) ).
thf(4949,plain,
! [SV810: $i,SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SV810 ) @ SV172 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV810 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(4950,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4878]) ).
thf(4951,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4878]) ).
thf(4952,plain,
! [SV696: $i,SV397: $i,SV819: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1553: $i] :
( ~ ( in @ ( ordered_pair @ SV811 @ SY1553 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1553 @ SV819 ) @ SV397 ) )
| ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4879]) ).
thf(4953,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
| ~ ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4880]) ).
thf(4954,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV174 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(4955,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
!= SV288 ) )
= $true )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4882]) ).
thf(4956,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i,SV821: $i] :
( ( ( ( SV821 != SV174 )
| ( in @ SV821 @ SV582 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(4957,plain,
! [SV526: $i,SV174: $i,SV582: $i,SV288: $i,SV822: $i] :
( ( ( ( SV822 != SV288 )
| ( in @ SV822 @ SV582 ) )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4885]) ).
thf(4958,plain,
! [SV583: $i,SV664: $i] :
( ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ SV664 )
= $false )
| ( ( in @ ( sK51_C @ SV664 @ SV583 ) @ ( sK52_SY636 @ SV664 @ SV583 ) )
= $false )
| ( ( SV664
= ( set_meet @ SV583 ) )
= $true )
| ( ( SV583 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(4959,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( in @ ( sK50_D @ SV779 @ SV665 @ SV584 ) @ SV584 )
= $true )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4888]) ).
thf(4960,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) ) )
= $true )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4889]) ).
thf(4961,plain,
! [SV665: $i,SV780: $i,SV584: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV584 ) )
= $true )
| ( ( in @ SV780 @ SV813 )
= $true )
| ( ( in @ SV780 @ SV665 )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4890]) ).
thf(4962,plain,
! [SV289: $i,SV748: $i,SV176: $i] :
( ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV748 @ SV289 ) ) )
= $false )
| ( ( in @ SV176 @ ( relation_dom @ SV748 ) )
= $true )
| ( ( function @ SV748 )
= $false )
| ( ( relation @ SV748 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(4963,plain,
! [SV289: $i,SV749: $i,SV176: $i] :
( ( ( in @ SV176 @ ( relation_dom @ ( relation_composition @ SV749 @ SV289 ) ) )
= $false )
| ( ( in @ ( apply @ SV749 @ SV176 ) @ ( relation_dom @ SV289 ) )
= $true )
| ( ( function @ SV749 )
= $false )
| ( ( relation @ SV749 )
= $false )
| ( ( function @ SV289 )
= $false )
| ( ( relation @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(4964,plain,
! [SV785: $i,SV182: $i,SV669: $i] :
( ( ( in @ ( sK30_C @ SV669 @ SV182 ) @ SV669 )
= $false )
| ( ( ( sK30_C @ SV669 @ SV182 )
= ( apply @ SV182 @ SV785 ) )
= $false )
| ( ( in @ SV785 @ ( relation_dom @ SV182 ) )
= $false )
| ( ( SV669
= ( relation_rng @ SV182 ) )
= $true )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(4965,plain,
! [SV670: $i,SV806: $i,SV182: $i,SV786: $i] :
( ( ( SV786
= ( apply @ SV182 @ SV806 ) )
= $false )
| ( ( ~ ( in @ SV806 @ ( relation_dom @ SV182 ) ) )
= $true )
| ( ( in @ SV786 @ SV670 )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(4966,plain,
! [SV670: $i,SV182: $i,SV787: $i] :
( ( ( ( SV787
!= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) ) )
= $false )
| ( ( in @ SV787 @ SV670 )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4899]) ).
thf(4967,plain,
! [SV182: $i,SV670: $i,SV787: $i] :
( ( ( ~ ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) ) )
= $false )
| ( ( in @ SV787 @ SV670 )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4899]) ).
thf(4968,plain,
! [SV184: $i,SV292: $i,SV701: $i] :
( ( ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
= $true )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4900]) ).
thf(4969,plain,
! [SV184: $i,SV701: $i,SV292: $i] :
( ( ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
!= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4901]) ).
thf(4970,plain,
! [SV184: $i,SV750: $i,SV292: $i] :
( ( ( SV292
= ( relation_dom_restriction @ SV750 @ SV184 ) )
= $false )
| ( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SY1524 )
= ( apply @ SV750 @ SY1524 ) ) ) )
= $true )
| ( ( function @ SV750 )
= $false )
| ( ( relation @ SV750 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4902]) ).
thf(4971,plain,
! [SV184: $i,SV751: $i,SV292: $i] :
( ( ( SV292
= ( relation_dom_restriction @ SV751 @ SV184 ) )
= $false )
| ( ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV751 ) @ SV184 ) )
= $true )
| ( ( function @ SV751 )
= $false )
| ( ( relation @ SV751 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(4972,plain,
! [SV185: $i,SV594: $i,SV636: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV636 )
= $false )
| ( ( in @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ SV594 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK65_D @ SV636 @ SV594 @ SV185 ) @ ( sK66_SY644 @ SV636 @ SV594 @ SV185 ) ) @ SV185 )
= $false )
| ( ( SV636
= ( relation_dom_restriction @ SV185 @ SV594 ) )
= $true )
| ( ( relation @ SV636 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4904]) ).
thf(4973,plain,
! [SV637: $i,SV185: $i,SV807: $i,SV595: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV595 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV185 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV637 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(4974,plain,
! [SV185: $i,SV595: $i,SV637: $i,SV823: $i] :
( ( ( ! [SY1554: $i] :
~ ( in @ ( ordered_pair @ SV823 @ SY1554 ) @ SV637 )
| ( in @ SV823 @ SV595 ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4908]) ).
thf(4975,plain,
! [SV595: $i,SV185: $i,SV637: $i,SV824: $i] :
( ( ( ! [SY1555: $i] :
( ~ ( in @ ( ordered_pair @ SV824 @ SY1555 ) @ SV637 )
| ( in @ ( ordered_pair @ SV824 @ SY1555 ) @ SV185 ) ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4909]) ).
thf(4976,plain,
! [SV641: $i,SV192: $i,SV763: $i,SV604: $i,SV802: $i] :
( ( ( in @ SV802 @ SV604 )
= $false )
| ( ( in @ ( ordered_pair @ SV763 @ SV802 ) @ SV192 )
= $false )
| ( ( in @ SV763 @ SV641 )
= $true )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(4977,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( in @ ( ordered_pair @ SV764 @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) ) @ SV192 )
= $true )
| ( ( in @ SV764 @ SV641 )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4912]) ).
thf(4978,plain,
! [SV192: $i,SV604: $i,SV641: $i,SV764: $i] :
( ( ( in @ ( sK55_E @ SV764 @ SV641 @ SV604 @ SV192 ) @ SV604 )
= $true )
| ( ( in @ SV764 @ SV641 )
= $false )
| ( ( SV641
= ( relation_inverse_image @ SV192 @ SV604 ) )
= $false )
| ( ( relation @ SV192 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4913]) ).
thf(4979,plain,
! [SV423: $i,SV503: $i,SV808: $i,SV803: $i] :
( ( ( in @ ( ordered_pair @ SV803 @ SV808 ) @ SV503 )
= $false )
| ( ( SV803 = SV808 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4915]) ).
thf(4980,plain,
! [SV423: $i,SV503: $i,SV814: $i,SV804: $i] :
( ( ( in @ ( ordered_pair @ SV804 @ SV814 ) @ SV503 )
= $false )
| ( ( in @ SV804 @ SV423 )
= $true )
| ( ( SV503
= ( identity_relation @ SV423 ) )
= $false )
| ( ( relation @ SV503 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4916]) ).
thf(4981,plain,
! [SV139: $i,SV543: $i] :
( ( ( in @ ( sK24_C @ SV543 @ SV139 ) @ SV543 )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4917]) ).
thf(4982,plain,
! [SV139: $i,SV543: $i] :
( ( ( in @ ( sK25_SY621 @ SV543 @ SV139 ) @ SV543 )
= $true )
| ( ( is_connected_in @ SV139 @ SV543 )
= $true )
| ( ( relation @ SV139 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4918]) ).
thf(4983,plain,
! [SV141: $i,SV547: $i] :
( ( ( in @ ( sK36_C @ SV547 @ SV141 ) @ SV547 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4922]) ).
thf(4984,plain,
! [SV141: $i,SV547: $i] :
( ( ( in @ ( sK37_SY628 @ SV547 @ SV141 ) @ SV547 )
= $true )
| ( ( is_antisymmetric_in @ SV141 @ SV547 )
= $true )
| ( ( relation @ SV141 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4923]) ).
thf(4985,plain,
! [SV608: $i,SV282: $i,SV791: $i,SV142: $i,SV805: $i] :
( ( ( in @ SV805 @ SV142 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV282 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV608 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4926]) ).
thf(4986,plain,
! [SV282: $i,SV142: $i,SV608: $i,SV825: $i,SV815: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV815 @ SV825 ) @ SV608 )
| ( in @ SV825 @ SV142 ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4927]) ).
thf(4987,plain,
! [SV142: $i,SV282: $i,SV608: $i,SV826: $i,SV816: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV608 )
| ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV282 ) )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(4988,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) ) )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4929]) ).
thf(4989,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( sK15_SY613 @ SV557 @ SV149 ) @ SV557 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4930]) ).
thf(4990,plain,
! [SV149: $i,SV708: $i,SV684: $i,SV558: $i,SV723: $i] :
( ( ( in @ SV723 @ SV558 )
= $false )
| ( ( in @ SV684 @ SV558 )
= $false )
| ( ( in @ SV708 @ SV558 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(4991,plain,
! [SV509: $i,SV450: $i,SV153: $i,SV772: $i,SV757: $i,SV725: $i] :
( ( ( SV725
= ( ordered_pair @ SV757 @ SV772 ) )
= $false )
| ( ( in @ SV757 @ SV153 )
= $false )
| ( ( in @ SV772 @ SV450 )
= $false )
| ( ( in @ SV725 @ SV509 )
= $true )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4933]) ).
thf(4992,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( in @ ( sK41_E @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV153 )
= $true )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4934]) ).
thf(4993,plain,
! [SV153: $i,SV450: $i,SV509: $i,SV726: $i] :
( ( ( in @ ( sK42_SY630 @ SV726 @ SV509 @ SV450 @ SV153 ) @ SV450 )
= $true )
| ( ( in @ SV726 @ SV509 )
= $false )
| ( ( SV509
= ( cartesian_product2 @ SV153 @ SV450 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4935]) ).
thf(4994,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(4995,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[4936]) ).
thf(4996,plain,
! [SV686: $i,SV154: $i,SV647: $i,SV794: $i] :
( ( ( in @ SV794 @ SV647 )
= $false )
| ( ( in @ SV794 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
!= ( apply @ SV154 @ SV794 ) ) )
= $true )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4937]) ).
thf(4997,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4938]) ).
thf(4998,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( ~ ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 ) )
= $false )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4938]) ).
thf(4999,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ ( relation_dom @ SV154 ) ) )
= $true )
| ( ( ~ ( in @ SV809 @ SV648 ) )
= $true )
| ( ( ( SV795
!= ( apply @ SV154 @ SV809 ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4939]) ).
thf(5000,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4940]) ).
thf(5001,plain,
! [SV648: $i,SV687: $i,SV154: $i,SV796: $i] :
( ( ( ( SV796
!= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4940]) ).
thf(5002,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4941]) ).
thf(5003,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4942]) ).
thf(5004,plain,
! [SV157: $i,SV758: $i] :
( ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) ) )
= $true )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5005,plain,
! [SV157: $i,SV759: $i] :
( ( ( SV759
= ( function_inverse @ SV157 ) )
= $false )
| ( ( ( relation_dom @ SV759 )
= ( relation_rng @ SV157 ) )
= $true )
| ( ( function @ SV759 )
= $false )
| ( ( relation @ SV759 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5006,plain,
! [SV694: $i,SV659: $i,SV797: $i,SV169: $i] :
( ( ( in @ ( apply @ SV169 @ SV797 ) @ SV659 )
= $false )
| ( ( in @ SV797 @ ( relation_dom @ SV169 ) )
= $false )
| ( ( in @ SV797 @ SV694 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5007,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV694 ) )
= $true )
| ( ( in @ SV817 @ ( relation_dom @ SV169 ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4947]) ).
thf(5008,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV694 ) )
= $true )
| ( ( in @ ( apply @ SV169 @ SV818 ) @ SV659 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4948]) ).
thf(5009,plain,
! [SV810: $i,SV172: $i,SV397: $i,SV695: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SV810 ) @ SV172 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV810 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5010,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) ) @ SV172 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4950]) ).
thf(5011,plain,
! [SV172: $i,SV397: $i,SV695: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_SY618 @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4951]) ).
thf(5012,plain,
! [SV696: $i,SV397: $i,SV819: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1553: $i] :
( ~ ( in @ ( ordered_pair @ SV811 @ SY1553 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SY1553 @ SV819 ) @ SV397 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(5013,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(5014,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV174 )
= $false )
| ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(5015,plain,
! [SV174: $i,SV288: $i,SV525: $i,SV581: $i] :
( ( ( ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 )
= SV288 )
= $false )
| ( ( in @ ( sK54_E @ SV581 @ SV525 @ SV288 @ SV174 ) @ SV581 )
= $false )
| ( ( SV581
= ( unordered_triple @ SV174 @ SV288 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(5016,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i,SV821: $i] :
( ( ( ( SV821 != SV174 ) )
= $true )
| ( ( in @ SV821 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(5017,plain,
! [SV526: $i,SV174: $i,SV582: $i,SV288: $i,SV822: $i] :
( ( ( ( SV822 != SV288 ) )
= $true )
| ( ( in @ SV822 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4957]) ).
thf(5018,plain,
! [SV584: $i,SV665: $i,SV779: $i] :
( ( ( in @ SV779 @ ( sK50_D @ SV779 @ SV665 @ SV584 ) )
= $false )
| ( ( in @ SV779 @ SV665 )
= $true )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4960]) ).
thf(5019,plain,
! [SV665: $i,SV780: $i,SV584: $i,SV813: $i] :
( ( ( in @ SV813 @ SV584 )
= $false )
| ( ( in @ SV780 @ SV813 )
= $true )
| ( ( in @ SV780 @ SV665 )
= $false )
| ( ( SV665
= ( set_meet @ SV584 ) )
= $false )
| ( ( SV584 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4961]) ).
thf(5020,plain,
! [SV670: $i,SV786: $i,SV182: $i,SV806: $i] :
( ( ( in @ SV806 @ ( relation_dom @ SV182 ) )
= $false )
| ( ( SV786
= ( apply @ SV182 @ SV806 ) )
= $false )
| ( ( in @ SV786 @ SV670 )
= $true )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(5021,plain,
! [SV670: $i,SV182: $i,SV787: $i] :
( ( ( SV787
= ( apply @ SV182 @ ( sK29_D @ SV787 @ SV670 @ SV182 ) ) )
= $true )
| ( ( in @ SV787 @ SV670 )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4966]) ).
thf(5022,plain,
! [SV182: $i,SV670: $i,SV787: $i] :
( ( ( in @ ( sK29_D @ SV787 @ SV670 @ SV182 ) @ ( relation_dom @ SV182 ) )
= $true )
| ( ( in @ SV787 @ SV670 )
= $false )
| ( ( SV670
= ( relation_rng @ SV182 ) )
= $false )
| ( ( function @ SV182 )
= $false )
| ( ( relation @ SV182 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4967]) ).
thf(5023,plain,
! [SV184: $i,SV701: $i,SV292: $i] :
( ( ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
= $false )
| ( ( in @ ( sK69_D @ SV701 @ SV292 @ SV184 ) @ ( relation_dom @ SV292 ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4968]) ).
thf(5024,plain,
! [SV184: $i,SV701: $i,SV292: $i] :
( ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV292 )
!= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5025,plain,
! [SV184: $i,SV750: $i,SV292: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ ( relation_dom @ SV292 ) )
| ( ( apply @ SV292 @ SV827 )
= ( apply @ SV750 @ SV827 ) ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV750 @ SV184 ) )
= $false )
| ( ( function @ SV750 )
= $false )
| ( ( relation @ SV750 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4970]) ).
thf(5026,plain,
! [SV637: $i,SV185: $i,SV807: $i,SV595: $i,SV801: $i] :
( ( ( in @ SV801 @ SV595 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV185 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV637 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5027,plain,
! [SV185: $i,SV595: $i,SV637: $i,SV823: $i] :
( ( ( ! [SY1554: $i] :
~ ( in @ ( ordered_pair @ SV823 @ SY1554 ) @ SV637 ) )
= $true )
| ( ( in @ SV823 @ SV595 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5028,plain,
! [SV595: $i,SV185: $i,SV637: $i,SV828: $i,SV824: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV637 )
| ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV185 ) )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4975]) ).
thf(5029,plain,
! [SV608: $i,SV142: $i,SV282: $i,SV805: $i,SV791: $i] :
( ( ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV282 )
= $false )
| ( ( in @ SV805 @ SV142 )
= $false )
| ( ( in @ ( ordered_pair @ SV791 @ SV805 ) @ SV608 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4985]) ).
thf(5030,plain,
! [SV282: $i,SV142: $i,SV608: $i,SV825: $i,SV815: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV815 @ SV825 ) @ SV608 ) )
= $true )
| ( ( in @ SV825 @ SV142 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5031,plain,
! [SV142: $i,SV282: $i,SV608: $i,SV826: $i,SV816: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV608 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV282 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4987]) ).
thf(5032,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
| ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5033,plain,
! [SV723: $i,SV558: $i,SV149: $i,SV708: $i,SV684: $i] :
( ( ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 )
= $false )
| ( ( in @ SV708 @ SV558 )
= $false )
| ( ( in @ SV684 @ SV558 )
= $false )
| ( ( in @ SV723 @ SV558 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5034,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4994]) ).
thf(5035,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4995]) ).
thf(5036,plain,
! [SV794: $i,SV154: $i,SV647: $i,SV686: $i] :
( ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
= ( apply @ SV154 @ SV794 ) )
= $false )
| ( ( in @ SV794 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( in @ SV794 @ SV647 )
= $false )
| ( ( ~ ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 ) )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4996]) ).
thf(5037,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ ( relation_dom @ SV154 ) )
= $true )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4997]) ).
thf(5038,plain,
! [SV154: $i,SV647: $i,SV686: $i] :
( ( ( in @ ( sK64_SY643 @ SV686 @ SV647 @ SV154 ) @ SV647 )
= $true )
| ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $true )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4998]) ).
thf(5039,plain,
! [SV687: $i,SV795: $i,SV648: $i,SV154: $i,SV809: $i] :
( ( ( in @ SV809 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ~ ( in @ SV809 @ SV648 ) )
= $true )
| ( ( ( SV795
!= ( apply @ SV154 @ SV809 ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4999]) ).
thf(5040,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) ) )
= $true )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5000]) ).
thf(5041,plain,
! [SV648: $i,SV687: $i,SV154: $i,SV796: $i] :
( ( ( SV796
= ( apply @ SV154 @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) ) )
= $true )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5001]) ).
thf(5042,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5043,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5044,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
| ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5004]) ).
thf(5045,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV817: $i] :
( ( ( in @ SV817 @ SV694 )
= $false )
| ( ( in @ SV817 @ ( relation_dom @ SV169 ) )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5046,plain,
! [SV659: $i,SV169: $i,SV694: $i,SV818: $i] :
( ( ( in @ SV818 @ SV694 )
= $false )
| ( ( in @ ( apply @ SV169 @ SV818 ) @ SV659 )
= $true )
| ( ( SV694
= ( relation_inverse_image @ SV169 @ SV659 ) )
= $false )
| ( ( function @ SV169 )
= $false )
| ( ( relation @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5047,plain,
! [SV172: $i,SV397: $i,SV695: $i,SV810: $i] :
( ( ( in @ ( ordered_pair @ SV810 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SV810 ) @ SV172 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 ) )
= $true )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5048,plain,
! [SV696: $i,SV397: $i,SV819: $i,SV172: $i,SV829: $i,SV811: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV811 @ SV829 ) @ SV172 )
| ~ ( in @ ( ordered_pair @ SV829 @ SV819 ) @ SV397 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5012]) ).
thf(5049,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 ) ) )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5050,plain,
! [SV526: $i,SV288: $i,SV582: $i,SV174: $i,SV821: $i] :
( ( ( SV821 = SV174 )
= $false )
| ( ( in @ SV821 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5051,plain,
! [SV526: $i,SV174: $i,SV582: $i,SV288: $i,SV822: $i] :
( ( ( SV822 = SV288 )
= $false )
| ( ( in @ SV822 @ SV582 )
= $true )
| ( ( SV582
= ( unordered_triple @ SV174 @ SV288 @ SV526 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5017]) ).
thf(5052,plain,
! [SV184: $i,SV701: $i,SV292: $i] :
( ( ( ( relation_dom @ SV292 )
= ( set_intersection2 @ ( relation_dom @ SV701 ) @ SV184 ) )
= $false )
| ( ( ( apply @ SV292 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) )
= ( apply @ SV701 @ ( sK69_D @ SV701 @ SV292 @ SV184 ) ) )
= $false )
| ( ( SV292
= ( relation_dom_restriction @ SV701 @ SV184 ) )
= $true )
| ( ( function @ SV701 )
= $false )
| ( ( relation @ SV701 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5053,plain,
! [SV184: $i,SV750: $i,SV292: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ ( relation_dom @ SV292 ) ) )
= $true )
| ( ( ( apply @ SV292 @ SV827 )
= ( apply @ SV750 @ SV827 ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV750 @ SV184 ) )
= $false )
| ( ( function @ SV750 )
= $false )
| ( ( relation @ SV750 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5054,plain,
! [SV637: $i,SV595: $i,SV185: $i,SV807: $i,SV801: $i] :
( ( ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV185 )
= $false )
| ( ( in @ SV801 @ SV595 )
= $false )
| ( ( in @ ( ordered_pair @ SV801 @ SV807 ) @ SV637 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5055,plain,
! [SV185: $i,SV595: $i,SV637: $i,SV830: $i,SV823: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV823 @ SV830 ) @ SV637 ) )
= $true )
| ( ( in @ SV823 @ SV595 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5027]) ).
thf(5056,plain,
! [SV595: $i,SV185: $i,SV637: $i,SV828: $i,SV824: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV637 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV185 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(5057,plain,
! [SV282: $i,SV142: $i,SV608: $i,SV825: $i,SV815: $i] :
( ( ( in @ ( ordered_pair @ SV815 @ SV825 ) @ SV608 )
= $false )
| ( ( in @ SV825 @ SV142 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5058,plain,
! [SV142: $i,SV282: $i,SV608: $i,SV826: $i,SV816: $i] :
( ( ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV608 )
= $false )
| ( ( in @ ( ordered_pair @ SV816 @ SV826 ) @ SV282 )
= $true )
| ( ( SV608
= ( relation_rng_restriction @ SV142 @ SV282 ) )
= $false )
| ( ( relation @ SV608 )
= $false )
| ( ( relation @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5059,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5032]) ).
thf(5060,plain,
! [SV149: $i,SV557: $i] :
( ( ( ~ ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 ) )
= $false )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5032]) ).
thf(5061,plain,
! [SV684: $i,SV558: $i,SV149: $i,SV723: $i,SV708: $i] :
( ( ( in @ ( ordered_pair @ SV708 @ SV723 ) @ SV149 )
= $false )
| ( ( in @ SV723 @ SV558 )
= $false )
| ( ( in @ SV684 @ SV558 )
= $false )
| ( ( in @ SV708 @ SV558 )
= $false )
| ( ( in @ ( ordered_pair @ SV684 @ SV708 ) @ SV149 )
= $false )
| ( ( in @ ( ordered_pair @ SV684 @ SV723 ) @ SV149 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV558 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5062,plain,
! [SV794: $i,SV154: $i,SV647: $i,SV686: $i] :
( ( ( in @ ( sK63_D @ SV686 @ SV647 @ SV154 ) @ SV686 )
= $false )
| ( ( in @ SV794 @ SV647 )
= $false )
| ( ( in @ SV794 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ( sK63_D @ SV686 @ SV647 @ SV154 )
= ( apply @ SV154 @ SV794 ) )
= $false )
| ( ( SV686
= ( relation_image @ SV154 @ SV647 ) )
= $true )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5063,plain,
! [SV687: $i,SV795: $i,SV154: $i,SV648: $i,SV809: $i] :
( ( ( in @ SV809 @ SV648 )
= $false )
| ( ( in @ SV809 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( ( SV795
!= ( apply @ SV154 @ SV809 ) ) )
= $true )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5064,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
| ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5065,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5042]) ).
thf(5066,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5042]) ).
thf(5067,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5043]) ).
thf(5068,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5043]) ).
thf(5069,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5044]) ).
thf(5070,plain,
! [SV758: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5044]) ).
thf(5071,plain,
! [SV810: $i,SV172: $i,SV397: $i,SV695: $i] :
( ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV695 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK17_D @ SV695 @ SV397 @ SV172 ) @ SV810 ) @ SV172 )
= $false )
| ( ( in @ ( ordered_pair @ SV810 @ ( sK18_SY614 @ SV695 @ SV397 @ SV172 ) ) @ SV397 )
= $false )
| ( ( SV695
= ( relation_composition @ SV172 @ SV397 ) )
= $true )
| ( ( relation @ SV695 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5047]) ).
thf(5072,plain,
! [SV696: $i,SV397: $i,SV819: $i,SV172: $i,SV829: $i,SV811: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV811 @ SV829 ) @ SV172 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV829 @ SV819 ) @ SV397 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5073,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
| ~ ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5074,plain,
! [SV184: $i,SV750: $i,SV292: $i,SV827: $i] :
( ( ( in @ SV827 @ ( relation_dom @ SV292 ) )
= $false )
| ( ( ( apply @ SV292 @ SV827 )
= ( apply @ SV750 @ SV827 ) )
= $true )
| ( ( SV292
= ( relation_dom_restriction @ SV750 @ SV184 ) )
= $false )
| ( ( function @ SV750 )
= $false )
| ( ( relation @ SV750 )
= $false )
| ( ( function @ SV292 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5075,plain,
! [SV185: $i,SV595: $i,SV637: $i,SV830: $i,SV823: $i] :
( ( ( in @ ( ordered_pair @ SV823 @ SV830 ) @ SV637 )
= $false )
| ( ( in @ SV823 @ SV595 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5076,plain,
! [SV595: $i,SV185: $i,SV637: $i,SV828: $i,SV824: $i] :
( ( ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV637 )
= $false )
| ( ( in @ ( ordered_pair @ SV824 @ SV828 ) @ SV185 )
= $true )
| ( ( SV637
= ( relation_dom_restriction @ SV185 @ SV595 ) )
= $false )
| ( ( relation @ SV637 )
= $false )
| ( ( relation @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5077,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( sK13_C @ SV557 @ SV149 ) @ SV557 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5059]) ).
thf(5078,plain,
! [SV149: $i,SV557: $i] :
( ( ( in @ ( sK14_SY611 @ SV557 @ SV149 ) @ SV557 )
= $true )
| ( ( is_transitive_in @ SV149 @ SV557 )
= $true )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5060]) ).
thf(5079,plain,
! [SV687: $i,SV648: $i,SV809: $i,SV154: $i,SV795: $i] :
( ( ( SV795
= ( apply @ SV154 @ SV809 ) )
= $false )
| ( ( in @ SV809 @ ( relation_dom @ SV154 ) )
= $false )
| ( ( in @ SV809 @ SV648 )
= $false )
| ( ( in @ SV795 @ SV687 )
= $true )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5063]) ).
thf(5080,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5064]) ).
thf(5081,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( ~ ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 ) )
= $false )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5064]) ).
thf(5082,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5065]) ).
thf(5083,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5066]) ).
thf(5084,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5067]) ).
thf(5085,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5068]) ).
thf(5086,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5069]) ).
thf(5087,plain,
! [SV758: $i,SV157: $i] :
( ( ( ~ ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5070]) ).
thf(5088,plain,
! [SV696: $i,SV397: $i,SV819: $i,SV172: $i,SV829: $i,SV811: $i] :
( ( ( in @ ( ordered_pair @ SV811 @ SV829 ) @ SV172 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV829 @ SV819 ) @ SV397 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5072]) ).
thf(5089,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5073]) ).
thf(5090,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV812: $i,SV820: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5073]) ).
thf(5091,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ ( relation_dom @ SV154 ) )
= $true )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5080]) ).
thf(5092,plain,
! [SV154: $i,SV648: $i,SV687: $i,SV796: $i] :
( ( ( in @ ( sK62_E @ SV796 @ SV687 @ SV648 @ SV154 ) @ SV648 )
= $true )
| ( ( in @ SV796 @ SV687 )
= $false )
| ( ( SV687
= ( relation_image @ SV154 @ SV648 ) )
= $false )
| ( ( function @ SV154 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5081]) ).
thf(5093,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5094,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5095,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5096,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5097,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) )
| ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5086]) ).
thf(5098,plain,
! [SV758: $i,SV157: $i] :
( ( ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) )
| ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5099,plain,
! [SV696: $i,SV172: $i,SV811: $i,SV397: $i,SV819: $i,SV829: $i] :
( ( ( in @ ( ordered_pair @ SV829 @ SV819 ) @ SV397 )
= $false )
| ( ( in @ ( ordered_pair @ SV811 @ SV829 ) @ SV172 )
= $false )
| ( ( in @ ( ordered_pair @ SV811 @ SV819 ) @ SV696 )
= $true )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5088]) ).
thf(5100,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV820: $i,SV812: $i] :
( ( ( in @ ( ordered_pair @ SV812 @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) ) @ SV172 )
= $true )
| ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5089]) ).
thf(5101,plain,
! [SV172: $i,SV397: $i,SV696: $i,SV812: $i,SV820: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_F @ SV820 @ SV812 @ SV696 @ SV397 @ SV172 ) @ SV820 ) @ SV397 )
= $true )
| ( ( in @ ( ordered_pair @ SV812 @ SV820 ) @ SV696 )
= $false )
| ( ( SV696
= ( relation_composition @ SV172 @ SV397 ) )
= $false )
| ( ( relation @ SV696 )
= $false )
| ( ( relation @ SV397 )
= $false )
| ( ( relation @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5090]) ).
thf(5102,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5093]) ).
thf(5103,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5093]) ).
thf(5104,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5105,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5106,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5095]) ).
thf(5107,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5095]) ).
thf(5108,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(5109,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5097]) ).
thf(5110,plain,
! [SV157: $i,SV758: $i] :
( ( ( ~ ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5097]) ).
thf(5111,plain,
! [SV758: $i,SV157: $i] :
( ( ( ~ ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5112,plain,
! [SV758: $i,SV157: $i] :
( ( ( ~ ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) )
= $false )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5098]) ).
thf(5113,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5102]) ).
thf(5114,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5103]) ).
thf(5115,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5104]) ).
thf(5116,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5105]) ).
thf(5117,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5106]) ).
thf(5118,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5107]) ).
thf(5119,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5120,plain,
! [SV157: $i,SV758: $i] :
( ( ( ! [SY1528: $i,SY1529: $i] :
( ( SY1529
!= ( apply @ SV758 @ SY1528 ) )
| ~ ( in @ SY1528 @ ( relation_rng @ SV157 ) )
| ( SY1528
= ( apply @ SV157 @ SY1529 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5109]) ).
thf(5121,plain,
! [SV157: $i,SV758: $i] :
( ( ( ! [SY1530: $i,SY1531: $i] :
( ( SY1531
!= ( apply @ SV758 @ SY1530 ) )
| ~ ( in @ SY1530 @ ( relation_rng @ SV157 ) )
| ( in @ SY1531 @ ( relation_dom @ SV157 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5110]) ).
thf(5122,plain,
! [SV758: $i,SV157: $i] :
( ( ( ! [SY1532: $i,SY1533: $i] :
( ( SY1532
!= ( apply @ SV157 @ SY1533 ) )
| ~ ( in @ SY1533 @ ( relation_dom @ SV157 ) )
| ( SY1533
= ( apply @ SV758 @ SY1532 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5111]) ).
thf(5123,plain,
! [SV758: $i,SV157: $i] :
( ( ( ! [SY911: $i] :
( ! [SY912: $i] :
( ( SY911
!= ( apply @ SV157 @ SY912 ) )
| ~ ( in @ SY912 @ ( relation_dom @ SV157 ) ) )
| ( in @ SY911 @ ( relation_rng @ SV157 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5112]) ).
thf(5124,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5125,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5114]) ).
thf(5126,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
| ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5127,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5128,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5129,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5118]) ).
thf(5130,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5131,plain,
! [SV157: $i,SV831: $i,SV758: $i] :
( ( ( ! [SY1556: $i] :
( ( SY1556
!= ( apply @ SV758 @ SV831 ) )
| ~ ( in @ SV831 @ ( relation_rng @ SV157 ) )
| ( SV831
= ( apply @ SV157 @ SY1556 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5120]) ).
thf(5132,plain,
! [SV157: $i,SV832: $i,SV758: $i] :
( ( ( ! [SY1557: $i] :
( ( SY1557
!= ( apply @ SV758 @ SV832 ) )
| ~ ( in @ SV832 @ ( relation_rng @ SV157 ) )
| ( in @ SY1557 @ ( relation_dom @ SV157 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5121]) ).
thf(5133,plain,
! [SV758: $i,SV157: $i,SV833: $i] :
( ( ( ! [SY1558: $i] :
( ( SV833
!= ( apply @ SV157 @ SY1558 ) )
| ~ ( in @ SY1558 @ ( relation_dom @ SV157 ) )
| ( SY1558
= ( apply @ SV758 @ SV833 ) ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5122]) ).
thf(5134,plain,
! [SV758: $i,SV157: $i,SV834: $i] :
( ( ( ! [SY1559: $i] :
( ( SV834
!= ( apply @ SV157 @ SY1559 ) )
| ~ ( in @ SY1559 @ ( relation_dom @ SV157 ) ) )
| ( in @ SV834 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5123]) ).
thf(5135,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5124]) ).
thf(5136,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5124]) ).
thf(5137,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5138,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5126]) ).
thf(5139,plain,
! [SV157: $i,SV717: $i] :
( ( ( ~ ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5126]) ).
thf(5140,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5141,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5142,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK72_C @ SV717 @ SV157 )
!= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5143,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
!= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5130]) ).
thf(5144,plain,
! [SV157: $i,SV831: $i,SV758: $i,SV835: $i] :
( ( ( ( SV835
!= ( apply @ SV758 @ SV831 ) )
| ~ ( in @ SV831 @ ( relation_rng @ SV157 ) )
| ( SV831
= ( apply @ SV157 @ SV835 ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5131]) ).
thf(5145,plain,
! [SV157: $i,SV832: $i,SV758: $i,SV836: $i] :
( ( ( ( SV836
!= ( apply @ SV758 @ SV832 ) )
| ~ ( in @ SV832 @ ( relation_rng @ SV157 ) )
| ( in @ SV836 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5132]) ).
thf(5146,plain,
! [SV758: $i,SV837: $i,SV157: $i,SV833: $i] :
( ( ( ( SV833
!= ( apply @ SV157 @ SV837 ) )
| ~ ( in @ SV837 @ ( relation_dom @ SV157 ) )
| ( SV837
= ( apply @ SV758 @ SV833 ) ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5133]) ).
thf(5147,plain,
! [SV758: $i,SV157: $i,SV834: $i] :
( ( ( ! [SY1559: $i] :
( ( SV834
!= ( apply @ SV157 @ SY1559 ) )
| ~ ( in @ SY1559 @ ( relation_dom @ SV157 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5134]) ).
thf(5148,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5135]) ).
thf(5149,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5136]) ).
thf(5150,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5137]) ).
thf(5151,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5138]) ).
thf(5152,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
| ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5139]) ).
thf(5153,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5140]) ).
thf(5154,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5141]) ).
thf(5155,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5156,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( ~ ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5157,plain,
! [SV157: $i,SV831: $i,SV758: $i,SV835: $i] :
( ( ( ( SV835
!= ( apply @ SV758 @ SV831 ) )
| ~ ( in @ SV831 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV831
= ( apply @ SV157 @ SV835 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5144]) ).
thf(5158,plain,
! [SV157: $i,SV832: $i,SV758: $i,SV836: $i] :
( ( ( ( SV836
!= ( apply @ SV758 @ SV832 ) )
| ~ ( in @ SV832 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( in @ SV836 @ ( relation_dom @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5145]) ).
thf(5159,plain,
! [SV758: $i,SV837: $i,SV157: $i,SV833: $i] :
( ( ( ( SV833
!= ( apply @ SV157 @ SV837 ) )
| ~ ( in @ SV837 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV758 @ SV833 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5146]) ).
thf(5160,plain,
! [SV758: $i,SV838: $i,SV157: $i,SV834: $i] :
( ( ( ( SV834
!= ( apply @ SV157 @ SV838 ) )
| ~ ( in @ SV838 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ SV834 @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5147]) ).
thf(5161,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5162,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5163,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5164,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5151]) ).
thf(5165,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5152]) ).
thf(5166,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5153]) ).
thf(5167,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5154]) ).
thf(5168,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5169,plain,
! [SV157: $i,SV717: $i] :
( ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( ( relation_dom @ SV717 )
!= ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5170,plain,
! [SV157: $i,SV831: $i,SV758: $i,SV835: $i] :
( ( ( ( SV835
!= ( apply @ SV758 @ SV831 ) ) )
= $true )
| ( ( ~ ( in @ SV831 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV831
= ( apply @ SV157 @ SV835 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5171,plain,
! [SV157: $i,SV832: $i,SV758: $i,SV836: $i] :
( ( ( ( SV836
!= ( apply @ SV758 @ SV832 ) ) )
= $true )
| ( ( ~ ( in @ SV832 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( in @ SV836 @ ( relation_dom @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5158]) ).
thf(5172,plain,
! [SV758: $i,SV837: $i,SV157: $i,SV833: $i] :
( ( ( ( SV833
!= ( apply @ SV157 @ SV837 ) ) )
= $true )
| ( ( ~ ( in @ SV837 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV758 @ SV833 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5159]) ).
thf(5173,plain,
! [SV758: $i,SV838: $i,SV157: $i,SV834: $i] :
( ( ( ( SV834
!= ( apply @ SV157 @ SV838 ) ) )
= $true )
| ( ( ~ ( in @ SV838 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ SV834 @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(5174,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5161]) ).
thf(5175,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5176,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5177,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5164]) ).
thf(5178,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5179,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $true )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5180,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5181,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $true )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5182,plain,
! [SV157: $i,SV717: $i] :
( ( ( ( relation_dom @ SV717 )
= ( relation_rng @ SV157 ) )
= $false )
| ( ( in @ ( sK73_SY647 @ SV717 @ SV157 ) @ ( relation_dom @ SV157 ) )
= $false )
| ( ( ( sK72_C @ SV717 @ SV157 )
= ( apply @ SV157 @ ( sK73_SY647 @ SV717 @ SV157 ) ) )
= $false )
| ( ( ( sK73_SY647 @ SV717 @ SV157 )
= ( apply @ SV717 @ ( sK72_C @ SV717 @ SV157 ) ) )
= $false )
| ( ( in @ ( sK72_C @ SV717 @ SV157 ) @ ( relation_rng @ SV157 ) )
= $false )
| ( ( SV717
= ( function_inverse @ SV157 ) )
= $true )
| ( ( function @ SV717 )
= $false )
| ( ( relation @ SV717 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5183,plain,
! [SV157: $i,SV831: $i,SV758: $i,SV835: $i] :
( ( ( SV835
= ( apply @ SV758 @ SV831 ) )
= $false )
| ( ( ~ ( in @ SV831 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( SV831
= ( apply @ SV157 @ SV835 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5184,plain,
! [SV157: $i,SV832: $i,SV758: $i,SV836: $i] :
( ( ( SV836
= ( apply @ SV758 @ SV832 ) )
= $false )
| ( ( ~ ( in @ SV832 @ ( relation_rng @ SV157 ) ) )
= $true )
| ( ( in @ SV836 @ ( relation_dom @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5185,plain,
! [SV758: $i,SV837: $i,SV157: $i,SV833: $i] :
( ( ( SV833
= ( apply @ SV157 @ SV837 ) )
= $false )
| ( ( ~ ( in @ SV837 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( SV837
= ( apply @ SV758 @ SV833 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5186,plain,
! [SV758: $i,SV838: $i,SV157: $i,SV834: $i] :
( ( ( SV834
= ( apply @ SV157 @ SV838 ) )
= $false )
| ( ( ~ ( in @ SV838 @ ( relation_dom @ SV157 ) ) )
= $true )
| ( ( in @ SV834 @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5173]) ).
thf(5187,plain,
! [SV758: $i,SV835: $i,SV157: $i,SV831: $i] :
( ( ( in @ SV831 @ ( relation_rng @ SV157 ) )
= $false )
| ( ( SV835
= ( apply @ SV758 @ SV831 ) )
= $false )
| ( ( SV831
= ( apply @ SV157 @ SV835 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5188,plain,
! [SV758: $i,SV836: $i,SV157: $i,SV832: $i] :
( ( ( in @ SV832 @ ( relation_rng @ SV157 ) )
= $false )
| ( ( SV836
= ( apply @ SV758 @ SV832 ) )
= $false )
| ( ( in @ SV836 @ ( relation_dom @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5189,plain,
! [SV758: $i,SV833: $i,SV157: $i,SV837: $i] :
( ( ( in @ SV837 @ ( relation_dom @ SV157 ) )
= $false )
| ( ( SV833
= ( apply @ SV157 @ SV837 ) )
= $false )
| ( ( SV837
= ( apply @ SV758 @ SV833 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5190,plain,
! [SV758: $i,SV834: $i,SV157: $i,SV838: $i] :
( ( ( in @ SV838 @ ( relation_dom @ SV157 ) )
= $false )
| ( ( SV834
= ( apply @ SV157 @ SV838 ) )
= $false )
| ( ( in @ SV834 @ ( relation_rng @ SV157 ) )
= $true )
| ( ( SV758
= ( function_inverse @ SV157 ) )
= $false )
| ( ( function @ SV758 )
= $false )
| ( ( relation @ SV758 )
= $false )
| ( ( one_to_one @ SV157 )
= $false )
| ( ( function @ SV157 )
= $false )
| ( ( relation @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5186]) ).
thf(5191,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[935,5190,5189,5188,5187,5182,5181,5180,5179,5178,5177,5176,5175,5174,5101,5100,5099,5092,5091,5079,5078,5077,5076,5075,5074,5071,5062,5061,5058,5057,5054,5052,5051,5050,5046,5045,5041,5038,5037,5035,5034,5029,5023,5022,5021,5020,5019,5018,5015,5014,5011,5010,5006,5005,4993,4992,4991,4989,4984,4983,4982,4981,4980,4979,4978,4977,4976,4972,4971,4964,4963,4962,4959,4958,4945,4932,4925,4924,4921,4920,4919,4914,4910,4906,4905,4896,4895,4894,4891,4886,4883,4873,4872,4870,4869,4865,4864,4863,4862,4859,4856,4851,4850,4844,4843,4836,4834,4827,4826,4819,4818,4812,4811,4803,4802,4799,4793,4790,4785,4784,4771,4760,4757,4756,4751,4749,4748,4747,4739,4734,4728,4725,4724,4720,4719,4718,4700,4693,4692,4680,4675,4674,4666,4665,4664,4659,4658,4657,4639,4634,4633,4630,4629,4628,4627,4616,4615,4607,4606,4596,4595,4592,4587,4571,4568,4556,4554,4542,4541,4539,4538,4535,4534,4526,4523,4522,4520,4514,4501,4500,4498,4495,4478,4463,4462,4459,4452,4440,4421,4403,4399,4391,4390,4382,4381,4380,4368,4363,4360,4358,4339,4313,4312,4309,4308,4307,4306,4292,4291,4286,4280,4279,4259,4258,4243,4242,4241,4234,4233,4230,4227,4226,4217,4216,4214,4209,4208,4206,4205,4179,4164,4163,4154,4153,4139,4132,4120,4119,4108,4105,4104,4094,4088,4072,4068,4061,4037,4033,4024,4019,4018,4015,4011,4005,4004,4000,3993,3991,3990,3978,3946,3945,3940,3913,3906,3899,3898,3897,3894,3893,3873,3864,3863,3843,3829,3826,3814,3813,3805,3790,3770,3767,3766,3765,3730,3728,3727,3726,3721,3720,3716,3715,3714,3701,3674,3672,3671,3648,3647,3646,3634,3633,3623,3622,3615,3614,3613,3608,3607,3599,3598,3588,3578,3577,3567,3554,3553,3540,3539,3533,3532,3522,3521,3505,3501,3500,3474,3463,3462,3461,3444,3435,3419,3418,3417,3416,3415,3414,3398,3376,3360,3359,3322,3319,3303,3300,3299,3298,3271,3270,3256,3255,3249,3246,3245,3228,3221,3202,3199,3197,3196,3193,3192,3191,3190,3189,3188,3181,3096,3091,3090,3074,3073,3064,3063,3049,3048,3030,3029,3024,3022,3021,3017,3016,2971,2970,2969,2968,2967,2964,2954,2953,2952,2951,2948,2947,2946,2937,2936,2915,2914,2909,2908,2900,2885,2884,2868,2867,2866,2865,2861,2860,2855,2854,2817,2816,2811,2810,2809,2804,2780,2768,2767,2760,2750,2733,2732,2710,2709,2706,2696,2693,2688,2686,2684,2682,2681,2680,2679,2674,2673,2669,2629,2502,2478,2438,2435,2432,2428,2427,2426,2425,2424,2404,2403,2402,2395,2390,2389,2384,2369,2368,2343,2342,2316,2312,2311,2180,2179,2176,2175,2174,2172,2171,2170,2168,2167,2166,2164,2163,2157,2152,2149,2146,2132,2126,2125,2123,2122,2121,2120,2118,2117,2112,2108,2104,2103,2101,2099,2098,2096,2094,2093,2092,2091,2090,2083,2082,2081,2058,2042,2041,2020,2018,2012,2006,1982,1981,1970,1969,1966,1957,1956,1937,1925,1878,1865,1863,1855,1851,1823,1820,1811,1809,1795,1791,1784,1571,1564,1562,1561,1552,1549,1548,1547,1533,1530,1528,1511,1493,1483,1475,1337,1331,1330,1328,1326,1321,1317,1316,1307,1301,1295,1285,1280,1258,1251,1242,1220,1074,1052,1035]) ).
thf(5192,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU248+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.18/0.33 % DateTime : Sun Jun 19 18:56:52 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.19/0.45 ........
% 0.19/0.56
% 0.19/0.56 No.of.Axioms: 305
% 0.19/0.56
% 0.19/0.56 Length.of.Defs: 0
% 0.19/0.56
% 0.19/0.56 Contains.Choice.Funs: false
% 0.48/0.65 .....................
% 0.55/0.76 (rf:2,axioms:264,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:307,loop_count:0,foatp_calls:0,translation:fof_full)................................................................................................................................................................................................................................................................................................................................................................................................
% 73.52/73.69
% 73.52/73.69 ********************************
% 73.52/73.69 * All subproblems solved! *
% 73.52/73.69 ********************************
% 73.52/73.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:265,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5191,loop_count:0,foatp_calls:1,translation:fof_full)
% 81.84/82.04
% 81.84/82.04 %**** Beginning of derivation protocol ****
% 81.84/82.04 % SZS output start CNFRefutation
% See solution above
% 81.84/82.06
% 81.84/82.06 %**** End of derivation protocol ****
% 81.84/82.06 %**** no. of clauses in derivation: 5151 ****
% 81.84/82.06 %**** clause counter: 5191 ****
% 81.84/82.06
% 81.84/82.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:265,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5191,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------